Problems

Navigation page for Problems/ at upstream snapshot b1d673668c6d1bc06a152e4607048833d830ca53.

Contents

• Hanna’s diagonal ghost-power integrality conjecture
• A320043: an additional square value
• The Shapley allocation of a graph energy game can leave its core
• Acosta Babb’s weighted Bessel-kernel positivity conjecture
• Three weak measurements of projections below minus one eighth
• The lazy two-causal inequality $J_1$ induces a facet for every $$\begin{gathered} N \\ ge2 \end{gathered}$$
• Optimal quantum states depend on the Rényi orders
• Abdesselam’s Problem 3: the PGG inequalities at arbitrary positive exponents
• Abdesselam’s Problem 2: padded general Ginibre inequalities for the XY model
• Density-independent Alhasan–Fawwaz boundedness
• Negativity at most (χ − 1)/2 does not imply positivity under the χ-reduction map
• Zero forcing the ordinary powers of equal-legged spiders
• abiad-flagg-ghasemi-nezhad-zeijlemaker-2026-grid-power-zero-forcing
• Ruleset domination does not imply nimber domination
• Refutation of the dual-frame cross-Gramian Welch bound
• An exclusive Grassmannian dual need not be canonical
• GHZ phase tangents refute a rank-only lower bound for normalized Pauli Fisher information
• The spectral degree exponent is not submodular
• Adamaszek’s Conjecture 7.4 on necklace cycle lengths
• The Grassmann entwining Yang–Baxter map S over Γ(3) does not preserve the measure y₁₁⁻³
• Connectivity of prefix normal generators
• An explicit membership graph outside G₂
• adamson-flaherty-potapov-spirakis-2023-two-swap-greedy
• Every positive-uniform adjacent class inclusion is proper
• Agoh’s alternating-numerator characterization
• The extremal matching number of almost regular triangle-free graphs
• Maximum purity in the 4-by-4 absolutely PPT sector
• The exact maximum purity of absolutely PPT qutrit–qudit states
• The linear spectral condition (31) and absolute separability
• All-direction maximal clique partitions of mixed-alphabet Hamming graphs
• Non-shortening in the one-wall hypereclectic spin chain
• The n = 3 collapse of the genuine four-party multi-entropy for stabilizer states
• Two centered abelian period lengths
• An infinite twin-free theta family separating the Laplacian equalities
• Both proposed spectral-radius bounds for asynchronous iteration are false
• Alai’s Staircase for faithful GHZ–Mermin measurement dependence
• The order-seven unicyclic CDSO minimizer has no universal vertex
• The exact five-dimensional bad science optimum
• The path does not minimize Kemeny’s edge derivative
• Lazy and invertible cellular automata do not generate all cellular automata
• The Alcaraz–Ramos lowest-mode conformal prediction fails
• Halving partitions admit no finite integral decimation family
• Multiset rook-Eulerian interlacing on Ferrers boards
• Word-trace domination does not control fractional Schatten norms
• Collective dephasing of two qutrits admits nonstationary states with constant positive negativity
• Aliabadi’s uncapped subspace-product conjecture is false
• Aliabadi’s finite nonabelian quotient-multiset problem
• Aliabadi–Zerbib Question 2.7 has a negative answer
• Two four-cycles sharing a vertex refute elliptic Sombor Conjecture 3.9
• Strong domination under clique gluing
• Connected graphs with ordinary domination root minus four
• Refutation of order-33 minimality for domination root minus four
• The Allen–Meyer family does not give the entire three-qutrit negativity region
• Sixfold evil and odious representation counts
• Question 6 of Alofi and Dukes: do the stochastically recurrent states of K_{m,n} dominate?
• Validity of the five three-outcome PI Bell inequalities
• The Alsing–Birrittella logarithmic-negativity sandwich
• Altizio’s geometric-sum disk classification
• The coherence vector and spectrum satisfy the product bound in every positive dimension
• Every (n,d)↦1 random access code has a quantum advantage with two measurement settings
• Equal mixed and ordinary palindromic costs on Thue–Morse prefixes
• Floors of reciprocal generalized Fibonacci tails
• Andoyo Question 5.2: infinitude of exact prime fibers
• Andoyo’s equal Pisano sets question
• Andrade–Severini star-graph evolution maps are unitarily similar
• The minimum of the long-time algebra OTOC
• Positivity of the Two-Color Partition Series C’(2,4,n)
• Positivity of the Two-Color Partition Series D’(2,2,n)
• The Negative Coefficients of the Two-Color Partition Series D’(2,3,n)
• Eventual positivity of the complete D-prime family
• The averaged enumerator of B-form codes
• Global-coalition graph universality
• The fixed-polynomial hypergraph Alon-Tarsi bound
• Antipin’s four-qubit subspaces are not genuinely entangled for every parameter
• apte-parekh-sud-2025-token-graph-cut-bound
• Advantage-quantum measurements are not quantum n-simulable
• The Yang–Baxter cellular automata over F_{2^n} have period dividing 2^n
• Problem 15.5 answered negatively by a five-element Clifford semigroup
• The quantum crystal potential is not a Yangian combination on the bosonic states
• Archer-Bourne cube-avoidance counting equality
• The Archer–Bourne Square Recurrence Fails at n = 11
• Cyclic Permutations Avoiding 4123 with 1324-Avoiding Cycle Forms
• Cyclic Permutations Avoiding 4132 with 1324-Avoiding Cycle Forms
• Avoiders of 231 and 312 Fixed by the Third Iterate of the Fundamental Bijection
• Permutations Whose First Iterates under the Fundamental Bijection Avoid 132
• Majorization need not survive normalization in a common charge sector
• The toppling count of the n × 1 torus sandpile
• No generalized Choi map detects absolutely PPT entanglement
• Bob cannot perfectly hedge more than n/2 of n parallel games
• arxiv-2506-09912-shkolnikov-sandpile-limit-divisible
• A polynomial bound for binary-polynomial Collatz length
• A uniform family of reduced-coordinate cube recursions
• Asgarli–Yip two-dimensional pseudo-Paley cliques
• Alternating binary words need not minimize positional autocorrelation
• Positional autocorrelation does not determine finite deletion-channel entropy ordering
• The peakon transfer matrices expand in the Hamiltonians h^(k) with explicit universal coefficients
• A four-level system whose triplets all violate the three-level conditions, yet shows the Markovian Mpemba effect
• ayad-bouchenna-base-b-reverse-multiple-divisors
• Ayyer–Mallick maximal degeneracy of the annihilation-process generator
• Half-density modes of the asymmetric K-exclusion process
• Browne’s Chebyshev numerator and floor product
• Badhani–Das noisy-unitary conditional min-entropy
• Bădică–Bădică: the Jaccard triangle inequality on arbitrary lattices
• Four MUBs detect a PPT state in dimension eight
• baek-jo-nha-2026-maximal-coherence-monotonicity
• bahturin-centrone-pereira-2026-peak-group-refutation
• Monotonicity of the residual-correlation sum of four qubits
• The quasidistillable candidates are not two-qutrit negativity maximizers for fixed marginals
• The original Bajnok–Beatty Conjecture 4.1
• Perfect restricted bases of size s + 1 force cyclicity
• Without shared entanglement the odd-prime communication task succeeds with probability at most 2/(d + 1)
• Bala’s A258899 and A258903 totient-period conjectures
• The exact halting time of Wolfram machine 3626
• The A126156 eventual totient-period conjecture is false
• Bala’s A193236 congruences modulo five and seven
• Bala’s A193237 congruences modulo five and seven
• Bala’s A295462 binary-spacing parity conjecture
• Bala’s A361034 parity conjecture
• Bala’s A361035 parity conjecture
• Three-adic nondivisibility
• Paired three-adic valuations
• Type-one primes through 101
• Bala’s OEIS A363411 and A363412 valuation conjectures
• Balanced Compositions and Nonnegative Walks from Height Two
• Ball–Galvin–Hyry–Weingartner: unimodal coefficient permutations
• Refutation of the regular elementary symmetric image table
• A closest product vector to a q-Dicke state need not be q-symmetric
• A max multiflow need not reproduce the Ingleton entropy combination
• The supremum of the elliptic remainder parameter exponent
• The finite-length Pareto conjecture
• The universal hyperbolic retrieval bound
• Skewness at most two does not force randomness at most one in multicyclic enzyme networks
• Tight purification circuits need not have monotone output error
• The unrestricted rank-only Jensen converse is false
• A two-element T1-groupoid whose reduct is not a reduced T1-groupoid
• Fixed-point-free permutation solutions of the n-simplex equation
• A three-dimensional minimal idempotent subspace
• Refutation of the normalized Bessel Redheffer lower bound
• Refutation of order log-convexity for the modified Bessel product
• A counterexample to the gamma-gamma NBU assertion
• Barker’s coordination formulas for the tsi alternating prism graph
• Ferrers Boards with Prescribed Ordered Level Numbers
• A 23-edge coupling realizes the ten-mode Fourier transform
• Positive polygonal couplings realize every discrete Fourier transform
• Barry’s Riordan-Pascal kernel determinant
• The alternating vortex polygon has exactly $N/2-2$ distinct real eigenvalue pairs
• Bartoli–Stănică reduced critical-point conjecture
• Classify negative base-phi prefix occurrence sequences
• Global ZZ gates admit schedules within the parity bound
• The l1-norm correlated coherence is not monogamous for tripartite pure states
• Bastien–Khormali link-irregular tournament existence
• A Unique Indecomposable Basis Without Intersection Closure
• The complex matrix exponential does not determine the halved commutator
• The source-digraph polytope
• A local counterexample to the triangle inequality ineq_l1
• A fully symmetric triangle-local distribution with p(A = B = C) above 1/4
• Classical permutations admit a strict two-query sequential advantage
• Beccaria–Hagendorf endpoint-density conjecture for the open staggered M1 chain
• Even-depth permuted brickwork has a negative moment direction
• Refutation of Beluhov’s invariant-kernel dimension conjecture at type (1,3,6)
• A type-4c diagonal state refutes the geometric tangle ansatz
• The repetition-count variance of the noisy voter model
• Weak Ascent Sequences Avoiding 210 and the Semi-Baxter Numbers
• The k-positive region of the diagonal-perturbed Tomiyama maps
• The gcd-three equator formula for optimized positive maps is false
• A CSS-T doubling map with better distance than the identity
• Bergman’s Question 15
• Bergman’s Question 19: the field condition in Question 16
• Bernards–Gühne hybrid classical bound
• Exact quantum bound of the Bernards–Gühne nonlocality-depth family
• Bernáth’s OEIS A400645 consecutive-ratio conjecture
• The original simplex coverage optimizer
• Optimal calibrated visibility for joint quantum work measurements
• Refutation of Bhagat, Kulkarni, Larsson and Murali Conjecture 4
• Unequal minima for sumsets with at most two distinct terms
• All-ring coordinates for unrestricted face-magic hypercubes
• Bhatia–Jain: Stolarsky mean matrices in class A
• The ceiling formula for monochromatic sublattices is false
• The proposed union-closed counting threshold is false
• Pretty good state transfer in double blow-ups of paths
• The no-signalling optimum of the relaxed multipartite Hardy test
• The overpartition threshold identity
• Edge marginals at least one half do not imply GHS for general exponential random graphs
• The classical network coherence maximum is $1/4$ for every $$\begin{gathered} n \\ ge2 \end{gathered}$$
• The averaged-kernel characterization fails
• Equal third and unequal second principal specializations for a caterpillar family
• The exhaustive-pairs question for caterpillar principal specializations
• Generating Function of Perfect Matchings Avoiding {123, 132, 213}
• The double-root row of Ballot–Kimberling–Moses Table 5
• Blecher’s reversible four-by-four algebra is not unique up to unitary equivalence
• The whole prescribed packing-maximum conjecture
• A single-formula feasibility witness for the qubit simplex-and-interval inclusion
• The exact compatibility degree of four dichotomic qubit measurements
• Quantum twins in three finite classical graphs
• The Fuchs–Caves fidelity measurement need not give optimal ROC points
• Strongly polynomial graph families with constant depth
• The plus-count statistic is insufficient for exact-weight discrimination
• Half letter frequency characterizes balanced borders
• Bonetto–Jardón Kojakhmetov Conjecture 1
• Bonin’s shadow Markoff positivity region
• Arithmetic complexity of singleton partitions
• The unified-entropy correlation triangle inequality is not universally valid
• Right multiplication maximizes CHSH over the nonlocal-box orbit
• Hyperbolic bounds for the Kilbas–Saigo function
• Two or three prime occurrences in Bouras A363102
• Prime multiplicities in Bouras’s continued fractions
• bouras372763-once
• Bourin’s matrix subadditivity Question 1
• Essentially Hermitian off-diagonal blocks
• The normal-modulus triangle constant in dimension two
• The one-term formula at the boundary
• The two identities of Remark 4.3
• Refuting the unrestricted well-hued graph characterization
