Exact topology, geometric threshold laws, and the information needed to identify a physical response.
Matching One studies square-lattice site percolation. Its strongest current questions are no longer "which exponent fits?" or "which familiar field name looks plausible?" They are:
- When does a topological balance root locate the infinite-volume threshold, even when the whole finite-volume threshold law does not concentrate?
- Which finite states preserve a declared observable under future updates and physical source interventions?
- Which additional prediction or measurement can actually distinguish the remaining mechanisms of the original normalized response U?
Start with the research frontier, then the execution roadmap. This entry point was reset under the owner's research delegation dated 2026-09-13. Historical data, failed tests of physical hypotheses, and unmerged branches are retained. Main integration, mathematical correctness, independent evidence and publication novelty are separate questions.
For an occupied configuration on a torus,
r = rank im[H1(occupied complex) -> H1(torus)] in {0,1,2},
X = r-1,
M = E[X] = P2-P0, E_top = E[X^2] = P2+P0,
F(p) = E_p[r]/2 = (1+M(p))/2.
The balance root is Q(1/2), where Q=F^{-1}. In contrast, H=P2/(P0+P2) conditions on the rare non-rank-one sectors; it is NOT F. The identity X^3=X defines a two-dimensional nonconstant observable algebra, not a two-state dynamical model or a two-field continuum theory. These observables sit in the established matching/wrapping/homological percolation literature; their names alone are not a novelty claim.
| Lane | Current asset | Next result worth obtaining |
|---|---|---|
| Geometric separation of root and full-law consistency | #735: arbitrary-period balance roots; #736: sharp axial full-law criterion | Check the supplied proof and novelty once; prove or refute the uniform oblique winding-corridor lemma |
| Observable- and source-dependent minimal state | #708, #710, #733: exact rank closure, visible spectrum, physical site sources | An all-width structural closure theorem or one source-faithful separating response, not another width count |
| Original-U physical identifiability | #275: current assets do not identify the named candidates | Two same-source, same-normalizer forward maps; nuisance-profiled separation before further acquisition |
The linked research PRs are open/unmerged at this snapshot; these links do not silently install their code on main. The frontier pins their commits and distinguishes results from remaining hypotheses.
For axial w-by-m tori with m>=w and w->infinity, the new organizing contrast is
balance-root consistency: no aspect-ratio restriction (#718/#735),
convergence of every fixed Q(u): log(m)/w -> 0 iff (#736 + #613 inputs).
The iff proof uses critical square-site RSW, finite-product continuity, a seam-closed crossing ring and independent transverse bands. It is not derived by fitting sizes. Its arbitrary-oblique necessity extension remains open, and no near-critical rate or new numerical p_c is claimed.
The global orientation-sensitive matching-odd signal and several frozen H4 transfer comparisons remain substantive finite-size evidence. A successful harmonic comparison is not a standalone nonzero detection and not a field identification. Single-multiplier full-curve closure and several scalar correction models have failed; their raw blocks are not discarded.
The primitive-C3 Gaussian observer has a later exact unit-rotation explanation; its old H8 near-alias must not be exported to square-site U. N580's recovered covariance and bounded-H8 reanalysis do not establish a bare-aspect physical law. See current adjudications, not the historical opening text of an issue, for these distinctions. N denotes site count; on square-period geometries the linear scale is sqrt(N), not N.
The cut-network/branching program #549 separates complete unbranched survival from branching prediction. Its exact class-count lower bound is not a noise-robust effective-dimension theorem. Bounded algebraic exclusion and projective inference remain publication units, not reasons to grow a polynomial census or claim a new statistical principle. The research atlas preserves less prominent work and closed-unmerged assets; its old execution priorities are historical.
REPRODUCIBILITY.md describes the existing engines and data. GOVERNANCE.md keeps exploration lightweight; raw data and chronology are preserved. AGENTS.md routes new work to the current scientific question instead of stale acquisition instructions.
The old README, roadmap, map and status ledger are preserved byte-for-byte in docs/history. This is a navigation and allocation reset, not a claim that older experiments were never run.