Hadamard's Determinant Problem: Structural, Constructive, Empirical, and Global C‑Phase Foundations (Papers 1–4)
Fuente:
Zenodo
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Recurso digital |
| Lingua: | inglese |
| Pubblicazione: |
Zenodo
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866902206970593280 |
|---|---|
| author | Mulnix, David |
| author_facet | Mulnix, David |
| contents | <p>This work presents a unified structural and analytic framework for Hadamard’s determinant problem, offering a complete geometric and algebraic description of the space in which both Hadamard and non‑Hadamard {±1}-matrices live. Across four integrated papers, it develops the invariant geometry of the fluctuation Gram matrix, classifies extremal families, identifies the universal C‑phase governing non‑Hadamard extremals, and establishes collapse laws, spectral regimes, and analytic invariant floors. The program combines structural discovery, constructive dynamics, empirical universality, and a global analytic theorem to reveal a coherent picture of extremal behavior across all admissible orders. This collection provides a fundamentally new perspective on maximal determinants and mod‑4 structure, offering readers a comprehensive and self‑contained theory.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19041716 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Hadamard's Determinant Problem: Structural, Constructive, Empirical, and Global C‑Phase Foundations (Papers 1–4) Mulnix, David Hadamard determinant problem maximal determinant extremal ±1 matrices invariant geometry C‑phase spectral collapse universal determinant law Mathematics Combinatorics Mathematics Linear Algebra <p>This work presents a unified structural and analytic framework for Hadamard’s determinant problem, offering a complete geometric and algebraic description of the space in which both Hadamard and non‑Hadamard {±1}-matrices live. Across four integrated papers, it develops the invariant geometry of the fluctuation Gram matrix, classifies extremal families, identifies the universal C‑phase governing non‑Hadamard extremals, and establishes collapse laws, spectral regimes, and analytic invariant floors. The program combines structural discovery, constructive dynamics, empirical universality, and a global analytic theorem to reveal a coherent picture of extremal behavior across all admissible orders. This collection provides a fundamentally new perspective on maximal determinants and mod‑4 structure, offering readers a comprehensive and self‑contained theory.</p> |
| title | Hadamard's Determinant Problem: Structural, Constructive, Empirical, and Global C‑Phase Foundations (Papers 1–4) |
| topic | Hadamard determinant problem maximal determinant extremal ±1 matrices invariant geometry C‑phase spectral collapse universal determinant law Mathematics Combinatorics Mathematics Linear Algebra |
| url | https://doi.org/10.5281/zenodo.19041716 |