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Contents

• Actual rectangular residuals and port absorption
• Saturated geometry of an even rectangle
• Adjacent supports and harmonic payment
• A bad Anderson potential without nontrivial shared symmetry
• Density from Hereditary Bipartite Cut Bounds
• Brooks
• Upsets in neighbourhood convex geometries
• Capacity ports and parity absorption
• A CDSO minimizer without a universal vertex
• Residual graphs after positive private deletion
• Weighted induced deletion
• Reciprocal estimates for singleton color leaves
• The finite-palette boundary of coloring compactness
• Italian dominating functions on cycles
• Cyclic mixed-demand coloring
• The cyclic stable-marriage arc-lemma upper bound
• Charging saturated link components
• The component correction identity
• Reciprocal fibers and actual link components
• Two incidence counts and the codegree-four bound
• Actual deletion and global balance
• A cone with a linear remainder
• Mixed vertices and actual triangle packets
• Exact stars at a marked packet
• Ownership at a marked exchange
• Local graphs and reciprocal double counting
• Local graphs and owned triangle rows
• Payment for marked triangle rows
• Fifteen-vertex separation and the fourteen-vertex bound
• Disjoint-union uniqueness and intersecting links
• The exact triple forcing threshold
• Unordered wedges and four-edge common links
• Zero energy of the edgeless graph
• Directed all-minors matrix-tree identity
• Directed forest gluing signs
• Increasing DomiRank entropy on connected nonregular graphs
• A Seven-Vertex Saturated Packing Refutation
• An integer elliptic Sombor energy
• A directed graph with democracy coefficient above one
• Honeycomb trapezia and reduced Pascal determinants
• The Boolean hypercube and its edge count
• Sahbi’s hypercube sub-quorum conjecture
• Density from Pairs and Triangles
• Octahedral cochain sharpness
• Rerouting Pair Selections
• Zero-Star Prefix-Reversal Complements
• Four-cube exact degree-two repair budget
• Four-cube coordinate geodesics
• Weighted Density from Local Trace Cuts
• Redundant leaves and maximal matchings
• Božović Conjecture 12: limited domination in Sierpiński graphs
• An integer Sombor energy
• Suvagiya Conjecture 28 is false
• Three-color incidence and population reduction
• Reciprocal estimates at the outer mixed counts
• The outer mixed-count obstruction
• Three-color reciprocal inequality
• Small mixed graph inequality
• Small mixed-population certificate
• The outer general position vertex-removal bound is false
• A disconnected counterexample to the token-radius conjecture
• Tripartite degree-one cochain repair
• Nonsingularity of actual uniform reflection cross-Grams
• Component parity of uniform reflection arrays
• Invariant partitions of relative moved support