Research reset: expose geometric consistency, source-visible state, and the original-U bottleneck

AGENTS.md

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+# Working on Matching One
+
+Read `docs/RESEARCH-FRONTIER.md` and `docs/ROADMAP.md`, then the relevant live
+Issue and its latest comments. `docs/STATUS.md` distinguishes current scope
+from the verbatim historical ledger. Old acquisition instructions, opening
+Issue bodies and publication-portfolio snapshots are not a current run queue.
+
+Owner-delegated focus dated 2026-09-13:
+- #613: geometric root/full-law separation; #736's axial iff is delivered.
+  The new proof target is uniform oblique winding corridors, not a duplicate census.
+- #636: structural observable closure and physical source-visible states;
+  reuse #708/#710/#733 at their pinned refs.
+- #275: original-U candidate maps before more sampling; theory-blocked P1,
+  with its original source/normalizer/moving-root contract retained.
+
+Choose work by the mathematical or physical distinction it can settle, not by
+how many PRs, scripts, new widths or compatibility scores it generates. A useful
+new idea may replace this allocation, but state the new question and why its
+answer would change the research. Do the small calculation now rather than
+opening an issue asking someone else to repeat an already available result.
+
+Preserve existing data and frozen target history. Count one random block once.
+Name site versus bond, occupied graph versus matching complement, rank versus
+directional wrapping, and fixed-p versus moving-root readouts. N is the number
+of sites, not the linear size. Distinguish actual operator Jordan structure
+from a derivative-jet lift and from an observed polynomial length factor.
+
+Open/closed, merged/unmerged and correct/incorrect are separate. Do not silently
+merge another research PR, alter a source contract, or change a result's claim
+level merely to tidy navigation. Use a narrow branch and a clear diff. Run
+mathematical checks proportional to the change; report exactly what ran.
+Do not claim parent CI for a child commit or full CI from local tests.
+
+`GOVERNANCE.md` keeps exploration lightweight. Do not add document-wording
+tests, digest ceremonies, a new audit framework or a speculative production
+scheduler. Keep proof, executable control, inference and novelty claims apart.

analysis/research_agenda.json

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+{
+  "schema": "matching-one.research-allocation.v1",
+  "date": "2026-09-13",
+  "authority": "owner-delegated research reset; live Issue updates supersede this snapshot",
+  "baseline_main": "eb89e9422791d9e3c3a78f0e65d56912b815a7bd",
+  "role": "allocation and navigation only; not a claim ledger, evidence multiplier, scheduler, or production authorization",
+  "primary": {
+    "issue": 613,
+    "priority": "P0",
+    "question": "Uniform fixed-subcritical winding corridors for arbitrary shortest integer periods, or a geometric counterexample",
+    "delivered": "PR736 supplies axial full-law necessity; PR735 supplies arbitrary-period balance-root consistency",
+    "do_not_repeat": "The axial iff proof or its tiny enumeration as a new research task"
+  },
+  "bounded_parallel": {
+    "issue": 636,
+    "priority": "P1",
+    "question": "Actual site-transfer closure weights and source-visible cancellations beyond the completed width-four oracle",
+    "reuse_prs": [708, 710, 733],
+    "boundary": "No automatic width scan; deterministic, lumped, scalar, positive and noise-limited orders differ"
+  },
+  "theory_blocked_flagship": {
+    "issue": 275,
+    "priority": "P1",
+    "status": "UNIDENTIFIABLE_WITH_CURRENT_ASSETS",
+    "next_input": "Two same-source normalized thermal-jet and moving-root forward maps; profile represented coordinates before sampling",
+    "contract_changed": false
+  },
+  "reserve": [537, 549, 550, 589],
+  "completed_or_retired_acquisitions_not_reopened": [276, 575, 583],
+  "existing_shape_delivery": {"issue": 622, "pr": 706, "new_sampling": false},
+  "new_research_pr": 736,
+  "new_research_commit": "64d809b4404f80ff3f9adf9713337cc76008e92d",
+  "research_stack_merged_by_navigation_reset": false,
+  "new_random_samples": 0,
+  "hardware_or_credential_changes": false,
+  "automation_created": false,
+  "historical_result_files_modified": false
+}

docs/RESEARCH-FRONTIER.md

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+# Research frontier: three claims, not a catalogue of tasks
+
+**Owner-delegated reset, 2026-09-13.** Baseline read: main at
+`eb89e9422791d9e3c3a78f0e65d56912b815a7bd`, including #702--#705.