• Božović Conjecture 12: k-limited domination of Sierpiński graphs
• Bradshaw’s Conjecture 20
• The relabelled chained inequality holds for every odd-input binary COD model
• Braun–Bruegge Conjecture 5.1
• Refutation of Braunstein–Ghosh–Severini Conjecture 6.7
• Problem 5 of Brešar, Hedžet and Herrman: m(C_n × P_m, 2)
• Six broadcast-dominating packing classes on the two-way infinite path
• Packing k-Domatic Colourings of Paths Need More Than k + 1 Colours
• The trace exponential is not exponentially convex on density matrices
• A SUNTF_R(2, 5, 3) exists
• The damped angular-momentum kernel positivity conjecture
• Brown–George’s argument-dependent degree-root bound
• The Bu–Gu–Jaffe mixed-state quantum inverse sumset bound is false
• Every upset in a neighbourhood convex geometry is convex
• The threshold prior of the G-test is O/(M + O)
• The classical value of the odd polygon game is its Fibonacci bound
• A maximally entangled (3, 3, 7) state of length 9 refutes the length formula Σ d_i − 2
• A qubit dephasing midpoint refutes convexity of Wasserstein complexity
• The all-order increasing-function endpoint-jet assertion
• The original ari coproduct preserves every right-factor level filtration
• Burri’s SW–Petz decoder comparison
• The dimer bounds for k at most 4 on regular biconnected graphs
• Greatest Pell indices dividing initial partial sums
• Positive couplings do not force a real spectrum for U_q(sl_2)-invariant spin chains
• Calderon’s reciprocal moments in imaginary quadratic orders
• Caldwell and coauthors’ super Catalan action-graph identity
• Inversion Sequences Avoiding {010, 100, 102, 210} and {011, 201, 210}
• Weak Ascent Sequences Avoiding {100, 101, 110, 201} and {021, 101, 201, 210}
• The large-squeezing law of the genuine multi-entropy of fully symmetric Gaussian states
• Strong subadditivity of bosonic Gaussian Rényi entropy for $$\begin{gathered} 0< \\ alpha \\ le2 \end{gathered}$$, $$\begin{gathered} alpha \\ ne1 \end{gathered}$$
• Log-negativity entangling capacity depends on the input resource for CPTP maps
• Campbell’s classification of irreducible reciprocal pairs is false
• Equation (11) for the reduced abelian complexity of the Thue-Morse word
• Factorized ladders for generalized quantum Zernike Hamiltonians
• Cao-Chen-Miller Conjecture 1: the multidimensional egg-drop bound
• A non-semi-positive semi-nonnegative qutrit map can signal information backflow
• Cao–Zhang–Shi–Zhao MABK positivity for the two remaining blocks
• Classical Markov monogamy for every finite alphabet and every permutation
• All-odd randomized subtraction games do not converge
• Subsystem Lanczos positivity for general initial states
• The theta representation set: Question (iv), first convexity clause
• The upper-boundary joint instrument is unique
• Carnero Bravo’s hereditary lexicographic product question
• The Caro–Graswald maximal index is $2d-5$ for $$\begin{gathered} d \\ ge5 \end{gathered}$$, and $2$ for $d=3$
• Dense Independent Sets of the Square Grid Contain a Full Cross
• Costa–Catarino bidimensional Fibonacci matrices
• Local versus joint Gaussian thermometry for unequal-frequency modes
• Centered reduced residue progression maximum
• Three-central edge extremality against all metrics
• Zero-magic-gap three-dimensional subspaces in every power-of-two dimension
• The maximal three-qubit violation of Cabello’s nonlocality argument
• The equiprobable pretty-good-measurement comparison of Cha and Lee
• Chaffin-Linderman-Sloane-Wilks Gijswijt Merge Refutation
• The eigenvalues of symmetric two-qubit entanglement witnesses satisfy µ3 ≥ −√(µ1µ2)
• A non-Mersenne exception to the Rule 30 / Rule 22 sign pattern
• Weak Abelian Periodicity Does Not Force Finitely Many Weakly Abelian Unbordered Factors
• Chauve–Zhang condensed-neighborhood unary minimality
• Chauve–Zhang super-condensed-neighborhood unary minimality
• Complete homogeneous symmetric norms of complete multipartite graphs
• Complete homogeneous symmetric norms of paths
• Complete homogeneous symmetric norms of regular graphs
• Effective resistance is the optimal finite-graph moving particle constant
• Chen and Chen’s step-m Eulerian parity positivity
• Completely symmetric three-qutrit states need not be fully separable
• The naive orthostochastic equations are insufficient at order five
• No reverse perfect state transfer in the seven-state bipartite walk
• Chen–He–Lai–Li Conjecture 6.1: the local average at a stem
• Chen–Kato–Brandão completely contractive CMI data processing
• A completely contractive data-processing inequality for the trace-norm CMI
• The one-negative-eigenvalue bound for Hildebrand’s APPT matrices fails in dimension four
• Chen-Sun’s full double-character sum modulo sixteen
• Four-qubit pair-correlation monogamy
• CKZ Conjecture 2: the four actual record distributions
• The fixed CDK image of improper partition matrices
• CayleyPy Growth Conjecture 1 is false
• CayleyPy-4 Conjecture 11: consecutive four-cycle diameter
• CayleyPy-4 Conjecture 15 fails at k = 5, L = 4, N = 13
• CayleyPy-4 Conjecture 16 fails at k = 4, L = 2, N = 5
• The diameter of the inverse-closed consecutive 3-cycle Schreier coset graph
• No randomisation-consistent time reversal on the full channel set
• PPT-squared and IPT-squared equivalence
• A sign obstruction to Chirvasitu–Cusick Conjecture 6.1
• Entanglement assistance raises the communication value by at most the output dimension
• Choi–Kiem–Kye maximal bi-rank edge states
• The temporal Hardy maximum 1/4 is attained with spin measurements for every spin
• The HOMFLYPT Yang–Baxter Künneth subcomplex need not split
• Christiansen’s fermionic correlational bound
• A rank-one partner breaks the negative-q bound for a traceless matrix
• A traceless counterexample to the q-deformed Böttcher–Wenzel bound
• The pure-state scale does not confine purely dissipative spectra to the unit disk
• The first q = 2 Schreier-multiset recurrence
• Linear growth for every Gamma-label split
• The tribonacci and four-Bonacci local Dold observations
• Reduced Denominators for Hankel Determinants of Boundary-Weighted Motzkin Paths
• Shifted Hankel Determinants of Odd Catalan Powers
• Reduced Denominators for Hankel Determinants of Motzkin-Triangle Columns
• Expansions of Narayana-Weighted Dyck Paths in an Even Strip
• A Product Formula for Narayana Strip Series of Heights 4m and 4m + 1
• Hankel Determinants of Backward Shifts of Partial Theta Coefficients
• Signed Dyck Paths in the Strip of Height 4k − 2 Count Walks on the 4k-Cycle
• The literal numerator degree in Cigler’s Conjecture 16
• Simple Permutations Sortable by Two Parallel Pop Stacks with Bypass
• A canonical fixed-fiber bijection for circular two-choice parking
• Locality tensor products need not be locality vector spaces
• The Cobucci–Tavakoli ten-setting GHZ witness in odd dimensions
• Cohen Conjecture 29
• Cohen Conjecture 28
• The L n-omino instance sequence
• A unit-gain circulant on three vertices with universal perfect state transfer
• A closest fully separable state of an X-MEMS need not have the conjectured shape
• Refutation of the symmetric binary-outcome detection-threshold conjecture
• Pairwise Coprime Ordered Tuples of Divisors
• Positivity of the JNR triple sum
• Coşkun–Eden Remark 5.9: the octonion clause
• The uncertainty condition suffices for the mixed discrete Gaussian
• Coulter–Do Conjecture 5.8
• Coulter–Do Conjecture 5.4(a)
• A seventeen-vertex tree admits normalized-Laplacian perfect state transfer
• Infinitely many non-star trees admit Laplacian peak state transfer
• Cowtan–Burton Conjecture D.1: LDPC monic CSS pushouts
• Refutation of the CRIM square-rectair formula at its boundary
• Every three-site improper marginalization is birational for open-boundary binary bond-two MPS
• Crown order-polytope f-vector log-concavity
• Refutation of Crux Problem 2623
• Refutation of the fixed-resistance Fiedler invariance conjecture
• A product decomposition of the generalized CHSH groups
• Cui–Sun Conjecture 2.1: integral Legendre telescopers
• Cullinan–Young Remark 8 leading coefficient
• Cuntz’s integral Fourier zero-free column question
• Edge irregularity strength of cycle-star graphs
• Two-site uniform matrix product states need not have expected dimension
• The lower boundary of the entropy region of qutrit channels and their complements is the conjectured curve
• Removing intermediate memory resets can increase permutation approximation error
• Czerwińska–Franco–Merino: radial convexity and matrix monotonicity
• Face counts for coordinate cross-polytope Minkowski sums
• Dalfó-Fiol-Reyes Conjecture 2.4
• A non-extreme minimum-rank superchannel extension
• The whole finite-cyclic SGB extension
• The NHCRB/HCRB ratio for full orthonormal qudit tomography is at most $d+1$
• The complete singular squared-distance Laplacian conjecture
• A full-rank qutrit refutes the purification lower bound on Krylov operator complexity
• Conditional subentropy and guessing min-entropy
• Datta–Dorlas–Jozsa–Benatti: conditional subentropy and guessing
• Datta–Dorlas–Jozsa–Benatti: subadditivity of subentropy
• Daugherty et al., Latin tableaux Conjecture 6.3
• Divisibility does not force entanglement breaking for qutrits
• A circulant counterexample to Davies–Marigliano Conjecture 4.4
• The unrestricted multivariate hard-core occupancy bound is false
• Deterministic-input violations exist at every positive energy budget below one half
• Davis’s coprime width-descent difference formula
• Refutation of the printed partition-polynomial derivative question
• The optimal T-parameter is not monotone in edge density
• Strong noncommutativity without complete incompatibility in every dimension at least four
• Vacuum and one-photon Wigner-majorization chains
• The exact linear-span dimension of binary bond-two uniform matrix product states
• Symmetric GHZ resources for complete symmetric Boolean functions
• The unitary scaling landscape has a nonglobal local minimum
• The sharp Hoggar-SIC sum negativity is seven eighths
• The inverse Gram matrix of an orthocross MIC is half-integral
• Orthocross MIC elements are never orthogonal, and their Gram entries tend to zero
• A rank-one qutrit MIC with nine orthogonal pairs
• Entropy saturation of a Lüders MIC channel forces SIC existence
• Refutation of the printed barrycade omitted-element relation
• Convexity of the spatial numerical range in non-unital normed algebras
• The Thue–Morse two-block fixed point has frequency one half
• A nonfactorizable doubled triangle
• Dement’s odd-index square conjecture for OEIS A113249
• Refutation of the unrestricted strong distance-two period bound
• Trace-distance anticoherence can decrease under covariant spin noise
• The geometric measure of the flip-conjugate symmetric subspace
• A mixed density tensor attains the nuclear-norm maximum
• A binary-stabilized six-qubit state that is not locally a stabilizer state
• Refutation of the symmetric Bell cross-polytope conjecture
• The cross-integral bound for continuous-time walks on two cycles
• A regular subset of a four-dimensional hyperdisk has no finite hyperdisk cover
• The within-DOF minimum clause of equipartition duality
• Extended local permutations do not suffice for block-shift form
• The exact three-coherence threshold of the Ramsey moment ratio R3
• The bound L_k(M) ≤ k L(M) is not tight for k ≥ 3
• A Multiple with Fewer than Twice as Many Divisors Divides the Square
• Dmitrović: constant-one mixed-norm point evaluation
• The symmetric coin maximizes full-mode entanglement of the Hadamard walk on every finite circle
• At most binomially many inputs certify failure of d-message simulation
• The distinct upper degrees of deterministic simplicial complexes shift by dimension
• Ducci Modular Cycle Factorization
• Minimal bipartite Erdős–Gyárfás counterexamples are 2-edge-connected
• The $mathrm{F}_3$ steering inequality has the sharp ellipsoid-centre threshold two thirds
• The largest root of Dukes’s permaspin cubic dominates the two explicit eigenvalues
• Characterizing rigid alternative means
• Concatenation can increase the cHaar moment norm
• Equatorial multiplicativity of the qubit Wigner distance
• The positive-branch Wigner-distance deficit does not factor through the equatorial input
• Self-tensor superadditivity on the nonpositive Bloch-product branch
• Optimal Cycle–Clique Unions Without Regular Induced Subgraphs of Prime Order
• The Dzhenzher–Sakbaev random semigroup SLLN holds on every Banach space
• Easlick’s complete minimal-advantage dice cycle conjecture
• Wilf Classes of Rotation Avoidance for Patterns of Length Four
• Fishburn Permutations Avoiding 2143, 1423 and 3124
• Fishburn Permutations Avoiding 1243 and 2134
• Fishburn Permutations Avoiding 1243 and 3124
• Fishburn Permutations Avoiding 2413 and 2431, or 2431 and 3241
• Fishburn Permutations Avoiding Pairs Counted by (n − 1)2^(n−2) + 1
• Fishburn Permutations Avoiding Pairs Counted by Odd-Indexed Fibonacci Numbers
• Fishburn Permutations Avoiding Three Patterns from {1324, 2143, 1423, 3124}
• Fishburn Permutations Avoiding 2143 and 3124
