Multi-advance 20260913: spatial-source Hessian, invisible marks, annealed/quenched roots, rank-source zero-free strip, conditional-odds integration, limit-order audit (do not merge)

HIGH_PRECISION.json

@@ -0,0 +1,26 @@
+{
+  "source_zero_dps": [
+    100,
+    140
+  ],
+  "zero_log_coordinate_checks": 60,
+  "max_abs_zero_coordinate_difference": "0.0",
+  "integrated_root_dps": [
+    70,
+    110
+  ],
+  "integrated_root_abs_difference": "0.0",
+  "marked_field_dps": [
+    70,
+    110
+  ],
+  "mark_root_checks": 16,
+  "max_mark_root_difference": "0.0",
+  "finite_field_dps": [
+    65,
+    105
+  ],
+  "finite_field_root_checks": 15,
+  "max_field_root_difference": "0.0",
+  "qualification": "Differences are between separately recomputed values at their stored display precision, not interval certificates."
+}

REMOTE_ACTIONS.json

@@ -0,0 +1,22 @@
+{
+  "actions": [
+    {
+      "type": "PR conversation comment",
+      "pr": 734,
+      "comment_id": 5647070359,
+      "url": "https://github.com/LightChainr/Matching-One/pull/734#issuecomment-5647070359",
+      "purpose": "continuum mesh/cusp versus fixed microscopic width correction"
+    },
+    {
+      "type": "PR conversation comment",
+      "pr": 733,
+      "comment_id": 5647076916,
+      "url": "https://github.com/LightChainr/Matching-One/pull/733#issuecomment-5647076916",
+      "purpose": "completed full spatial Hessian, invisible marks, and averaging results"
+    }
+  ],
+  "branches_changed": false,
+  "prs_merged": false,
+  "issue_lifecycle_changes": false,
+  "STATUS_changes": false
+}