+This document changes research allocation, not historical experimental verdicts.
+[ROADMAP](ROADMAP.md) owns the current work choices; live Issue updates override
+this dated snapshot. [STATUS](STATUS.md) separates current adjudications from the
+[verbatim older ledger](history/STATUS-before-20260913.md).
+
+**Live addition during this reset:** [#737](https://github.com/LightChainr/Matching-One/pull/737)
+arrived after the first scan. Its spatial Hessian and invisible-mark calculations
+are completed finite assets, not tasks to commission again; see section 2 below.
+
+## 1. Primary: geometry can separate a correct root from an incorrect full law
+
+The most immediately tractable theorem programme is now #613, not another
+attempt to assign a continuum field to a fitted exponent.
+
+For independent NN square-site percolation on an honest torus, let
+`M=P2-P0`, `F=E[r]/2=(1+M)/2`, and `Q=F^{-1}`. The balance root is Q(1/2).
+The conditional rare-sector function `H=P2/(P0+P2)` is a different object.
+
+**Supplied results.** #735 proves balance-root consistency on arbitrary integer
+period lattices as the genuine shortest period ell grows, without an aspect or
+area-versus-systole condition. Its fixed-subcritical bound is
+`P2/P0 <= exp[-kappa(p) N/ell]`. #736 supplies a sharp contrast on axial w-by-m
+tori: all fixed interior Q(u) converge to p_c **iff** `log(m)/w -> 0`.
+Both statements depend on their named probability/topology inputs. Neither
+claims a numerical threshold, an L^-4 shift, or publication priority.
+
+**What was done in this reset.** #736 adds necessity to #613's sufficiency.
+Critical square-site RSW and finite-product continuity produce a seam-closed
+occupied winding ring with probability at least exp(-eta*w) at a fixed
+p_eta<p_c. Independent transverse bands amplify it. If log(m)>=d*w along a
+subsequence, every fixed lower quantile is bounded away from p_c, even though
+the median can remain consistent. This closes the logarithmic-width case,
+not only the earlier fixed-width or w=o(log m) examples.
+
+**Next missing lemma, not another simulation.** Extend the fixed-subcritical
+winding-ring construction uniformly around an arbitrary shortest integer
+period u, with cost exp(-eta*|u|) and bounded-thickness disjoint corridors.
+Oblique orientation and ambient nonprimitivity must be handled on the physical
+NN lattice. Changing a period basis does not rotate its interaction. This is
+the specific route towards necessity of `log N/ell -> 0` beyond axial tori;
+that general necessity is still open in this repository.
+
+A second possible outcome is a geometric obstruction showing that a finer
+quantity than the shortest period is necessary. Either would change the paper.
+Preparing a paper also requires one independent examination of the supplied
+proof and a systematic comparison with strip-percolation/RSW and homological
+percolation literature. Repeated negative web searches are not a novelty proof.
+
+## 2. Parallel: the minimal state is determined by the allowed sources
+
+#708 supplies rank-future sufficient lifted states and 509 deterministic
+continuation classes at width four. #710 supplies the all-p scalar spectrum:
+common modes in P0 and P2 cancel in M. #733 supplies physical site interventions,
+source-compatible quotients and an exact final-rank-conditioned backward sampler.
+Two independently addressed adjacent columns already require all 509 classes
+within the investigated common-strong-lumping class.
+
+The scientific claim is not "509 fields" or "a new transfer-matrix technique".
+It is that state compression can be exact for one observer/source language and
+fail for another, with an explicit topology-preserving construction and witnesses.