• A nice-error-basis code whose stabilizer group is not normal
• Signed cardinality is not 0-mesic on [3] × [12]
• Nonnesting Permutations Avoiding 1132 and 2213
• Nonnesting Permutations Avoiding 1231, 1312, 2231 and 3221
• Nonnesting Permutations Avoiding 1233 and 1322
• Nonnesting Permutations Avoiding 1322
• The minimum average trace distance of a rebit strategy for Elliott’s exclusion task is exactly 1/12
• ellis-thanatipanonda-2022-cut-family-a-conjecture-1
• El Zein-Mortada Saturated Packing Refutation
• A perfect classical strategy for the Torpedo Game
• Unique minimum of the nearest-neighbor QES chain potential
• Divergence of the last site of the nearest-neighbor QES chain
• The Order Gadget of the Erdős–Graham Two-Set Problem Is Infeasible at Every Scale
• Refutation of the one-divisor interval-density unimodality suggestion
• Starting value 47 refutes Erdős’s proposed unique counterexample
• Refutation of Erdős’s report of Mahler’s binary-digit square uniqueness
• Erdős #7: odd covering systems
• Erdos Deep Triple Classification Refutation
• A qutrit SIC fiducial that is not a Clifford-stabilizer state
• Equal totals characterize margins of alternating signed square matrices
• Early state exclusion in seven-site chains with symmetric spectrum
• The extinction set of the wheel W_18 contains 4
• The Katz cut-off limit for path graphs
• Even-hypergraph inverse-positivity refutation
• A uniform mass gap for the π/2-flux Hofstadter model
• Centred convex bodies and Gaussian dilation
• Fan Conjecture 5.9: moving three-point circle capacity
• Fan–Wu–Fei channel coherence domination is false
• Class 69 Mesh Patterns Are Not Equidistributed on Involutions
• The three-state root-fidelity Holevo bound
• Once-subdivided complete graphs have infinite edge multiset dimension
• Weak-four metric dimension of complete graph direct squares
• A singular nonzero point of the odd spectral-invariant variety
• Refutation of the equality conclusion in Fazekas et al. Conjecture 4
• Feldman–Wilce Question 1: finite, unbounded cliques
• Feldman’s Conjecture 9.3: balanced zigzag choices
• Ferenczi–Zamboni Conjecture 1 on longest clustering words
• Symmetric Order and No Connections Do Not Force Full Palindromic Complexity
• A partition strictly between group isomorphism and simultaneous power equivalence
• A non-exhaustive periodic orbit in Fernandez’s three-cell degrade-and-fire chain
• Fibonacci Numbers That Are Pythagorean Perimeters
• Runs in the Second Binary Digit of the Fibonacci Numbers
• Equality of Lucas periods when p and m are both even, at q = -1
• The even-parameter descent dichotomy for Lucas sequences
• The single exceptional modulus for equality of even Lucas periods
• Necessary and sufficient conditions for the vertical slice result
• Filimonova–Puzynina’s rank-one iteration-bound question
• Positive joint weights and all-vertex physical weights in the tree Lee–Yang conjecture
• An odd midpoint refutes Fiore-Nasr-Stone Conjecture 6.8
• Fisk Question 10: coefficient-Toeplitz minors
• Three two-strand boxes refute Jones–Wenzl generation at a root of unity
• Flórez-Junes-Ramírez xz-plane path-count refutation
• Flórez-Junes-Ramírez yz-plane path-count refutation
• Periodicity of generalized pseudostandard words
• Continued-fraction tails with u = 2 and v = 1 miss the Beatty sequence
• The whole positive coefficient anti-recurrence conjecture
• fokkink-rust-2024-splythoff-grundy-rows
• Foucart–Liao’s Chebyshev-center regularization question
• The Number of Indecomposable 321- and 1342-Avoiders with k Inversions
• Maximal connectivity of full mutual-visibility reconfiguration graphs
• Frid’s Fibonacci-prefix palindromic-length conjecture
• Period-doubling PPL-difference: Conjecture 17
• Fried’s Fibonacci Shift Conjecture
• Fu–Luo decoherence convexity is false
• Refutation of Fucci–Stanfill coefficient nonvanishing
• Fuchs’s physical-basis logarithm question
• The forbidden-subgraph conjecture for MMI in graph states holds
• Fukai–Yoshida–Katsura dissipative free-fermion root expectation
• A misclassified configuration for a ternary two-rule density classifier
• The diploid cellular automaton 10-245 has exact density 1/4 + λ/2
• The spatiotemporal Born rule for the LvN distribution has exactly two cases
• Subadditivity of the entropy of quantum states over time
• Furuichi–Eghbali Amlashi: the hyperbolic ratio below one
• Expected largest block-palindrome width
• Three product observables with useless pairs and a useful triple
• Positivity of the multi-entropy replica invariant
• The Three-Colour Restricted Schur Number S_3(k; 2) Exceeds k^3 + 3k^2 + k − 1
• A mixed-sign Gaussian refutes Galindo–Rowell Conjecture 10.6
• Gallardo–Rahavandrainy Conjecture 3.11
• Three-state overlap interval propagation is not always optimal
• Gan–Kim: weak log-majorization monotonicity of Wasserstein power means
• Negativity and the partial transpose distance to the PPT states
• garcia-2026-erdos64-agl29-orientation
• garcia-2026-erdos64-agl31-orientation
• Every gate ordering in an open-boundary integrable quantum circuit
• The minimum depth of open integrable circuits
• The uniform single-left-multiplier Toeplitz factorization assertion
• The Choi spectrum of unital product-unitary-equivariant maps
• Garcia–Volčič Conjecture 4.5
• Garg’s Fibonacci prefix antipower conjecture
• A counterexample to the universal Kummer modulus lower bound
• The sharp weighted Bessel K tail bound
• Gaussian atemporality implies entanglement
• gawron-ulas-2022-factorial-sign-conjecture-4-4
• An asymmetric mixed memory outside Gayrard’s hierarchy
• Gazeau Problem 4.3: no normal Hilbert realization
• The Geiger–Kedem spin-1 spin-entropy depends on the relative phases
• Prefix closure for squares with three digits
• Every vertex an identity Seidel switch
• Quantum max-flow equals min-cut in the symmetric bridge regions
• The reverse Mittag-Leffler modulus characterization is false
• Ghanbari’s integer Sombor energy conjecture
• The exact critical concurrence for universal teleportation through qubit channels
• Ghosh, Birbonshi and Ojha: the unique polynomial root
• The work stored in a stabilizer battery is not a function of the degree difference
• Ghosh–Ramachandran’s capacity-one area decay question
• Ghosh–Ramachandran’s connected-set Fekete area question
• Giacomelli’s cone of infinitely log-concave initial data
• Logarithmic scalar curvature is strictly Schur-increasing
• Quantum cube-root scalar curvature is strictly Schur-increasing
• Gil–Liang–Odetola–Weiner antidiagonal traffic
• Gingrich’s proposed three-qubit monotone built from the Kempe invariant
• The two-qubit binegativity lower bound at fixed negativity
• Binegativity monotonicity for two qubits
• The upper binegativity bound for two qubits
• The fixed-support Davenport limit of integer boxes
• Compatible quantum channels need not be Jordan compatible
• The unital-block overlap lower bound fails for qutrit channels
• Model-level ensemble equivalence does not imply measure-level equivalence
• The original unnormalized achievement-set residue converse
• Generalized Glasby–Paseman Conjecture 1.1(d)
• Jacobi and reducedness obstruct the second E6 and truck Poisson bracket conjectures
• Christoffel words need not attain the Lyndon-factor minimum
• GNP arXiv v4 Question 8.20: Dicke extension cones
• Gobel-Misra Colored-Path Determinant Refutation
• ColorSym optimality is false
• Godrèche–Luck moving-average record bound
• The discriminant clears average mixing denominators
• Sharp return-probability bounds for conference graphs
• The complete graph maximizes the trace of the average mixing matrix
• Goel’s OQ4: Fibonacci period-to-rank ratios omit five
• Refutation of the unconditional entropic Glibichuk–Konyagin conjecture
• Minimality of the base-4 golden-ratio DFAO
• Refutation of Gonzalez D’Leon-Wachs Conjecture 4.13(2)
• Connected progenitor graphs give perfect adaptive fusion strategies
• Refutation of the PNim heavy-interval conjecture
• The generic quadratic Nambu KHK map has a Cremona decomposition
• Graham–O’Bryant Conjecture 5.2: ordinary residue-set refutation
• The Grandjean et al. Mermin-CGLMP facet conjecture
• The local-bound clause of the Grandjean et al. conjecture on (B1)
• Granvik’s A292273 real-part identity
• A stochastic qutrit channel that is not unital
• Gerzon equality fixes the equiangular parameters in every dimension at least two
• Closed Form for the Greedy Fibonacci-Average Sequence
• Two-parameter greedy three-sumfree membership
• Four-dimensional determinant-one representations and cyclic singlets
• The inverse of a critical Carleman Jordan chain is an increasing-path sum
• The binary kite construction works exactly when $n$ is not one modulo three
• Endpoint comparison of Gini means on a bounded interval
• Stationary characterization of Gini mean comparisons
• Pure programs need more dimension than mixed covariant programs
• The activity bound on cross-correlation asymmetry fails for general networks
• Gu’s pseudo-coarse-grained dissipation-time trade-off is false
• Informationally complete pairs are exactly complementary pairs with forest fiber graphs
• Conditional randomness implies uniform attenuation without sharpness
• An unsharp qubit Lüders image violates ambient Sob sum closure
• The upper local degree comparison fails on P6
• The multilayer percolation determinant can have three zeros in [0, 1]
• The reduced function of the partial negativity is not concave
• Guo’s partial-negativity subadditivity conjecture
• Purely Automatic Apwenian Sequences over an Alphabet with One Odd Letter
• Binary automatic apwenian sequences have finite level generators
• Maximum single-party entropy need not decrease on average under LOCC
• Gupta’s rectangular-grid dispersion inequality
• Gupta’s uniform residual degree bound
• Weak-product closure of the edge-complexity equality class
• Gürses and Pekcan’s four-soliton conjecture for higher order Hirota forms
• gurvich-krnc-vyalyi-conjecture-1-total-amoeba-confinement
• The d-orthostochastic dimension is not eventually bounded by 3
• Maximal mutual correlation dominates the square root of geometric discord for all two-qubit states
• Hanna’s mixed trigonometric and hyperbolic congruence
• h277403-div10
• Hanna’s A369673 square classification and five-adic orders
• Hanna’s prime-power correction formula
• Every equal-modulus HMR qutrit channel has a unitary and doubly extreme decomposition
• The rank vector $(3_2,2_6{)}_7$ is realized by an extreme POVM
• Polygon and three-time Leggett–Garg inequalities are insufficient at six times
• The Number of Distinct Terms of the q-Derivatives of y₀ in the Grammar G_Sec
• Han–Liu’s twirling phase-retrievability conjecture
• Han–Pedon Conjecture C: all higher-shift metallic Hankel residue polynomials
• Periodicity of the Shift n + 2 Hankel Determinants of q-Metallic Numbers
• Unboundedness of the Large-Shift Hankel Determinants of q-Metallic Numbers
• The Han–Wang–Yu gluing spectral hull conjecture is false
• The five-cycle graph state is strongly 1-resistant
• The six-cycle graph state is not strongly 2-resistant
• Hanaoka–Konno Conjecture 4.2: self-similarity of the Riesz walk
• Exact preparation-noncontextuality threshold of the twenty-four-cell
• hanna-a107099-half-iterate-mod-three
• hanna-a174470
• Hanna’s ternary-digit residue conjecture
• Hanna’s power-of-two residue conjecture
• Hanna’s OEIS A271960 dyadic vanishing conjecture
• Hanna’s A274479 coefficient congruence
• Hanna’s OEIS A338632 congruence
• Hanna’s square-composition congruence for OEIS A372527
• Hanna’s A377100 coefficient congruence
• Hanna’s bilateral theta congruence, OEIS A380060
• Hanna’s A382318 congruence modulo three
• Hanna’s A382319 congruence modulo three
• Hanna’s bilateral reversion parity conjecture
• The Nested-Square Generating Function Has Even Coefficients at Odd Indices
• Hanna’s Series A(x - A(x)) = x^2 + x A(x) Is Rational Modulo Eight
• Hanna’s A323689 Gaussian coefficient parity
• Hanna’s A324300 Gaussian coefficient parity
• Hanna’s second congruence for A365771
• Hanna’s third congruence for A365771
• Hanna’s three congruences for A365771
• Integer existence and dyadic parity for OEIS A397594
• Linear spin measurements never violate CHSH for any spin $$\begin{gathered} s \\ ge1 \end{gathered}$$
• Square-root Jensen–Shannon balls need not admit majorization-minimizers
• Hardin–Barker five-column clockwise-edge-difference formulas
• Hardin’s six-column trace-avoidance recurrence
• Distance Seidel energy after deleting an edge
• Tight penalty coefficients for the QUBO reformulations of max k-cut
• The tentative Hart–Rowley prefix/suffix equality
• Mixed imitation and best-response dynamics need not equilibrate on general graphs
• No parity Majorana code on at most fourteen modes has distance four and a logical qubit
• A counterexample to Hausmann Question 5.4
• Hayajneh–Hayajneh–Kittaneh: mixed-power monotonicity for unitarily invariant norms
• Hedemann’s proposed diagonal-correlance normalization is exceeded by seven qubits
• Hanna’s derivative-substitution congruences for A232686
