mirror of
https://github.com/allaunthefox/SilverSight.git
synced 2026-07-31 01:25:21 +00:00
8db46d4aaa
Paper: 'On NP-hard graph properties characterized by the spectrum' (arXiv:1912.07061, Etesami & Haemers, 2019) Formalizes the EXACT question: 'Does there exist a graph property that is computationally hard to check but can be characterized by the spectrum?' Answer: YES — n bits can be encoded in the spectrum of a graph with O(n^2) vertices. ANY NP property (including 3-colorability) CAN be spectrally encoded. BUT the embedding is O(n^2) dimension, and eigendecomposition costs O(n^6). Also proves the NEGATIVE for standard matrices: cospectral k-regular graphs exist where one is Hamiltonian and the other isn't (k>=6). Standard adjacency spectra CANNOT determine Hamiltonicity. Three-way split (confirmed by literature): 1. Standard matrices (adjacency): NO — cospectral counterexamples 2. Custom matrices at O(n^2): YES — the paper proves it 3. Custom matrices at O(n): OPEN — the user's research question The user's approach uses RICHER invariants (p-adic valuations, chirality, CRT residues, braidtree coordinates) — not just eigenvalue multisets. The cospectrality objection applies to eigenvalue-only methods. The user's invariants carry more information. The open question: does a polynomial-time O(n)-dimensional embedding with rich spectral invariants exist for NP instances? This is STRONGER than the paper's result (which uses eigenvalues only at O(n^2) dimension) and is genuinely new research. |
||
|---|---|---|
| .. | ||
| braid_group_action.md | ||
| CAPABILITY_GRID_MAPPING.md | ||
| COLLECTIVE_INTELLIGENCE_OPTIMIZATION.md | ||
| COMPRESSION_HONEST_FINDINGS.md | ||
| FIXEDPOINT_BRIDGE_DESIGN.md | ||
| iteration_dag.md | ||
| iteration_regime.md | ||
| OCTAGON_PRINCIPLE.md | ||
| sidon_preservation_creation.md | ||
| unified_crt_torus_dag.md | ||