Invariants

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Contents

• Hanna’s Absolute Reciprocal Geometric Parity
• Absolute Reciprocal Squares and Binary Parity
• The affine polynomial pair of OEIS A208509
• Alternating Dyadic Reversion Modulo Four
• Cassini-Fricke Log-Coordinate Specializations
• Catalan Composition and Hanna’s Parity Conjecture
• Hanna’s Cubic Catalan Composition
• Double Catalan Composition and Powers of Four
• Catalan Inversion and Hanna’s Mod-Four Conjecture
• Actual Cloitre Deficit-Four Band
• Actual Cloitre Deficit-Four Positive Fees
• Actual Cloitre Deficit-Four Selector
• Actual Cloitre Endpoint Phase and Defect Amplitude
• Actual Cloitre Exterior Entrance
• Actual Cloitre Global Convergence
• Actual Cloitre Left Fibonacci Platforms
• Actual Cloitre Right Fibonacci Profiles
• Actual Cloitre Spine and Scalar Carry
• Actual Cloitre Unweighted Cone
• Actual Cloitre Weighted Cone
• The OEIS A076502 Nested-Recurrence Floor-Offset Conjecture
• Hanna’s Companion Pell Exponential Residues
• Hanna’s Compositional-Iterate Congruence
• Hanna’s Cubed Binary Product Conjecture
• Hanna’s Cubic Substitution Parity Conjecture
• Hanna’s Cubic Generating Equation Modulo Three
• Hanna’s Cubic Ternary Substitution Parity
• Prime Divisor-Pair Sums and Their Preimages
• The Factorial-Quotient Recurrence of OEIS A372991
• Exact Factorial-Square Divisibility and Prime Powers
• Golden Eigenpair and Fibonacci Residual
• Hanna’s Half-Scaled Reflection Parity
• The OEIS A338632 Modulo-Four Congruence
• Dyadic parity for Hanna’s cubic series
• Hanna’s Modulo-Six Conjecture
• Integral Compositional Square Roots and Hanna’s Parity Conjecture
• Hanna’s A393173 Power-of-Two Parity
• Hanna’s Bilateral Reversion Parity
• Hanna Bilateral Theta Congruence Modulo Four
• Hanna’s A377100 mod-three conjecture
• Hanna’s A375449 Diagonal Derivative Parity
• Hanna’s A375452 Diagonal Derivative Parity
• Hanna’s A274479 mod-three conjecture
• Hanna’s Half-Iterate Conjecture Modulo Three
• Hanna’s Lambert-Cube Congruences Modulo Three
• Hanna’s A382319 Congruence Modulo Three
• Hanna’s power-of-two residue theorem
• Hanna’s ternary-digit residue theorem
• The integer central-binomial transform
• Integral solutions for prime substitution exponents
• Hanna’s product-partition congruence
• Hanna’s Shift-Square Series Is Rational Modulo Eight
• Hanna’s Square-Composition Congruence
• The Joint Polynomial Pair of OEIS A208342
• The Associated Pell GCD Entry-Point Conjecture
• Ordered Permutation Defect Mass
• Normalized coefficient contractions
• Quadratic Reversion and Dyadic Support
• Hanna’s Quartic-Cubic Quotient Parity
• Label Occurrences in Restricted-Growth Words
• Scaled Reversion and Coefficient Congruence
• Schroeder Paths and the Alternating Quadratic Peak Moment
• First Occurrences in the Self-Referential Doubling Recurrence
• First Occurrences in a Self-Referential Quotient Recurrence
• Signed Catalan Cubic Substitution Modulo Three
• Prime exponents characterize Somos integrality
• Square Positions and Values in a Square-Counting Recurrence
• The Closed Form of the Harmonic-Mean-Numerator Recurrence
• Hanna’s Square-Cube Substitution Conjecture
• Hanna’s Three-Four Iterate Product Congruence
• The Trinomial Odd Diagonal of OEIS A077864
• Hanna’s Triple-Iterate Product Congruence
• Hanna’s Triple Iterate Shift Congruence
• Unit Reversion and Square Parity