• Hanna’s derivative-substitution congruences for A232694
• Hanna’s derivative-substitution congruences for A232695
• Hanna’s derivative-substitution congruences for A232696
• A hidden central direction refutes Heib–Bruschi Conjecture 80
• The affine Lie algebra refutes Heib–Bruschi Conjecture 83
• The flag partition maximizes the squared sizes of affine parts outside the origin
• The Hemmer–Straub–Westrem Ev character identity
• The Hemmer–Straub–Westrem weighted Ev character average
• Herrera’s function-approximation conjecture
• The covariance-corrected entropy-power uncertainty relation fails for mixed states
• The purity of a state under loss is not always log-convex in the transmission
• Hiai’s spectral geometric Log-Euclidean comparison fails
• A corner in the group-invariant asymptotic overlap
• Hiai–Ruskai Conjecture 6.3: exact qubit CQ contraction coefficients
• Connectedness of weak Pareto solutions for continuous convex data
• higuchi-sudbery-2000-four-qubit-average-entropy-maximum
• Optimal hyperbolic cotangent constant
• Arimoto information combining convexity and concavity
• Cachin Rényi information combining convexity and concavity
• Conditional hockey-stick contraction coefficients reduce to orthogonal states and do not depend on γ
• Order-three Rényi information-combining equality
• Refutation of the Okada regular-trace discriminant identity
• The entanglement of formation has a supporting affine functional at every pure state
• A quantum behavior with rank of contextuality three
• Hoster–Stump Conjecture 1.5: simplicial-poset Chow polynomials
• Refutation of the rational Q-system infinite-root primitive count
• Hou–Zhao: the dimension of a sum-free function’s code
• Hou–Zhao: minimum-weight independence of sum-free codes
• The qudit CHSH orthogonality graph is (2d − 1)(d − 1)-regular for every prime d
• Identical TW measurements attain $2(d-1)$ for every $$\begin{gathered} d \\ ge2 \end{gathered}$$
• A null direct summand in a tensor power of a singular semigroup module
• The worst-case CNOT count for reflection-symmetric diagonal unitaries
• Huang–Ma Remark 2.7: the binary delta invariant
• The Huang–Stoica–Xia–Zhong conjecture on $T_2$ is refuted
• Hughes iteration-depth no-gap conjecture
• The minimum output overlap of orthogonal C–Q inputs
• Spin-1 tensor spin-K/2 precession separable bound
• Singlet padding refutes the universal precession GME threshold
• Hwang–Kim: log-Euclidean to Wasserstein near order
• The all-dimensional Hypercube Inequality
• Product formulas for periodic Temperley–Lieb seed recurrences
• The always-failing purification policy attains the sharp availability lower bound
• A projective toric two-design satisfying the MUB overlap condition need not be a subgroup
• Pure-state ECQC fails in dimension five
• The Least Base Maximizing the Digit Sum of n Is ceiling((n+1)/2) for n > 8
• Irwin’s hook-sum conjecture for OEIS A138099
• Ishida’s cyclic stable-marriage arc-lemma upper bound
• Ishikawa and Koutschan’s Pfaffian conjecture for the Motzkin triangle, part (i)
• Finite Otto congruence quotients are cancellative
• The Jacq–Lardizabal mean-hitting-time form is false
• Jaffe’s unrestricted primitive Frobenius successor-ratio conjecture
• Jain: multiplicity two for absolute-cosine Hadamard powers
• Maximal mutual correlation dominates the trace-norm geometric discord of two qubits
• Conjecture 29 on the path Steiner coefficient peak is false
• A weight density below Janssen’s moment lower bound for the annealed Potts critical parameter
• Refutation of Javaheri’s cyclic arrangement dimension conjecture
• A connected cubic counterexample to Jean–Seo Conjecture 1
• Jenzer’s permuted rotor-loop formula without the star condition
• The Jeudy–Rouleux global-permutation Lie-algebra expectation
• Generic logarithmic Lie-length of su(n)
• Cartesian-control angle matrices are invertible for mixed qudit dimensions
• The Gorenstein pairs for alternating adjacent-sum polytopes
• Complex testers do not detect every entangled Werner state
• Absolute two-incoherence beyond the purity bound
• Pick functions do not preserve embeddable matrices
• Pick functions do not preserve strong infinite divisibility
• Johnson–Wakefield Question 6.19: nonvanishing in rank three
• Johnston–Martín Duro–Rumynin Question 2.5
• The Fourier LDOI LOCC lower bound is not tight
• Non-tightness of the antidistinguishability overlap bound
• One generating measurement does not make pseudo-broadcasting equivalent to non-contextuality
• A stronger cumulative Sturmian progression bound is false
• First longest Thue-Morse progressions at power-of-two differences
• Infinite odd fibers of Thue-Morse global maxima
• Fibonacci-word MAP maximum
• First longest progressions at Fibonacci differences
• The box partition function of the six-vertex model
• Kagey’s order-eight recurrence for binary null polynomials modulo three
• Colliding blocks: the collision count leaves floor(π√n) only at records
• First letters of permutations with a fixed inversion number
• Rectangular-torus rotation descent
• Kagey’s A343881 eventual equality conjecture
• Binomial perfect-power counts over GF(2)
• Trinomial perfect-power counts over GF(2)
• Refutation of reciprocal Gamma coefficient positivity
• Refutation of reciprocal q-gamma coefficient positivity
• Refutation of reciprocal q-gamma function positivity
• Coefficients of the shifted Gamma product Turanian
• The function clause of the shifted Gamma Turanian conjecture
• Coefficients of the two-block hypergeometric Turanian
• Swapping an earliest adjacent pair minimizes dephasing for every number of segments
• Question 1.10: regular Toeplitz and strictly ergodic strengthening
• Kania–Kąkol Problem 8.2: the full Talagrand construction under CH
• The two Karlsson families are the only affine suborbits of BC_9^(2)
• Coefficient-wise Wright log-concavity of normalized incomplete beta functions
• First-parameter coefficient signs of the normalized incomplete beta function
• The Karp–Prilepkina Meijer zero-count conjecture
• Refutation of the sum-condition Luke lower bound
• Refutation of the sum-condition Luke upper bound
• Monotonicity and exact ranges of the shifted Kummer ratio
• Log-concavity of modified Bessel ratios
• Coefficientwise log-concavity of the triple rising-factorial series
• Coefficientwise log-concavity and log-convexity of Catalan-power series
• Coefficientwise log-concavity of the two Karp–Zhang series
• kasel-2026-displacement-ladder
• Kauffman–Mukherjee–Vojtěchovský Problem 5.24
• Kauffman–Mukherjee–Vojtěchovský Problem 5.22
• Kay’s transfer-rate conjecture for perfect state transfer chains
• Kaygorodov–Martín González–Viruel Conjecture 5
• The largest automorphism groups of perfect evolution algebras
• Infinite natural-basis quotient with finite full automorphisms
• Natural orthonormal bases of a dense-square Hilbert evolution algebra
• The ordinary nilpotency spectrum of evolution algebras
• kechrimparis-bae-2020-isolated-qubit-ensembles
• Kemp–Ramgoolam arbitrary-depth determinant and monomial-basis conjectures
• Perfect homogeneous Wronskian extensions exist exactly at order one
• The single-pass butterfly fails the relative exterior-square two-design bound
• Same-phase periodic SSH ground states can have positive averaged excess pseudo entropy
• Khavinson–Pereira–Putinar–Saff–Shimorin: nonunivalence radius
• Bipartite encoder forms in an operation-generated class differ only by permutations and row operations
• Divisibility of connected encoder equivalence classes
• Local distinguishability at every boundary projection state
• Kimberling’s A341249 strict bound is false
• First occurrences in Kimberling’s array
• The even Kimoto–Wakayama normalized Apéry congruence is refuted
• Interior perfect state transfer without endpoint transfer
• Strictly positive coefficients are not necessary for generalized action graphs
• Zero belongs to the spectrum of a finite-range translation-invariant lattice Lindbladian
• Mobile general position on the seven-cycle and ten-cycle cylinders
• The minimal translation-invariant MPS bond dimension of the W-state
• Realizability of the correlators of boxes violating chained monogamy
• Self-conjugate even polynomial Conjecture 2
• Natural-basis dependence of balance in degenerate evolution algebras
• The simple evolution-algebra automorphism maximum
• Kaygorodov–Martín González–Viruel Question 31
• The Knight-Dialler Recurrence
• The Koch-Narayan bipartite edge bound is false
• Refutation of the complete original Jaco addition law
• The original Jaco directed path-count equivalence
• Refutation of Kok’s dom-path diameter conjecture
• Refutation of Kok’s A000149 domination clause
• Kok’s unique maximum-degree values and infinite realizing family
• Kok’s maximum degree and literal A319433 deletion
• The minimum number of arcs requiring nSSP
• Even double paths with a nonempty loop set allow nSSP
• Optimality of the coefficient in the entanglement-breaking norm inequality
• Koprowski–Lewis Conjecture 3.1: the original masked hypermatrix count
• The three-distinguishability region in dimension four is not of product form
• Kotesovec’s weighted distinct-partition logarithmic limits
• Kotěšovec’s second A368959 conjecture
• Kotěšovec’s first A368959 conjecture
• One ancilla qubit and bounded rounds cannot simulate every channel with constant success
• Koutschan–Krattenthaler–Schlosser Conjecture 23, equation (10.12)
• Koutschan–Krattenthaler–Schlosser Conjecture 23, equation (10.11)
• Koutschan–Krattenthaler–Schlosser Conjecture 23, equation (10.10)
• The strengthened Marcus–de Oliveira conjecture has a three-dimensional counterexample
• Polynomial content has no maximizer on suitable unit-area polygons
• A resonant memory parameter refutes Krawec’s recycled-coin uniformity conjecture
• Refutation of the divergence sentence in Kreh’s Conjecture 18
• A matrix refutation of Krishna’s C*-algebraic Novak conjecture
• The C*-algebraic de Bruin–Sharma Conjecture is false
• The C*-algebraic Dubinin–Sugawa norm mean value conjecture is false
• The Higher Order C*-algebraic Smale Mean Value Conjecture
• The C*-algebraic Kushel–Tyaglov Conjecture is false
• The C*-algebraic Schoenberg Conjecture is false
• The Zero Forcing Number of P(n,3) Is Eight for Every n At Least Thirteen
• The right-special rotor word is the reversed prefix after the initial zero
• The tree–path conjecture for the game cordiality number
• No single polynomial inequality characterizes separability in every dimension
• Kim–Stanton Conjecture 8.3: integer polynomial denominators
• Kim–Stanton Conjecture 8.4: integer polynomial denominators
• Ku’s maximum-density conjecture for ordinary hypercubes
• The aligned general-dyne measurement attains the global steady-state optimum
• Cubic Grover walks cannot have twice an odd period
• Kulhandjian–Hanzo Conjecture 25: the odd-prime distance bound
• The q = 2 Singer-quadric qubit codes have minimum distance 2 for every d ≥ 2
• Kumar’s remaining rectangular weak two-metric dimensions
• Kumar–Peng–Tran Conjecture 4.4 fails at modulus 17
• Monogamy of the qutrit CGLMP inequality
• Negativity and structured negativity differ for a pure two-qutrit state
• Kurkov’s weighted-ballot formula for OEIS A107667
• Kurkov’s three-parameter Stirling-minor Vandermonde sum
• Eighteen-mode bosonic occupation assignments exist exactly for even particle numbers
• A design with the maximally mixed state is not the most discriminable qubit ensemble at N = N′(2,3) + 1
• Strict containment for graph quantum magic squares on the five-cycle
• Labelle’s Toda numerator unimodality conjecture
• Refutation of the panchromatic pairing conjecture
• The Fibonacci numbers are not 2-super-accessible
• A three-level QSP segment that collapses without a common monomial factor
• A qubit refutation of the maximal reverse Pinsker bound
• Finite generation of one-parameter polynomial Vassiliev algebras
• Rational collision density of bracket expressions
• The one-tenth synchronous doily value
• Exact rational attainment of finite-group subgroup conjugacy ratios
• Zero Slope Fits a Sample Best Exactly When Its Weighted Index Sum Is Balanced
• lee-2026-reduction-operator-invertibility
• The output maximal coherence of channels is not tensorization-stable
• A four-state qubit ensemble where an adaptive post-measurement query beats a pre-measurement query
• Pure-target quantum Černý complexity
• The Thue–Morse prefix 01101001 has quantum Černý complexity 3, not 2
• Lee–Liu integer {2}-domination of three-row grids
• Lemos–Moura–Ribas–Silva Conjecture 3.4
• Optimality of cat pairs for metrology with noisy measurements
• lesaulnier-vijay-2011-beta3-lower-density
• Reverse level order labeling gives one nonzero entry in every nonfinal column tail
• Three continuous invariant parity-odd variables are necessary for two interchangeable pairs
• A square discriminant refutes the odd clause of Levens Conjecture 6.4
• Every Natural Number Counts the Rook Placements of a Crossword Grid
• A Permutation Grid with 155 Rook Placements