VALIDATION.json

@@ -0,0 +1,188 @@
+{
+  "scope": "Actual clean MINIMAL Git-tree patch application with only the two pinned inputs; not complete repository CI",
+  "new_repository_file_count": 21,
+  "local_tests": 27,
+  "applied_tests": 27,
+  "all_tests_passed": true,
+  "full_repository_CI_run": false,
+  "python": "3.13.5",
+  "mpmath": "1.3.0",
+  "patch_sha256": "4f71286c2c58d316ea9c582273874cd8ac87a026db2528318ecbf007183fe7b5",
+  "inputs": [
+    {
+      "file": "width4-rank-closure-certificate.json",
+      "sha256": "508640f6a6be1461ca4738acdcf3226790f485dbaa3c43b8a00966c143f3f890"
+    },
+    {
+      "file": "width4-parametric-definition.json",
+      "sha256": "5edc624377399ad0878c7a608e722ebb65a7be454a6f022a1b6382a0661e91b0"
+    }
+  ],
+  "files": [
+    {
+      "path": "notes/annealed-quenched-root-20260913.md",
+      "sha256": "3f633592d3084948357bd4b264966c3f95f6fb43feba13ac17d08cac50376840",
+      "bytes": 4753,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "notes/conditional-odds-integration-20260913.md",
+      "sha256": "234e3430c455549fece5a3258c1a6def9141fadf4b154ed2f60245910722cc4b",
+      "bytes": 3578,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "notes/invisible-spatial-marks-20260913.md",
+      "sha256": "79b6dd273a486251a3179832a75c9ecc97ef7a8c60a99a4ef4a014e1e908ab7e",
+      "bytes": 4777,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "notes/limit-order-readout-audit-20260913.md",
+      "sha256": "f85d8ac364fb452319004ed92d8f04232c2e7d35cbf1e63db77039697251de9a",
+      "bytes": 5206,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "notes/multi-advance-handoff-20260913.md",
+      "sha256": "a036b32124d7832b3e434e3352a7daaef11e12a78880c6c9ab6ec54b8dee962a",
+      "bytes": 3099,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "notes/multi-advance-review-20260913-zh.md",
+      "sha256": "03321776c3cb0f68764ec8f74d7251486a253bd9028e09c5448c47e698a988a0",
+      "bytes": 5905,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "notes/rank-source-zero-free-strip-20260913.md",
+      "sha256": "20cd1e5508948abcd11280555e918f0b7e00644da79d8c1d46ec7faeb15fb6f2",
+      "bytes": 5417,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "notes/spatial-source-hessian-20260913.md",
+      "sha256": "32d326df2090f8802c0e9c417603715ce72119bd1557a147ad062d74d3c9a273",
+      "bytes": 8041,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "results/research-control-20260912/conditional-odds-integration.json",
+      "sha256": "02cfa3456fcbb66005287282ddb4295c5a6fc502256c79047df8aacbbdf20694",
+      "bytes": 3728,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "results/research-control-20260912/full-site-hessian-independent.json",
+      "sha256": "598e4cead845f509d44835beaad764b01c866d538187f829f5757080ca1ed247",
+      "bytes": 14803,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "results/research-control-20260912/full-site-hessian.json",
+      "sha256": "b5caac534fa720a2ab0b84b9e7ca5fd09514df4a0d7bbda7f1918292a1b00190",
+      "bytes": 118841,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "results/research-control-20260912/invisible-spatial-marks.json",
+      "sha256": "67ba43b3c4b597687e8a11ba9194457c23d79b6316c3700cf8f42e7415cc2530",
+      "bytes": 10631,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "results/research-control-20260912/topological-source-zeros.json",
+      "sha256": "657171582ede2fc23dab31fdc2e52ad8e9771e01c3d3c100f1a0a5d1d80da111",
+      "bytes": 41798,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "scripts/conditional_odds_integration.py",
+      "sha256": "f424b41b0051ee30cf0db37c14edf141ef9e5036876779077056ddda64cb51f1",
+      "bytes": 4503,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "scripts/invisible_spatial_marks.py",
+      "sha256": "faae8b5d8a37262bdd99e0388efba3e577a571f165db4a4f81f36163f04f05ed",
+      "bytes": 5923,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "scripts/topological_source_zeros.py",
+      "sha256": "6fa6a2aefd210bf55378d44f6947ad383ab9ea3301bc2d428b654c558b225ca7",
+      "bytes": 7041,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "scripts/torus_source_hessian.py",
+      "sha256": "956d5f4d776800fe7e8cd01170881ea96c6ca77ee5b0e147f7c587d3205bf0a0",
+      "bytes": 9536,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "scripts/verify_source_hessian.py",
+      "sha256": "7e002dd9d16e201b6ebb886782481d7b568bccf272eec0de0a7408a8a5166ecc",
+      "bytes": 7048,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "tests/test_rank_source_zeros.py",
+      "sha256": "9423003c0ec0b78f5c9d56c5e89b262ddbaa79294abb48b6b66ffb80c131b2bf",
+      "bytes": 3295,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "tests/test_spatial_hessian.py",
+      "sha256": "68a2c52e7d4a0a564536fc5425afb230561056c1edd271b534a5ed9a033fd4fc",
+      "bytes": 2863,
+      "applied_byte_identical": true
+    },
+    {
+      "path": "tests/test_spatial_marks_and_integration.py",
+      "sha256": "92f0d25e0f7a59a84b65ba94c1085c4b77a89fb247bdd24d01a035c96fb5bda4",
+      "bytes": 3552,
+      "applied_byte_identical": true
+    }
+  ],
+  "reruns": [
+    {
+      "script": "torus_source_hessian.py",
+      "result": "full-site-hessian.json",
+      "identical_except_elapsed_seconds": true,
+      "actual_elapsed_seconds": 1.1012761350000346
+    },
+    {
+      "script": "verify_source_hessian.py",
+      "result": "full-site-hessian-independent.json",
+      "identical_except_elapsed_seconds": true,
+      "actual_elapsed_seconds": 0.4464508300000034
+    },
+    {
+      "script": "invisible_spatial_marks.py",
+      "result": "invisible-spatial-marks.json",
+      "identical_except_elapsed_seconds": true,
+      "actual_elapsed_seconds": 0.5653261269999348
+    },
+    {
+      "script": "topological_source_zeros.py",
+      "result": "topological-source-zeros.json",
+      "identical_except_elapsed_seconds": true,
+      "actual_elapsed_seconds": 0.1282181799999762
+    },
+    {
+      "script": "conditional_odds_integration.py",
+      "result": "conditional-odds-integration.json",
+      "identical_except_elapsed_seconds": true,
+      "actual_elapsed_seconds": 1.5825697859997945
+    }
+  ],
+  "higher_precision_check": "HIGH_PRECISION.json",
+  "scientific_boundaries": [
+    "No Monte Carlo or large computation.",
+    "Finite numerical roots and source zeros are diagnostics, not interval-certified values.",
+    "Additive Hessian signs and mark determinants have exact rational/integer certificates.",
+    "Fixed width and continuum/aspect limits remain distinct."
+  ]
+}