+The two-row square-site source is the preferred physical laboratory: its linear
+response vanishes while a mixed response is nonzero. P398 is the known periodic
+identified-connectivity O(1) TL calibration chain (#718), not the site process.
+
+**Next distinction:** determine the actual all-width topological closure weights
+and their observable cancellations, or separate two concrete candidate closures
+using the same physical source. A full-operator spectral gap need not be the gap
+seen by M. Fixed-width exponential convergence is not a width-uniform theorem.
+Reuse the width-four certificate; do not fund a duplicate state enumeration.
+
+### Newly delivered #737: spatial-source curvature is a structure-factor contrast
+
+The finite full-site Hessian and invisible-mark notes were read at
+`7b459c4809baee9dfc2b910091e00a3a8d508d1c`, including their limitations. For
+mean-zero logit source h and H=sum h_i n_i, its logit-root formula is
+
+    z_*''(h) = -[Var(H|r=2)-Var(H|r=0)] / [E(K|r=2)-E(K|r=0)].
+
+This exposes a physical bridge from a moving root to rank-conditioned spatial
+structure factors. Additive probability fields and logit fields have different
+second-order corrections; do not silently exchange them. The 4x4 root Hessian
+has both positive and negative directions in the reported additive coordinate.
+These are finite-volume claims, not a disorder-relevance or critical-exponent law.
+
+The invisible-mark construction preserves the entire uniform (r,K) distribution
+but separates under spatial sources. It uses strictly positive **dependent marked
+measures**, not two distinct predictions of the already specified Bernoulli law
+and not the two original-U candidate fields. A separate orbit calculation in this
+reset reproduced sizes 16/128/64 and the two-source contrast matrix
+`[[-512,-128],[0,-256]]`, determinant 131072. That check is not a rerun of the
+Hessian, all scripts, or full CI.
+
+#737 is still unmerged and its PR lists three uncommitted delivery artifacts.
+Use the actual `delivery/notes/` paths and resolve its declared reproduction
+inputs before reuse; a successful execution log from the source archive does
+not establish a complete fresh-checkout installation. Do not repeat its finite
+Hessian or marks. The larger question is a width-uniform/topology-resolved source
+response and an actual candidate map, not one more uniform thermal derivative.
+
+### Exact complexity is not finite-noise complexity
+
+#549's cut-network family has k+1 distinct branching-predictive classes within
+one identical full unbranched-survival class. In its specified single-fork
+readout the adjacent gap is `1/[2k(8k-1)^2]` and the entire family's span is
+`1/[2(8k-1)^2]`. Thus this readout becomes less separating as exact class count
+grows. This direct consequence of the existing formula is not a lower bound
+for every experiment in the full branching language.
+
+A worthwhile reserve question is whether a specified budget of admissible
+interventions can amplify those separations. More values of k alone do not
+answer it, and an exact discrete class-count theorem is not a Euclidean or
+noise-robust dimension theorem.
+
+## 3. High-upside flagship, theory-blocked: original-U identification
+
+#275 is retained as P1 rather than the default P0 expenditure. Its current-asset
+closure is UNIDENTIFIABLE_WITH_CURRENT_ASSETS, not "Jordan disproved" and not
+"the two physical theories are identical".
+
+The next input remains two candidate-specific maps through the SAME source,
+`s0,s1,s2,partial_p s0,partial_p s1,partial_p s2`, physical normalizer, rank-one
+denominator and pooled moving-root counterterm. Check each coordinate's baseline
+representability, then the nuisance-profiled prediction images on existing data.
+No new source or statistical coordinate should be substituted merely because it
+separates better without those physical maps.
+
+#735 strengthens the diagnostic warning: positive irreducible stochastic matrices
+can share every ordinary trace and thermal derivative while differing in Jordan
+structure. For a specified response it is `C N_lambda^k P_lambda B` that determines
+visibility. A repeated pole of a derivative-jet lift does not certify a Jordan
+block of the physical operator. Spin, a power, and a logarithm are not substitutes
+for this source/readout map.