• Skew-Merged Permutations Are Exactly Those With One or Two Rook Placements
• The coefficient matrix of a 2p-term separable qubit state has 2^(p-1) forms
• Arbitrary even-order convexity of split covariance intersection
• Li–Guo Conjecture 2.22
• The polar rank-one encoder of Li–Jiang is not exactly optimal at fixed noise
• Partial trace can increase Fisher discord
• li-morgan-siegrist-2026-inflection-points-conjecture-6-1
• Li–Tan circulant positivity is false at order four
• Purify-and-clone fails one-site worst-case optimality
• A Finite Andrews–Gordon Companion Identity
• The largest Bloch weight in the HKNN state
• A signed sum of three-qubit Pauli words of norm 21
• A general obstruction to the pinnacle middle-order lattice
• The averaged Zeitlin Ricci curvature tends to minus half of the harmonic number minus one
• Lichtenfelz–Modin–Preston Conjecture 1: four Zeitlin six-j identities
• Lidar’s QPU-restricted IQP anticoncentration conjecture
• Principal filters of the priority lattice
• Principal ideals of the priority lattice
• Sublattice dismantling of the priority lattice
• Lin’s operator Wielandt norm conjecture fails
• Lin: both spectral properties of the map Ψ
• Lin: the g-property of trace augmentation
• Lin’s matrix majorization conjecture fails at exponent four
• An order-19 counterexample to Conjecture 5.4
• Every data qubit of the delayed remote-controlled circuit violates the dimension witness S ≤ 4
• A bad Anderson potential without nontrivial shared symmetry
• Subsystem monotonicity of generalized concentratable entanglement
• QTD squared can exceed base-2 quantum Jensen–Shannon divergence
• The powered binary Rényi entropy is not monotone in the order
• The Liu–DeBrota fewer-effects construction does not minimize orthogonality
• The CZX parent Lindbladian reaches its conjectured even-ring steady state
• Every finite-dimensional signalling channel has a pure product input with positive PDM negativity
• Non-isotropic mixed-unitary qubit channels do not commute with marginal pinching
• Lin–Miao–Yu–Sheng Conjecture 5.11: second-norm uniqueness
• A stabilizer measurement exceeds every maximally entangled one
• Tightness of the lossy-qubit partial joint-measurability bound η ≤ 2/(2 + sin θ)
• A block measurement refutes mutual-unbiasedness necessity for two-classical dephasing
• Degree recovery from the ordinary Loopy polynomial with loops
• The ordinary Loopy polynomial does not determine the generalized degree polynomial
• Louvet symmetric absolutely-PPT spectrum conjecture
• Lovas and Andai’s conjecture on the least trace-distance contraction over a classical channel
• No β-invertible S₃ symmetry in the ℤ_N × ℤ_N SymTFT when 3 ∣ N
• The Luiz–Vieira generalized Blanuša closing conjecture is false
• Glauber annealing from a thermal state need not preserve neighbourhood passivity
• A shorter relaxation time does not imply a faster energy relaxation in Glauber annealing
• Joint Symmetry of the Mesh Patterns 123 and 321 with Shading {0,1,2}² ∪ {(3,3)}
• The Ma–Weigert derivative-sign regions form a descending chain
• Mourad–Abbas Conjecture 5.1 is false
• L∞-contraction for a weight
• Mahalingam–Pandoh maximum number of scattered palindromes
• Five is not the minimal quaternary extension-counterexample length
• Local-unitary inequivalence of the Question 5.4 stabilizer pairs
• Strict monotonicity of Wallis gamma remainders
• A closed form for the generalized Stirling numbers of boson ordering
• The Maity–Furuichi–Dutta noncommuting Tsallis bound ordering is false
• Maity–Krishna’s mutual abelian-border limit question
• The prime-dimensional stabilizer commutation-rank bound
• A bound on n² times a falling factorial
• Malkoun: the unrestricted subgroup permanent lower bound
• Malkoun’s Conjecture D fails for Young subgroups
• Malkoun’s two-matrix elementary symmetric inequality
• Non-local partial entanglement annihilation is not closed under aligned tensor products
• Mamede–Santos–Soares Conjecture 5.1
• Normalization of weak shuffle products
• manabe-2024-restricted-amalgamation-nim-conjecture-1
• manattu-lakshmanan-2025-cubic-ar-graphs
• Minimal rational faces of the fan of interlace certs
• Mane’s negative-index factorization
• The negative-index root-amplitude attainment clause is refuted
• The closed form of the higher-antibracket coefficients
• Independent extreme-point tests in polyhedral Banach spaces
• Level Sequences Avoiding 101 and 102
• Negative roots of the original Delannoy matrix square
• The multiplicative Hornich–Hlawka inequality in inner product spaces
• Variable-exponent Lebesgue spaces and the Hornich–Hlawka inequality
• Strength three of every Mariot–Manzoni MOCA array
• Sublinear edge completion for consecutive cycle sums
• The Lotka–Volterra integrals are birational coordinates in every dimension
• A qutrit obstruction to strong CP-filter equivalence
• A qutrit obstruction to positive/CP factorization of the channel transpose
• Martinez’s mirror-step gambler’s ruin limit
• The one-bit bound of the double CGLMP game
• Biased post-processed interferometric improvements are not faithful
• Mathar’s recurrence for the surviving walks A026023
• Mathar’s recurrence for the lattice-path returns A068551
• Mathar’s recurrence for the zero-quantum transition pairs A108958
• Mathar’s recurrence for OEIS A113409
• Mathar’s Conjecture 1 on two non-bonding dominoes
• Mathar and Kimberling’s self-convolution recurrence
• Mathar’s OEIS A174193 order-four recurrence
• mathar-oeis-a073759-least-prime-factor
• The full weighted orthogonal-minor inequality
• Affine support of the odd cyclic sign-matrix trace
• Inertia of a singular diagonal matrix after a structured rank-one downdate
• Uniform prime-square approximation for the full local moment
• Matveeva’s literal nonzero-parameter global-boundedness belief
• Tightness of the 0-fidelity lower bound and the worst-case processes
• Weighted Böttcher–Wenzel inequality, case (ii)
• Mazorchuk–Xu: every first-column deficit has a counting polynomial
• A self-dual irreducible extreme thermal process can factor on proper subspaces
• Mbirika-Schrader-Spilker Associated Pell GCD Entry-Point Refutation
• Gibonacci power-window gcd normalization
• Refutation of both Toda-prime denominator assertions
• McNulty’s path-robustness conjecture
• Weak mixing and neighborhood shadowing without small periodic sets
• Neighborhood two-shadowing without quasi-finite type
• The Meer–Weeks fifth-moment bounds for distributions bounded on one side
• A three-point law exceeds the Meer–Weeks two-sided kurtosis upper limit
• The first columns of A098052 and A098530
• Meeussen’s formula for two-layer solid partitions A381265
• n + 1 displaced on-off measurements stay incompatible under pure loss of transmissivity 1/n
• Binomial and kappa states do not exhaust truncated entropy minimizers
• Strict decrease in Mendonça’s min-plus configuration triangle
• Merca’s lifted residue sum at prime order
• Merca’s even-order residue-sum conjecture refutation
• Metya–Mukherjee’s exact independent-convolution L1 minimum
• Conjecture 15 fails for a commutativity-preserving qubit channel
• Data processing fails for the cumulant-based Rényi functional at every order above one
• Mi-Xu-Yang Conjecture 5.2 refutation
• The spacetime density matrix violates the Audenaert-type Schatten subadditivity
• CHSH nonlocality is tightly bounded by the steering-ellipsoid centre
• The fully entangled fraction is at most one minus half the steering-ellipsoid centre
• Mináč–Nguyen–Tân Question 3.5
• Miña-Díaz–Rubin’s Chebyshev–Faber equipotential question
• The Miró-Roig–Tran Strict-Sign Conjecture
• Gaussian quotient monotonicity does not force two exceptional signs
• The Cyclic Latin Eulerian Numbers Are Not Fully Symmetric
• Every Interior Multiple of n Is a Latin-Square Ascent Total
• Misawa–Nishimura harmonic-strength pair refutation
• Refutation of Miska–Ulas Conjecture 4.8
• The Mišta–Fiurášek qudit partial-estimation trade-off
• Mitra broadcasting-channel extrema
• Mitra’s instrument-independent unsharpness measure is not monotone under white noise for qubit observables
• Two completely useless channels with a useful concatenation switch branch
• Minimum Seidel energy of chain graphs
• The full zero-sum prefix-count characterization
• Mohan-Neetu Conjecture 6.1
• Mohan-Neetu Conjecture 6.2
• Mohan-Neetu Conjecture 6.3
• The attained coherence optimum for arbitrary finite qubit Lüders measurements
• Molinari’s honeycomb trapezium determinant
• Connected Hamming-weight gate patterns have an inverse-polynomial spectral gap
• Monkman–Sirker configurational entropy is Schur concave
• Two strongly cospectral vertices of $K_{2,3}$ exceed the multiplicity bound
• The twin end vertex of P’_9 is not sharply 1/9-sedentary
• Integral adjacency support gives transfer through uniform clone matchings
• Moradi–Rampersad–Shallit Problem 1: shifted Fibonacci–Thue–Morse state complexity
• The separable CHSH optimum under imprecise qubit measurements is attained
• A directed graph with democracy coefficient above one
• Integer diminished Sombor energy of edgeless graphs
• A fourth mutually unbiased basis in dimension six
• A closed formula for the bubble-eigenstate configuration count
• The non-unital channel conditions imply both network bounds
• A coherence lower bound on the magic of pure qutrits
• Non-backtracking Laplacian gap and minimum degree
• Every linear N-qubit doily has an odd number of negative lines
• Finite Gilbreath extension component maximum
• Optimal unambiguous discrimination without repetition for equal-overlap states
• The cell-order dynamics of two-dimensional granular systems can have two physical steady states
• A local measure-and-reset refutes the LOCC monotonicity of the MUB correlation $I_2$
• A cooling-map transition has no finite ground-space thermal realization
• Narayan’s expanded-generator delta-set conjecture
• Nathanson’s Problem 12: affine invariance of sum intersection sets
• Nathanson Problem 9: existence of a nontrivial proper spectrum
• Refutation of Nathanson’s additive h-basis strict inequality
• The Jordan obstruction for the Jones–Temperley–Lieb endpoint-sector seeds
• Sharpness of the high-degree fermionic Gaussian constants
• The proposed pruning ranges do not prepare every qutrit Dicke state
• The Rule 84 center column modulo three
• Nikandish Problem 4.2
• Nikiforov: asymptotic graph Ky Fan gaps
• Nonnegative Chebyshev expansions of snake polynomials
• Refutation of Nikolov–Savov Conjecture 3.7 at k = 4
• Nilforoushan-Parvaresh Conjecture 8.1
• Generalized doubly nonnegative cone inclusion
• A Bernoulli–harmonic–zeta identity for the free scalar on hyperbolic space
• The complete first growth assertion of OEIS A222759
• Novaes’s strong-absorption cumulant conjecture
• Novaes’s strong-absorption spectral and Wigner moment conjectures
• A strict gap between measured and Uhlmann average fidelities
• O’Bryant §5.7: the golden minimizer
• O’Bryant’s seven-point positive-real sum-product cell
• Identity and transposition classes have the two largest tensor high-temperature degrees
• Refutation of Detlefs’s A000040 Fibonacci-Fermat prime characterization
• Bala’s Fibonacci-power strong divisibility conjecture
• Refutation of the A000364 pure-periodicity conjecture
• Schulte’s A000680 half-factorial primality criterion
• The A001108 triangular-square indices have two odd divisor sums
• Schulte’s Ω/ω binomial convolution
• Bala’s cubic recurrence and its growing three-adic congruence
• Stern values invert the next Farey-tree numerator
• Forberg’s exponential formula for the quarter-squares
• Kurkov’s A003319 double-array conjecture
• Marcus’s tent-map cycle length and the signed suborder of two
• A004123 totient-period conjecture
• The A005590 zero set at multiples of three is characterized
• Kurkov’s highest-bit recurrence for inverse Gray code
• Schulte’s factorial-square primality criterion
• Rotondo’s A006972 Lucas-Carmichael sufficient condition
• Schulte’s A008287 alternating-binomial expansion
• Refutation of Detlefs’s A008365 four-residue characterization
• The A008474 prime-exponent sum iteration reaches five
• The A008590 gcd-filtered sums characterize the positive multiples of eight
• Refutation of the A018800 least-prime prefix suffix-bound conjecture
• Yanev’s general sigma-radical identity
• Yanev’s position identity for binary reversal
• Wythoff column residue pairs
• The A038867 no-square conjecture
• Products of distinct Mersenne primes satisfy exactly the sigma-tau rational-power relation
• The differences of A049473 occupy two shifted Beatty sequences
• Refutation of the A049591 divisor-count prime-gap characterization
• Yanev’s maximum prime exponent recurrence
• Stephan’s A054096 second-column conjecture
• Stephan’s A059894 complement-reversal conjectures
• Schulte’s alternating quadratic peak moment for Schröder paths
• A064618 totient-period conjecture
• Corneth’s second recurrence for OEIS A068012
• The A068012 subset sum doubling conjecture
• Refutation of the A072872 prime-index upper-bound conjecture
• The Marcus and Bala formulas for the power of three in F(4n)