delivery/README.md

@@ -0,0 +1,51 @@
+# Matching One multi-advance handoff — 2026-09-13
+
+## New completed results
+
+Read `delivery/notes/multi-advance-review-20260913-zh.md` first. The six technical notes
+cover (i) full spatial-source Hessians, (ii) invisible positive spatial marks,
+(iii) annealed versus quenched roots, (iv) the rank-source zero-free strip and
+extensive-source phases, (v) geometrically anchored conditional-odds integration,
+and (vi) continuum/lattice limit order. There is no novelty claim or new production.
+
+`delivery/` contains only NEW repository files. The patch is additive.
+
+## Prerequisites
+
+Python 3.10+ and mpmath. Exact enumeration/polynomial/sign components use only the
+standard library; mpmath is used for explicitly labelled numerical roots/integrals.
+The complete test set and independent comparison also require these existing files:
+
+- `results/research-control-20260912/width4-rank-closure-certificate.json`
+  from PR #708, Git blob `50b7297deefe7c50215aea2ed534ca5810461af3`.
+- `results/research-control-20260912/width4-parametric-definition.json`
+  from PR #710, SHA-256
+  `5edc624377399ad0878c7a608e722ebb65a7be454a6f022a1b6382a0661e91b0`.
+
+They are supplied unchanged in `source_inputs/` solely for reproduction, not duplicated
+by the new patch. A tree based on #710 has both. Neither is assumed present on main.
+
+## Reproduce after applying the patch
+
+```sh
+git apply --check matching-one-multi-advance-20260913.patch
+git apply matching-one-multi-advance-20260913.patch
+python -m unittest discover -s tests -p 'test_spatial*.py' -v
+python -m unittest discover -s tests -p 'test_rank_source_zeros.py' -v
+python scripts/torus_source_hessian.py --certificate results/research-control-20260912/width4-rank-closure-certificate.json --out /tmp/full-site-hessian-new.json
+python scripts/verify_source_hessian.py --certificate results/research-control-20260912/width4-rank-closure-certificate.json --hessian results/research-control-20260912/full-site-hessian.json --out /tmp/hessian-check-new.json
+python scripts/invisible_spatial_marks.py --certificate results/research-control-20260912/width4-rank-closure-certificate.json --hessian results/research-control-20260912/full-site-hessian.json --out /tmp/marks-new.json
+python scripts/topological_source_zeros.py --definition results/research-control-20260912/width4-parametric-definition.json --out /tmp/zeros-new.json
+python scripts/conditional_odds_integration.py --hessian results/research-control-20260912/full-site-hessian.json --out /tmp/integration-new.json
+```
+
+Scripts refuse to overwrite existing result paths. Use fresh output names on reruns.
+
+## Validation boundaries
+
+27 focused tests passed. The patch was applied in a clean MINIMAL Git tree containing
+the two source JSONs; all newly applied bytes were compared; all five result generators
+were rerun. This is not a checkout of the full repository and not full repository CI.
+`VALIDATION.json` and `HIGH_PRECISION.json` record checks actually executed.
+`REMOTE_ACTIONS.json` records two posted PR conversation comments only. No branch,
+issue lifecycle, PR merge, or STATUS mutation was performed.