+
+## Pinned research assets and integration boundaries
+
+All entries below were open/unmerged when this reset was prepared. The navigation
+commit does not merge them or certify their complete test suites.
+
+| PR | Pinned head | Evidence role |
+|---|---|---|
+| [#708](https://github.com/LightChainr/Matching-One/pull/708) | `f782061c1a592ed2f9fd0e9dabaa45f0e54bc4e7` | Finite lifted closure and deterministic/scalar rank certificates |
+| [#710](https://github.com/LightChainr/Matching-One/pull/710) | `d543ba1afe052a36682d2c1723c8a07281c28950` | Parametric spectrum; geometric minimal-winding configurations |
+| [#718](https://github.com/LightChainr/Matching-One/pull/718) | `72d2ee6b8e5d25bd96aaef586c113bc94201f64a` | Axial root consistency; P398 identification with published IC TL |
+| [#733](https://github.com/LightChainr/Matching-One/pull/733) | `525c8e98d99c44d4c76280a1f0f83064df9bfa72` | Physical site sources, conditional sampler, event dictionary correction |
+| [#734](https://github.com/LightChainr/Matching-One/pull/734) | `bb41df7da8021d922a48ad353709f35912977c37` | Bounded prior-art survey, not an originality certificate |
+| [#735](https://github.com/LightChainr/Matching-One/pull/735) | `9d29d014df28af7c635e6859d98a95ffe2b34d06` | Arbitrary-period root proof, marked robustness, Jordan controls |
+| [#736](https://github.com/LightChainr/Matching-One/pull/736) | `64d809b4404f80ff3f9adf9713337cc76008e92d` | New axial full-law iff proof and exact finite gluing controls |
+| [#737](https://github.com/LightChainr/Matching-One/pull/737) | `7b459c4809baee9dfc2b910091e00a3a8d508d1c` | Spatial-source Hessian and invisible marks; delivery-input gaps disclosed |
+
+#736 reports 21,760 exhaustive strip configurations, 2,365 deterministic uneven-
+cell controls, exact Fraction inequalities, three local mathematical tests and
+compilation. Full repository CI was not run. The all-size theorem rests on the
+written argument and imported inputs, not on those finite checks.
+
+## Corrections that must travel with the result
+
+| Old inference | Current reading |
+|---|---|
+| #628 bond duality fails | Implementation/convention errors; corrected by #631/#646/#653 |
+| Raw M(p)+M(1-p) diagnoses normalized shape | Wrong centre/gauge; use the corrected anchored-quantile quantity (#702/#706) |
+| #675 excludes any one-operator representation | Unrestricted no-go withdrawn; distinguish efficient local closure from existence |
+| #715 P398 has no named process | Periodic IC TL under the explicit fattening map (#718/#729) |
+| #717 finite 2D/0D weights categorically differ from rank2/rank0 | Same finite site ensemble has the event dictionary in #733; no all-width intertwiner follows |
+| #724/#731 linear eigenvalue split implies semisimplicity | Explicit counterexample in #735; m*lambda^m alone is not either diagnostic |
+| Primitive Gaussian C3's old H8 label identifies local spin | Later unit-rotation/H0 result in #275 supersedes that near-alias |
+| N580 compatibility identifies bare-aspect scaling | Same-block nominal compatibility after #703/#704; no physical-law identification |
+
+N is site count. For square-period geometries the linear size is sqrt(N).
+Do not compare N=425 with a published L=425 lattice, or treat site, bond,
+rank-two cross and rank-one spiral as interchangeable observables.
+
+## What is intentionally not expanded
+
+No default new Monte Carlo, GPU campaign, width ladder, descriptor ladder,
+angle grid, generic venue survey or polynomial-height census follows from this
+reset. A genuinely discriminating idea may change allocation. The test is the
+mathematical distinction it resolves, not its conformity to an ever-growing
+checklist. #537's proof obligations, #622's completed shape analysis, the finite
+terminal algebra and P2/P3/P4 manuscript work remain visible through the
+[atlas](RESEARCH-ATLAS.md); their historical data and failures are retained.