• Refutation of the A076502 nested-recurrence floor-offset conjecture
• The trinomial odd diagonal of OEIS A077864
• Least-two-element subset count
• Refutation of the A079063 square-root prime-gap lower-bound conjecture
• Quet’s A079278 reduced-denominator recurrence
• The A084068 Pell gcd conjecture
• Refutation of the A089610 eventual strict-increase conjecture
• Yanev’s closed form for binary run compression
• Refutation of Cloitre’s A090825 Bernoulli-integrality conjecture
• The Somos prime integrality family in OEIS A091190/A091200
• The A091259 congruence
• Stephan’s A091915 maximum even partition-product conjecture
• The least self-divisor exponent in OEIS A092028
• Perry’s A094802 least factorial index conjecture
• Exact factorial-square divisibility in A096127
• Square values in the A097602 square-counting recurrence
• Refutation of the A100952 log-bounded semiprime-partition conjecture
• Refutation of the A103585 period-43 comment
• Refutation of the A104863 floor-square-root recurrence conjecture
• Every row sum of the A105594 triangle is odd
• Closed form of the A107928 harmonic-mean-numerator recurrence
• The zero indices of A110454
• Ratajczak’s A110491 T-transform determinant conjecture
• The A112041 prime scalings force the index to be four or divisible by ten
• OEIS A112302: Meijer’s Lerch recurrence limit
• Morken’s first A112399 divisor-sum conjecture
• Prime square perfect-power representation
• Seven and five versus binary carryless multiplication
• Equivalent ordinary and binary carryless multiplier conditions
• The A115805 to A115803 carryless containment question
• Containment of the A115809 carryless multiplier condition
• Cubic divisibility of generalized harmonic numerators along Adamchuk’s progression
• Prime values of the divisor-pair product sum have exactly two preimages
• Layman’s odd-power factorial residue classification
• Prime periods of the A122399 Stirling power-factorial sum
• Hanna’s mixed-parity block partition product in A124418
• Kurkov’s reversed q-Bell row polynomial
• Refutation of the A126762 least-witness exponent-shift conjecture
• Refutation of the A129598 differing-position characterization
• Zeros of the A131853 binary Gaussian evaluation
• A132393: Kurkov’s nested Stirling identity
• Palindrome-square reversal infinitude in A133901
• Ordowski’s binomial and power-sum least-prime conjecture
• The A136162 next-prime product has four prime neighbors only at q=3
• The A140869 Sundaram-type triangle complement
• Bala’s Lucas recurrence and its growing five-adic congruence
• The A145110 conjectured Redheffer support counts
• The A146557 collinear triple divisibility conjecture
• The rational-denominator cube shift in A152020
• Mathar’s first recurrence for OEIS A152661
• Laguerre(n, 4) has odd numerator and denominator
• A Gray-code closed form for the A163617 binary recurrence
• A165719 integrality and the sole prime
• Hanna’s universal logarithmic integer-series closure
• Hanna’s full logarithmic arithmetic-subsequence closure
• OEIS A167857: three distinct prime divisors
• Refutation of the A175406 floor formula conjecture
• The A177680 twin-prime averages modulo five
• Collinear triples in the four-point grid
• Refutation of Barker’s A181278 recurrence
• Curtz’s six-residue denominator conjecture
• Refutation of the A192023 comb-Wiener determinant-count conjecture
• Granvik’s Möbius diagonal and Mertens row
• The A193020 minus-four eventual identity
• The A193020 plus-one eventual identity
• Prime alternating divisor sums in OEIS A193351
• Refutation of Layman’s A196226 divisor-power congruences
• Hanna’s A204061 coefficients modulo five
• The A208342 coefficient formula for a jointly generated polynomial pair
• Werner’s all-column formula for the affine polynomial pair
• Hanna’s overpartition logarithmic derivative congruences
• Prime periods of the A220181 alternating-weight Stirling sum
• Refutation of the all-prime A221077 period conjecture
• Three-column permutation arrays with compatible row orders
• Parity of the A222013 factorial product sum coefficients
• Parity of the A222014 factorial square-exponent sum
• The prime-period conjecture for OEIS A224899
• Hanna’s square-exponent EGF congruence modulo six
• Hanna’s triangular-exponent EGF congruence
• The A226857 Fibonacci sum-product recurrence is proved
• Price’s A228558 prime-exponent conjecture
• Refutation of Stephan’s A229140 least-coordinate distinctness conjecture
• Price’s A231329 prime-exponent conjecture
• Refutation of the A231548 antisigma gap-three conjecture
• The immediate successor is the least weak pseudoprime exactly when it is an odd composite
• Kurkov’s alternating binary run count
• Refutation of the A245786 integrality-implies-gcd-record conjecture
• OEIS A249621 terminal digits for square concatenations
• Krizek’s Fermat-Mersenne classification for A249759
• No A254074 term is a multiple of five
• The A254748 twin-prime mean has no superdivisor
• The divisor-difference gcd and Heinz decoding identity in A258409
• Refutation of the A260310 balanced-pair mod-six conjecture
• The A260407 condition holds at every positive multiple of the order
• Common positive threshold minima for reciprocal-sigma sums
• Barker’s and Zizka’s conjectures for the ON cells of Rule 13
• A266489: clause C1, index divisibility on the frozen object
• A266489: the mod-two congruence clause
• Barker’s conjectures for the ON cells of Rule 41
• Barker’s and Hasler’s conjectures for the rows of Rule 201
• The antepenultimate-label count in OEIS A270236
• The penultimate-label count in OEIS A270236
• Hanna’s prime substitution integrality conjecture
• Oudra’s divisor-count formula for the Stechkin function
• A277829 and A278770: squared-Catalan Hankel limits
• Krizek’s phitorial divisor-sum parity characterization
• Kurkov’s full lower-bit recurrence for A284005
• Kurkov’s binomial identity for binary-weight products
• The A290322 admissible residue sum conjecture
• A292394: square-index divisibility
• Schulte’s Liouville and cube-Möbius product formula
• Krizek’s A300657 noncomposite characterization
• A300732: index divisibility
• A300733: index divisibility
• A300734: square-index divisibility
• A301420: positive monomial coefficients for five data
• Kagey’s modulo-ten congruence for no-leaf grid subgraphs
• Barker’s recurrence for no-leaf subgraphs of the 3 X n grid
• OEIS A302975 divisor-count power-ratio denominator square
• Bala’s OEIS A305550 totient-period conjecture
• Bala’s general integral e.g.f. substitution conjecture
• Ordowski’s A306270 semiprime classification
• Caceres’ A308090 gcd-factorial-power primality criterion
• Mathar’s D-finite recurrence for OEIS A308815
• Dyadic divisibility at Lang’s Fibonacci indices
• Refutation of the A319927 odd non-unitary power-sum conjecture
• Schulte’s exponent-product multiplicativity conjecture
• Barker’s recurrence for crossing- and nesting-free labeled graphs
• The divisor-count prime-factor bound in A328959
• The triangular-residue descent count in A329278
• The printed index range of the sixth A329369 sum
• Barry’s A331474 Hankel generating-function conjecture
• The value-one terms of OEIS A334595 are exactly the powers of two
• First Occurrences in OEIS A335901
• First occurrences in the A335925 self-referential quotient recurrence
• Prime periods of the A338040 weighted Stirling power sum
• The EGF coefficients of A338193 and Kurkov’s recurrence
• Divisibility of the A338636 coefficients by eight
• Fibonacci divisor sums at square-plus-one arguments have even index
• Fibonacci Divisors of an Odd-Index Lucas Square Plus One
• Dequatre’s OEIS A343502 divisor-count prime conjecture
• Kagey’s eventual equality of power-sequence minima
• Marcus’s A344083 nonpolygonal Pythagorean triple conjecture
• Bala’s alternating gcd-sum formula for A344598
• The Karttunen–Munn prime-values conjecture for OEIS A344695
• oeis-a347285-de-vlieger-prime-power-descent
• OEIS A347293 shifted-product gcd row-sum convolution
• Bala’s A347854 fractional-factorial integrality
• Bala’s A347855 auxiliary b integrality
• Bala’s A347855 auxiliary c integrality
• Bala’s A347855 fractional-factorial integrality
• Bala’s A347856 fractional-factorial integrality
• Bala’s A347857 fractional-factorial integrality
• Bala’s A347858 fractional-factorial integrality
• Schulte’s gcd-quotient row-sum convolution
• Hanna’s OEIS A352700 Catalan power-series and modular-coefficient conjectures
• Coefficient congruences for the A355872 bilateral theta reversion
• Hanna’s OEIS A356508 product-partition congruence
• The permutation question for A359482
• The literal A361552 equation and ordinary partition parity
• The A363104 bilateral generating function modulo four
• The A363184 bilateral quarter-double-shift theta congruence
• Parity of the cubic Catalan composition A363308
• Hanna’s A363558 power-of-two coefficient formula
• Hanna’s A363558 prime-index coefficient formula
• Hanna’s A363559 power-of-two coefficient formula
• Hanna’s A363559 prime-index coefficient formula
• Divisibility of the A363560 coefficients
• Hanna’s A363561 power-of-two coefficient formula
• Hanna’s A363561 prime-index coefficient formula
• Hanna’s A363569 power-of-two coefficient formula
• Hanna’s A363569 prime-index coefficient formula
• The permutation conjecture for A363956
• Square divisibility of the A365095 perturbed diagonal
• Hanna’s A365574 Lagrange parity conjecture
• Cardinality-sum-avoiding subset generating function
• Binomial parity of the A369083 coefficients
• The one-common-Zeckendorf-term greedy sequence is a permutation
• Modulo-four classification of the A372577 coefficients
• Mathar’s linear recurrence for the A372991 factorial-quotient sequence
• Divisibility modulo three of the A373308 coefficients
• Square parity of the unit-reversion series A373312
• The A373561 divisor-bucketed quadruple sum
• Powers-of-four parity of the A374568 coefficients
• Parity of the Catalan-composition series A374570
• Fibbinary parity of the A374571 coefficients
• Parity of the A375439 coefficients
• Hanna’s OEIS A375449 diagonal derivative parity conjecture
• Hanna’s OEIS A375452 diagonal derivative parity conjecture
• Huber’s minimum-volume cuboid conjecture
• Kurkov’s periodic boundary recurrences and the large Schroder diagonal
• Parity of q-Catalan row square sums
• Integrality and dyadic parity of OEIS A377106
• The A378252 running-sum residue conjecture
• oeis-a378258-hanna-mod-six
• oeis-a378258-hanna-square-root-parity
• Alternating row sums of the Fibonacci harmonic triangle
• The literal adjacent difference of OEIS A378495
• The terminal difference of OEIS A378495
• The A378575 shifted-iterate fixed-point congruence
• The A378576 shifted-iterate fixed-point congruence
• Strip-three ternary Catalan parity for A378578
• Coefficients of the A378580 quotient theta composition modulo four
• The theta self-composition coefficients modulo four
• Hanna’s A379204 evenness conjecture
• Hanna’s A379764 theta-four coefficient conjectures
• The A380056 divisibility conjecture at multiples of four
• Hanna’s A380066 bilateral product congruence
• Parity of the A380558 square-reversion series
• Dyadic support of the odd coefficients of A380678
• Hanna’s square-residue conjecture for OEIS A380680
• Hanna’s prime bilateral integrality conjecture
• Fibbinary parity of the A380708 coefficients
• Binomial parity of the A380709 coefficients
• Absolute reciprocal squares and binary parity in A380710
• Hanna’s A380711 absolute cubic congruence
• OEIS A381190 trapezohedral domination series
• The A381362 bilateral product coefficient congruence
• The A381363 bilateral product coefficient congruence
• The A381364 scaled bilateral product congruence
• The A381365 scaled bilateral product congruence
• oeis-a381423-hermite-differences
• Absolute Hermite coefficient modes: the complete A381524 difference assertion
• Dyadic denominators of the A381670 compositional-square series
• The complete A381737 Conjecture 1 enumeration
• The complete A381737 Conjecture 3 generating function
• The complete A381737 Conjecture 2 recurrence
• Hanna’s A382124 congruence
• Hanna’s A382125 residue pattern
• The valuation-step greedy sequence is a permutation
• Constant Blocks and Distinct Run Sums
• Fibonachos ties and first-player majority
• Eventual periodicity of OEIS A383165
• Eventual periodicity of OEIS A383166
• Parity of the A383377 coefficients
• Palindromic composition of the A384222 rows
• Parity conjecture C.1 of OEIS A384267
• Parity of the A384270 coefficients
• oeis-a385590-alternating-binomial
• Hanna’s Lambert W coefficient congruences
• Signed Catalan cubic substitution modulo three
• Multiple-of-Three Residue Coincidences
• Choosable Initial Intervals and Reversed Partitions
• The A388986 Euler-form inclusion question
• The least simultaneous digit-sum witness in A389000
• Odd-index parity of the A389472 coefficients
• Dyadic parity support of the A389476 quadratic reversion
• The A389536 square-cube substitution conjecture
• Alternating dyadic reversion modulo four for A389537
• G.f. A(x) satisfies A(x)^2 = A(2x - 2A(x)) / 2.