delivery/notes/annealed-quenched-root-20260913.md

@@ -0,0 +1,106 @@
+# Averaging probabilities is not averaging their matching roots
+
+Date: 2026-09-13. Completed finite identity, perturbative theorem, and exact/tiny controls.
+
+## 1. An exact annealed identity
+
+Let random environment probabilities be p_i=p+sigma*xi_i, with independent xi_i of
+mean zero and bounded support. Keep p_i in [0,1]. Conditional on the environment,
+site occupations are independent. Separate affinity and independence imply
+
+    E_xi M(p+sigma xi_1,...,p+sigma xi_N)=M(p,...,p)          (1)
+
+EXACTLY for every legal sigma. Indeed the expectation of every product factorizes
+and E[p_i]=p. The annealed occupation law itself is homogeneous Bernoulli(p).
+Thus the zero of the averaged observable remains exactly p_*.
+
+This statement fails in general for spatially correlated xi: mean-zero marginals
+alone do not factorize the environment expectation. It also changes if the noise is
+added to log-odds instead of probabilities, since E[logistic(z+sigma xi)] need not
+be logistic(z). Neither distinction is optional.
+
+## 2. The quenched finite roots have a different mean
+
+For a transitive torus let q(a) solve M(q(a)+a_i)=0. The implicit-function theorem
+and the source-Hessian result give
+
+    grad q=-1/N,
+    R_ij=-M_ij/M' + M''/(N^2 M'),
+    R*1=0,
+    trace R = M''/(N M').                                  (2)
+
+For any bounded mean-zero random vector xi with covariance Sigma, as sigma->0,
+
+    E q(sigma xi)
+      =p_*+(sigma^2/2) trace(R Sigma)+O(sigma^3),
+    Var q(sigma xi)
+      =(sigma^2/N^2) 1^T Sigma 1+O(sigma^3).                 (3)
+
+The remainders improve to O(sigma^4) when the whole vector law is centrally symmetric.
+The constants are finite-system local constants; no assertion of uniformity in N is made.
+
+For independent unit-variance fields on all N sites,
+
+    E q = p_* + sigma^2 M''/(2N M') + O(sigma^4),
+    Var q = sigma^2/N + O(sigma^4).                         (4)
+
+Equation (1) and equation (4) are compatible. Root extraction is nonlinear and does
+not commute with averaging. No new macroscopic disorder transition follows from this.
+
+If only k sites fluctuate independently, the leading bias is
+
+    k sigma^2 M''/(2N^2 M').                               (5)
+
+At the 4x4 root the all-site coefficient in (4) is
+
+    0.020558979708451625... .
+
+For two addressed adjacent sites the coefficient is
+
+    0.002569872463556453... .
+
+## 3. Exact small experiment, no Monte Carlo
+
+Two adjacent sites have independent symmetric offsets +/-sigma, all other sites
+have no offset. There are only four environments. The site-occupation probabilities
+and annealed equality are checked with rational arithmetic at two p values and two
+amplitudes. The roots of all four environments are computed at 65 decimal digits.
+
+| sigma | (mean of the four roots - p_*)/sigma^2 |
+|---|---:|
+| 1/64 | 0.00257018011526596 |
+| 1/128 | 0.00256994938117334 |
+| 1/256 | 0.00256989169325377 |
+| second-order limit | 0.00256987246355645 |
+
+The root-averaging effect is directly present, although the annealed M is EXACTLY
+unchanged. This is not an estimated disorder effect and does not borrow a stochastic
+error bar from a deterministic calculation.
+
+## 4. Removing the empirical field mean does not remove the curvature bias
+
+Put xi_c=xi-(1/N)sum xi_i. For originally independent unit-variance xi,
+Cov(xi_c)=I-11^T/N. Since R*1=0, trace(R Cov(xi_c))=trace R. Thus the leading mean bias
+is unchanged, while the O(sigma) root fluctuation is removed exactly. The variance
+of the centered-field root is O(sigma^4) under the stated bounded-support assumptions.
+
+However xi_c has correlated coordinates. The exact annealed identity (1) no longer
+applies. Mean centering is not a free operation on the physical ensemble.
+
+For correlated environments supported on one unit-RMS Fourier pattern +/-h, the
+second-order mean shift is sigma^2 q''(h)/2. The complete 4x4 Hessian supplies both
+signs (stripes down, checkerboard up), so there is no universal convexity or Jensen
+sign for arbitrary zero-mean spatial noise.
+
+## 5. Practical interpretation
+
+Distinguish a pooled probability curve, an average of roots measured in different
+fixed environments, and a root estimated with random finite samples. The present
+calculation compares the first two, not the third. It gives an exact control for a
+pipeline that mixes them, without reinterpreting prior frozen analyses as disorder
+experiments. Statistical estimator bias requires its own sampling model.
+
+The proof uses only finite multilinearity and implicit differentiation. The formulas
+are applications of standard delta-method ideas; no novelty is claimed for them.
+All input polynomials and four-environment outputs are included in
+results/research-control-20260912/full-site-hessian-independent.json.