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Catalogue date 2026-10-21
Real stability of layer-refined antichain polynomials for three-chain products with a two-element factor
Real stability of layer-refined antichain polynomials for three-chain products with a two-element factor
Source PDFProves real stability of layer-refined antichain polynomials for three-chain products with a two-element factor.
Type-Voltage Covers and Finite Locally Kneser Graphs
Constructs type-voltage covers and finite locally Kneser graphs.
Bezoutian Decoupling for Conformal Yang–Mills Multiplets in (A)dS
Constructs and diagonalizes an all-dimensional Bezoutian extension and derives transformation formulas for Gram forms. It does not construct nonlinear interaction algebras in arbitrary dimensions.
Residual bounds for Schur-stable polynomials
Establishes quantitative residual bounds for Schur-stable polynomials and independently strengthens a negative answer to Erdős Problem 973, without claiming priority for that answer.
When Complementary Measurements Count the Same Classical Bit Twice: Counterexamples to CQC, ECQC, and Complementarity-Based Certification
When Complementary Measurements Count the Same Classical Bit Twice: Counterexamples to CQC, ECQC, and Complementarity-Based Certification
Read PDFConstructs higher-dimensional counterexamples to CQC and ECQC bounds and explains how complementary measurements can count the same classical information twice.
Complementary Quantum Correlations Are Universal for Qubits
Proves a universal complementary-quantum-correlation bound for two-qubit states and discusses correlation lower bounds without full state tomography.
Fröberg’s Conjecture for Quintics and Septics in Four Variables
Proves the quintic and septic cases of Fröberg's conjecture in four variables over characteristic zero, supported by exact computations.
A Proof of Shor's Orthogonal-Measurement Conjecture and the Structure of Information-Optimal Quantum Measurements
A Proof of Shor's Orthogonal-Measurement Conjecture and the Structure of Information-Optimal Quantum Measurements
Read PDFProves Shor's orthogonal-measurement conjecture for binary quantum ensembles and characterizes information-optimal measurements.
Flux-Enhanced Entanglement with an Unchanged Zero-Magnetization Spectrum in a Motzkin Ring
Studies flux-enhanced ground-state entanglement in periodic Motzkin rings while the zero-magnetization spectrum remains unchanged, and analyzes charge-sector ground states and bounds on the gap.
Integral homology lattices of matching and circulant complexes
Combines integral homology lattices, dihedral structures and homotopy results for matching and circulant complexes. The source records 33 complete and two partial problem resolutions; the combined paper does not upgrade the partial results.
Bayesian Weak Commutativity Does Not Guarantee Attainability of the Nagaoka–Hayashi Bound
Constructs a full-rank four-level model satisfying Bayesian weak commutativity whose optimal estimation risk nevertheless exceeds the Nagaoka–Hayashi bound. It determines the optimal risk and a seven-outcome measurement, and proves positive gap bounds across a family of models.
Low Smith Layers and Odd-Weight Stability for One-Hole Domino Tilings
Derives formulas for the first three Smith layers of one-hole domino counts, odd-weight stability and Kong's congruence modulo 16.
Genus Ranges and Extremal Rotation Counts of Rigid 4-Regular Graphs
Studies genus ranges and extremal rotation counts for rigid 4-regular graphs; some remaining top-genus cases are open.
Four Special Directions over Prime Fields: Structure and Complete Classification
Classifies sets with exactly four special directions over prime fields into 54 affine-equivalence classes, proves that 17 is the largest admissible prime, and extends the classification to higher dimensions. Structural results and large-prime exclusion are proved directly; the finite classification uses computer assistance.
Minimax Discrimination and the Cost of Adaptation in Periodic Grid Codes
Determines minimax discrimination rates and matching adaptation costs for the specified class of one-dimensional nested grid codes.
Charge transport, not interaction range, bounds the Lieb-Schultz-Mattis twist cost
Controls the Lieb–Schultz–Mattis twist cost using charge transport and derives explicit finite-ring gap bounds and structural extensions.
Compatibility Restores Spin Alignment for Three Qubits
Proves spectral majorization and stability for the full eight-support family of compatible three-qubit marginals. The general four-qubit case remains open.
Cotangent cohomology and higher-order obstructions of matroids
Computes cotangent cohomology of matroids, gives vanishing criteria and constructs essential deformation obstructions of arbitrarily high order.
q-Zeta positivity for root and Ferrers-cell posets
Gives positive formulas for q-Zeta numerators of crystallographic root posets and Ferrers-cell posets.
Integral Cayley graphs and abelian rigidity in cores of cubelike graphs
Proves rigidity of cubelike graph cores under a normal abelian Cayley representation and gives an integral-spectrum classification. The general Cubelike Core conjecture remains open.