• Quadratic square reversion modulo four for A389542
• The A390088 exception set
• First sums of decreasing partitions
• Howroyd’s full Andrasfai mutual-visibility generating function
• The full alternating Laurent-row formula in A391810
• The full Laurent rows in A391810 sum to zero
• The first weighted moment of A391810
• The full signed Laurent second moment in A391810
• The A392095 column and A088713 source series
• Parity of the A392525 coefficients
• Zero-Prepended First Sums and Odd Parts
• Trimmed Alternating Sums of Ordinary Partitions
• Strict First Sums and Gapfree Odd Partitions
• The mod-four coefficients of the Catalan-shift square series
• Hanna’s power-of-two parity conjecture for OEIS A393173
• Every integer occurs in the factorial Heraclitus transform
• Coefficients of A393856 are one modulo five
• Coefficients of A393857 are one modulo six
• A393867: every logarithmic-derivative coefficient is odd
• Prime divisibility of the A393867 logarithmic-derivative terms
• Twin-prime sigma-gcd three forces twice a square
• Huber’s prime conjecture for OEIS A394407
• The ratio-limit assertion for A394578
• Prime twin-center sigma-gcd values are two or three
• Divisibility of the A394757 terms
• The greedy-brick all-index identity
• OEIS A395833: diagonal-exponent self-divisibility
• A395833: the mod-three congruence clause
• The A396099 period-four coefficient pattern
• G.f. A(x) satisfies A(A(A(x))) = (1+x) * A(A(x))
• A396596 divisor-power union: a counterexample
• The A396659 universal edge-collision ratio
• Divisibility of the A396793 coefficients
• Divisibility of the A396794 coefficients
• Divisibility of the A396795 coefficients
• Coefficients of the A396797 three-four iterate product series modulo six
• The eighth compositional iterate of A396798 modulo eight
• The fifth compositional iterate of A396798 modulo eight
• The fourth compositional iterate of A396798 modulo eight
• The seventh compositional iterate of A396798 modulo eight
• The third compositional iterate of A396798 modulo eight
• A396803 coefficients modulo three
• Parity of the A396803 iterated-exponential coefficients
• OEIS A396804: the fourth-iterate EGF modulo four
• A396805 coefficients modulo three from index three
• Parity of the A396805 iterated-exponential coefficients
• A396806 coefficients modulo six
• Parity of the A396806 iterated-exponential coefficients
• Coefficient congruence for OEIS A396807
• OEIS A396843: all coefficients are odd
• Refutation of the A396844 mod-sixteen conjecture
• The A396846 logarithmic coefficients modulo eight
• Oddness of all A397241 terms
• OEIS A397241 coefficients modulo 4
• OEIS A397241 coefficients modulo 3
• Parity of the A397242 coefficients
• The residue-one conjecture of OEIS A397242
• The residue-two conjecture of OEIS A397242
• Fibbinary parity of the A397244 coefficients
• OEIS A397315: the Three-Row blackout conjecture
• A397345: square-weight congruence
• A397346: square-weight congruence
• A397348: square-weight congruence
• Alternation modulo three of the A397349 coefficients
• Parity of the A397349 logarithmic-weight coefficients
• Ternary support of the A397356 reciprocal square-exponent diagonals
• Parity of the A397356 reciprocal square-exponent diagonals
• A397436: the unrestricted product supercongruence
• oeis-a397578-sigma-neighbour-peaks
• The integer source and dyadic parity of A397592
• A398542 fixed-bottom polynomial conjecture
• Eventual periodicity of every A398589 row
• Palindromic numerators of OEIS A398690
• OEIS A398726: the distinct cycle size limit
• oeis-a399155-value-finiteness
• OEIS A399232 radical identity
• A399755: generalized Pell classes and the least square partner
• A400168 has a term greater than one
• Maximum length of a two-dense divisor block
• Three tetrahelix coordinate generating functions
• OEIS A400361: the exact second-order cumulative formula
• OEIS A400429 second semi-meander diagonal
• OEIS A400585: the odd-cofactor summatory asymptotic
• OEIS A400644 rounded three-term norm ratio
• Oh and Scrimshaw’s two-shifted q-Motzkin Hankel conjecture
• Okada’s pre-merged Gaussian determinants of width at least three are not almost palindromic
• Refutation of Onnis’s square convergence prohibition
• Optimality of the Ordered Zeckendorf Long Game Strategy
• The steering substitution need not preserve powers
• Direct four-copy universal entanglement concentration beats the bound of Eq. (8)
• Refutation of Ostrovskii–Shcherbakov Conjecture 6.2
• Oudra’s A248186 cubic floor formula
• Four clues are necessary for unique four by four SudoQ solvability
• Minimal matrices of fixed RSK shape need not be Hankel
• Second-family singlet-like data exist in every dimension
• Pandey’s Parity Conjecture 4.1
• Pandey–Patra subgraph core conjecture
• The Alternating Stirling Weighted Sum of Even-Index Fibonacci and Lucas Numbers
• Original cyclic-morphism string-attractor minimum
• Reversal and the Weighted Sum of a Partition
• Two-qubit conditional domains need not be C*-subalgebras
• For two qubits the SVD entanglement entropy is at least the smaller of the two entanglement entropies
• Pathak’s generic-state negativity conjecture
• Commuting product encoders define exactly the commuting-reflection qubit state class
• Four colours in small online majority edge-colouring games
• The correlation-minor bound fails without filter normal form
• Circular hypergraphs do not maximise orientation-count entropy
• Entropy maximisers need not have balanced degrees
• Peltomäki’s silver-slope abelian period set conjecture
• Diophantine exponents of aperiodic episturmian words
• Zero-dimensional shadowing extensions
• The Tsirelson bound of the d-outcome Bell functional of Perito et al.
• Perrier’s period-one generating functions
• Two indexed wreath eigenvalues coincide
• Alternative q-Charlier Fibonacci positivity: Petrov–Scott Conjecture 6.3
• Pham–Vu Question 3.9: diameter of graphs with well-covered powers
• Question 3 on outgoing digit-sum arcs
• The Order of a Pisano Period Is Not Confined to Two
• A pinned triangle refutes the spanning-tree dimension conjecture
• The Poncini–Rasmussen central factorial transfer expansion
• Natural valuations cannot preserve every abelian complexity function
• The normalized nonlocality–contextuality trade-off holds for every binary n-cycle
• The nullspace of the periodic XX chain on twice a prime number of sites
• Every classical six-leg perfect tensor factorization has perfect two-wire factors
• Pronko’s anti-adjoint expansion conjecture for the periodic Fredkin chain
• Pronko’s non-cyclic Fredkin eigenstate annihilation conjecture
• Pronko’s commutation of the Dyck-class operator Ξ with the periodic Fredkin Hamiltonian
• Pronko’s raising and lowering operators of the periodic Motzkin chain
• Pan–Skandera–Wang’s Permanental Inequality at Every Initial Split
• The Pan–Skandera–Wang Map Is Bruhat-Increasing for Every n
• The minimum skewness of a unidirectional unicyclic current
• The sharp lower bound on the kurtosis of a unidirectional unicyclic current
• The sharp upper bound on skewness minus kurtosis of a unidirectional unicyclic current
• The sharp lower bound on skewness plus kurtosis of a unidirectional unicyclic current
• The sharp lower bound on skewness times kurtosis for unidirectional unicyclic currents
• Ptaszyński’s exact lower endpoint of skewness minus kurtosis
• Refutation of Pudelko Conjecture 8 at position zero
• The Haar mean of two-qubit non-local nonstabilizerness is 10/3 − π
• qian-wang-2025-separable-states-stab-local-unitaries
• The four-qubit Fredkin gate generates more than two ebits across AD:BC
• Sharp parameter thresholds for the zero-balanced Gauss quotient
• Quasi-Injective Composition Refutation
• Quasi-Injective Order Separation
• The coefficient system of Quesne’s Kepler–Coulomb extensions on the sphere has the conjectured closed forms for every m
• M-resistant qudit states exist for every admissible loss parameter
• Second adjacency eigenvalue of the inner-face Apollonian stages
• Unrestricted qubit generalized-fidelity data processing
• The maximum number of pairwise strongly complementary permutation matrices
• Circulant bracelet sufficiency fails in dimension twelve
• A circulant unistochastic matrix without a circulant unitary lift
• Ramane–Kitturmath’s regular graph energy conjecture
• Relative entropy coherence is bounded by l1 coherence
• Gaussianity of random Zeckendorf game lengths via mixing
• Raney Conjecture 7.1: zero-run record families
• Rather’s book domination-root Conjecture 5.4
• Rather’s real-rootedness question for general position polynomials
• The termwise local-perception CHSH witness is at most 2 for every measurement setting
• Max-minus-min homomesy for rectangle interval-closed rowmotion
• Global dynamic cooling strictly beats equal parallel groups except at (N, M) = (6, 2)
• Positive Kraus operators do not exclude a side-entanglement advantage
• A strict Bayesian feedback advantage for the qutrit Werner–Holevo channel
• The constraint polynomials of the two-photon Rabi model at and beyond the critical coupling
• Successive new Laplacian layer maxima of token graphs
• Richman’s congruence for the deranged-matching numbers
• A commuting obstruction to the nonlinear measurement monotone
• Rivin’s cycle-geodesic midpoint formula
• Rivin’s cycle-geodesic universal function
• Unitary entanglement-assisted encoding beats every unassisted strategy in an energy-restricted four-message task
• The instability count of a clamped Lennard–Jones chain
• Conjecture 3.1: APN functions and large binary flats
• Squares do not maximize the mean exit time of lattice clusters
• Unique integral circulant energy maximum at order $p^2{q}^3$
• The noisy qutrit Werner–Holevo channel is a GKSL exponential only at zero noise on \[0,2/3\]
• Rosenzweig–Stanfill Open Problem 1.3
• Rosenzweig–Stanfill even residue vanishing
• The optimal W-state PPT measurement is outside SEP
• The extended MUB mixed-norm equality is false
• Rouleux’s affine-determinant conjecture for alternating polynomials
• The boundary α-z Rényi relative entropies of magic are not additive on three qubits
• The most classical orthonormal basis of spin 3/2
• The steady-state block of a Markov generator with a commuting symmetry need not admit a Markov form
• Every q-transversal matroid is representable over a finite extension
• Refutation of the numerator conjecture of OEIS A362534
• Sahbi’s Conjecture 4.1: bipartite equality for all positive k
• Sahbi’s Conjecture 4.2: bipartite two-independence and upper star formation
• Sahbi’s Conjecture 7.2: triangle-free equality at two
• Sahbi Conjecture 6.4
• The ideal heralding rate of Fourier photon distillation decreases strictly to 1/4 from n = 5
• The K-number and extreme-point K-sets of real finite-dimensional sup-norm spaces
• Subsystem size does not order coherent information in noisy graph states
• A disordered exclusion ring whose ε² current response vanishes although neither symmetry condition holds
• A passive incoherent memory realizes a non-classical dephasing superchannel in dimension 3
• Noisy entanglement curvature can exceed quantum Fisher information
• The Harrow channel pair’s parallel Chernoff exponent is not one
• Conjecture 1 on paired coalition numbers of perfect binary trees is false
• Equal multipartite powers of diagonal phase gates
• The perp hyperplane refutes the three-qubit hexagon contextuality generalization
• Even-legged hyperlinks reconstruct the entanglement entropies with N-independent leg-factors
• Four physical levels admit a $U(1)$-symmetric injective matrix-product family
• A 1225-vertex graph refutes the star bound on the minimal-energy uniform overlap of quantum batteries
• The expected two-bath Bose-selection bound is refuted for cubic spectra
• Explicit flat-spectrum probe probabilities
• Ancilla-free testers with a common normalization state have canonical POVM robustness
• No finite measure-and-prepare process perfectly clones the amplitude-damping family
• Distinct optimal entanglement witnesses can have an optimal sum
• Actual separable occupied-diagonal lower bound
• The minimum of purity plus time-reversal overlap
• Local-channel monotonicity of Rényi conditional quantum mutual information
• The signalling game has equal classical, quantum and no-signalling values
• Shah–Kiselev Conjecture 3.1: the late growing ratio
• Shala Question 7.4: weakly but not strongly coset-like atomistic lattices
• Shao–Zhao cycle Italian-domination recurrence
• Shapiro Conjecture 1(iii): identity words on finite trees
• shapiro-2026-unweighted-fourth-moment-inversion
• Sharma’s primitive-polynomial Conjecture 4.2
• The zero higher-order EPR bound is tight at every positive order
• Convergence of the Shieh-Yang-Yu dotted-pattern machine
• The 12̇-Machine Sorts a Central Binomial Number of Permutations
• Shin’s four-point sumset compression question
• Selective LOCC can increase Shirokov’s Moreau-Yosida entanglement of formation
• Concealment-equivalent channels with different adjoint kernels
• Iterated moment minor inequalities
• The minimal separable numerical range ratio of one two-qubit observable
• Odd order does not ensure the conjectured minimum of Hadamardness
• Maximal input entropy for binary two-deletion and two-insertion channels
• A negative third difference of exponential remainder ratios
• Three volume ratios for generalized Pauli eigenvalue regions
• Skalski and Stroiński’s conjecture on the smallest set of uniqueness for the Ising cone
• A faithful mixed-state counterexample to KD-real SLD exclusion
• The normalized expected range of a knight’s random walk is an integer
• Parity-position sequences in the Sobolewski–Ulas recurrence
• Nonvanishing Indices of the Binary Digit Hankel Determinants at t = −2
• Zeros of Binary Digit Hankel Determinants at Twice a Root of Unity
• Complex hopping can increase parity-twisted ground-state coherences
• Measurement can extract more than half the ergotropy of a non-stationary state
• Tournament solid-metric lower bounds
• Somer-Krizek uniform-subsequence conjecture
• Formation is not constant on the Song–Chen–Đoković subspace
• A disconnected counterexample to the token-radius conjecture
• Steering does not guarantee atemporality
• A steady prior does not imply tabletop time reversibility
• Unrestricted two-state dequantumness power can exceed its maximal-quantumness restriction
• Song and Lin’s parity conjecture for zero transfer on oriented circulant graphs
• The higher exterior traces of Spezia’s serpentine matrix
• The second exterior trace of Spezia’s serpentine matrix
• Higher exterior traces of Spezia’s perimeter matrix
• Spezia’s Pell circulant permanent-to-determinant ratio
• The component count is the graph count plus loop-free strange components
• Squarefree Numbers Have No Partition Whose Parts and Multiplicities Agree in Mean
• Sra’s reciprocal-permanent Lorentzian question
• Sra’s symmetric alpha-permanent question
• A Clifford unitary that changes the operator norm of the MUB autocorrelation matrix
• Štampach–Waclawek’s alternative Birman weight expansion
• The improved entanglement-swapping product bound fails in dimension four
• The remaining correlation domain admits the weight gap exactly when $$\begin{gathered} c< \\ sigma \end{gathered}$$
• Stirling Lucky Displacement Spectrum
• Bound-coherent states exist in every dimension at least three
• Level-one QAOA reaches a genuine four-state superposition on three qubits
• The sharp worst-case MATEN process fidelity is $4^{-N}$ for $$\begin{gathered} N \\ ge2 \end{gathered}$$
• Boundedness of the Damascus violation sets
• Sun’s Conjecture 3.8: circular permutations with primitive adjacent products
• Sun’s weighted distinct-sum bound
• Sun Conjecture 5.2: both lowercase strict Turan clauses
• The Sun–Luo–Ye projection-matrix AM-GM conjecture
• Sun Conjecture 4.2(i) absolute-difference permanent congruences
• Composite prime divisors of the gcd determinant
• A sharp Weyl–Bloch ℓ1 entanglement criterion for two qutrits
• Suvagiya Conjecture 28 refutation
• svinin-2015-discrete-polynomial-identity
• Noninteger parameters do not ensure injectivity of the Szalay–Tóth partition generators
• Ta Problem 11.6: three invariants do not determine the count
• Ta Problem 11.7: the good-involution bound need not be strict
• First-level SDP inexactness on the weighted-crown interval
• Takemura’s fixed-point first appearance degree
• Takemura’s fixed-point first appearance value
• The Wagner graph and the rank-5 eight-vertex graph have no qutrit violation, so d* = 4
• Tang–Zhang: the sharp order −2 Schoenberg inequality
• Tang–Zhang: real-order reciprocal critical-point moments
• A three-qubit counterexample to the Shannon branch-and-bound lower bound
• Tărnăuceanu’s reciprocal subgroup-order conjecture
• Multipartite partial tightness of the entangled-measurement bound
• A SIC-compound in dimension 8 from Hoggar SICs
• The MUB and SIC correlation trace norms agree up to the factor K
• Conjecture 2 of Tavakoli–Morelli: the Schmidt-number bound for equiangular measurements
• Conjecture 3 of Tavakoli–Morelli: the Schmidt-number bound for incomplete sets of MUBs
• Pure preparations cannot violate the HTMB inequality in finite dimension
• Tebni’s prime and dyadic row-divisibility conjectures for A341724
• Tebni’s OEIS A350759 prime congruences
• Tebni’s odd-prime congruence for OEIS A364822
• Tebni’s power-of-two congruence for OEIS A364822
• A ring of four complete blocks refutes the flat-graph clique-root conjecture
• Faal’s Open Problem 1: non-chordal graphs with unstable restricted clique polynomials
• Interaction-picture asymptotics
• Testart Question 1: the native tree side and a type-C permutation model
• A connected K₄-free graph with nonreal clique roots
• Thanatipanonda’s shifted binomial power linearization
• The vertex position ratio is unbounded on connected graphs
• Odd-index reduced abelian complexity of the Thue-Morse word
• Tian–Dokyeesun–Klavžar Conjecture 3.4 refutation
• The traceless BPS cohomology at (p, N) = (5, 4) is not free over the diagonal creators
• Three-weight Pauli channels have Bayesian inverses only at the maximally mixed state
• All odd kinetic frequency moments
• The temporal Bell endpoint contraction identity for every open XX chain
• Operational comparison of qubit incompatibility without equal lengths
• The separable modified Wasserstein distance can exceed the De Palma–Trevisan one
• Tyagi’s sharper Sprague–Grundy bound for Divisor Nim
• Uhlmann’s unrestricted diagonal-majorization question
• Ulfarsson’s alternating mesh-pattern basis conjecture
• Ulgenes’s truncated-binomial Hadamard limit
• Compatibility under every Heisenberg channel equals compatibility in every subspace
• The orthogonal absolute-product minimum is attained at one
• A rotating replacement state refutes purely non-unital eternal non-Markovianity impossibility
• Two singlets give more than twice the statistical strength of CHSH
• Non-negativity of the photon-addition coefficients
• Finite-Fock beam-splitter states need not be extreme Wigner-positive states
• Van Herstraeten–Guha–Cerf Conjecture 2: coherent inputs for phase-covariant attenuators
• Condensation need not preserve LC-equivalence
• Vatter’s largest derangement limit below one
• A negative answer to Vatter’s Question 4.3
• Endpoint homomorphisms of everywhere overlapping flat pairs
• Bell-diagonal entanglement distance is not twice the squared concurrence
• Visomirski–Griffin frozen-wave conjecture
• Volkoff’s exact-ground-state pair-tunnelling ansatz
• Infinitely many extreme classes survive the commuting-unitary quotient in matrix D-majorization
• Simple-spectrum Gibbs-stochastic matrices for every positive Gibbs vector
• Spectral bound for conditionally 2-positive maps
• The kernel criterion for witness optimality does not imply the trace criterion
• The Eq. (10) set does not generate the 3 × 3 stochastic matrices
• Exact classification of elementary channel divisibility
• Exact W-state Bell-state-measurement optimum
• Wall-Sun-Sun primes as a golden-unit lift problem
• Token-1 spectral contraction for every finite positive-velocity chain
• Disorder-free localization on even hypercubes
• The quantum value of balanced hypercube rendezvous is strictly below its no-signalling value
• The sharp six-level bound for extreme two-qutrit absolutely PPT states
• Wang Conjecture 3.26: finite algebraic constant does not bound the relative constants
• Wang’s Conjecture 5.3
• The unrestricted exact Wang–Tian saturation formula is false
• Every localized quantum Bernoulli noise walk has the standard Gaussian limit
• Comparability of conical-design concurrence bounds
• Refutation and exact classification of exponential derivative ratios
• Wei–Liu CCZ magic-capacity threshold
• Cube polynomial of the associated Mersenne graphs
• Degree generating function of Associated Mersenne graphs
• Critical values of parametrized quantum circuits
• The coherent discrimination bias is not a metric on quantum channels
• wiseman-a344611
• Wiseman A387118 total partition identity
• Wiseman A388713 maximum-refined partition identity
• Resolved-count coherent-state weak values
• Wiseman’s nonchoosable partition identity
• Gurland’s original logarithmic remainder
• Degrees of the order-eleven quasi-Fibonacci polynomials
• Wolford’s generalized binomial biroot convergence conjecture
• The balanced-cut gradient bound of Wölk and Gühne fails for eight qubits
• The phase-shifted extension of Conjecture 2
• Monotonicity of the negativity of randomized graph states
• Wu-Lou permutation-invariant Niven digit-sum bound
• Wu’s k-gonal-pyramidal complement formula
• Comparing the Wu–Wu unified imaginarity monotones in every finite dimension
• The exact A|BC constant of the GHZ measure
• Wu’s adjacent-index Fibonacci divisibility conjecture
• The entropic tetrahedron is not a genuine four-qudit entanglement measure
• Xu’s oblique-discord mutual-information conjecture
• The optimized GHZ witness bound need not equal the geometric GME measure
• Two unbounded classicalization gaps with a qubit
• Complete monotonicity of the Xu–Yang Mills remainders
• Xu-Zhao Conjecture 1.3
• The exact triplewise joint-measurability threshold of biased trine qubit measurements
• Every incoherent channel with coherence-breaking index at least two is amended by one unitary
• The quantum coherence fraction can increase under incoherent operations
• Destruction covariance need not be a superchannel fixed set
• Yoshida’s rapid-decrease closure question
• Yu’s mixed-state skew-coherence polygamy conjecture is false
• Schur-channel diamond-distance equality
• A finite set supplies one state entangled for all fixed tensor partitions in every frame
• λ_f = min{1, 1/[4f(0)]} fails for a regular symmetric operator monotone function
• Unimodality of the X-state conditional entropy
• Walks of near-maximal algebraic area
• Maximum order complexity along polynomial Zeckendorf subsequences
• Refutation of Zelinsky and Zhang’s Conjecture 22
• Zhan–Bie consecutive cyclic-stack fibres
• Dicke optimality for detector-sensor identification
• Strict averaging need not improve detector-sensor probes
• Eventual stability of Zhang’s l-complexity
• Zhang’s three-operator Clarkson–McCarthy conjecture is false
• Taylor-coefficient weak majorization for Hermitian matrices
• Independence polynomials do not determine T2-threshold hypergraphs
• Refutation of Zhang’s character-sum constant restriction
• The incompatibility probability of random qubit measurements
• Zhang–Jing Theorem 2.3: the upper power interval
• Zhang–Jing Question 2.14: block positivity and normality
• Zhang–Li rank-one Hadamard product variational problem
• Compatible projective tests do not imply compatible quantum channels
• Zhang–Singh–Pati: strong subadditivity of subentropy
• Zhang–Tian Conjecture 5.1: Steiner diameter and anchored radius of trees
• Zhang–Wu–Fei: relative-entropy superadditivity after unitary conjugation
• All qubit tuples maximizing the imaginary Bargmann invariant
• Normal limits for Speyer g-polynomials of growing uniform-matroid rank
• DomiRank entropy need not decrease with competition
• A mixed four-dimensional state has equal coherence roofs
• Refutation of Zhao’s maximum preimage conjecture
• Refutation of Zhao’s second-largest preimage conjecture
• Schröder Enumeration of the Sorting Class of the Stack Avoiding 23-1
• Equal Sorting Classes and Outputs of the Stacks Avoiding 312, 31-2 and 3-12
• Logical Z operators with Z support on every stabilizer coset need not exist
• In-between-state optimality for transmissivity sensing with a beta prior
• In-between-state optimality for Bayesian transmissivity sensing
• The Zhou–Wu–Chau endpoint lower bound on overall error is false
• Enumeration of the Arrow Pattern (32; 1 → 3)
• The Arrow Patterns (12; 3 → 3) and (23; 1 → 1) Are Arrow-Wilf-Equivalent
• Derivative signs of the power-weighted hyperbolic cotangent remainder
• The isotropic aggregate of a two-qudit state in dimension five is below six
• A negative Clifford third-moment expectation at dimension eleven
• At dimension five the full and non-symmetric aggregates of a two-qudit state fall below their conjectured lower bounds
• Exact Hilbert–Schmidt distances for noisy four-qubit Smolin states
• Ziętak’s strict spectral approximant convergence conjecture
• The controlled-rotation channel assemblages do not obey the proposed LOSR angle ordering
• The overlap entropy bound is not c-optimal for qutrits
• The two-qubit non-selective measurement optimum N/2 + 1/4 is global