Mister-Meeseeks · Oct 22, 2026 · Oct 22, 2026
diff --git a/research/native-lift-4635-delta-check/.gitattributes b/research/native-lift-4635-delta-check/.gitattributes
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+vendor/** -text
diff --git a/research/native-lift-4635-delta-check/README.md b/research/native-lift-4635-delta-check/README.md
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+# Independent check: where #4635's +0.0000016099 comes from
+
+**No new κ.** This package checks Dugongue's native Word RAM line:
+#4630 (κ = 0.0030201655, head `f4b974db1f651250a252721cf127d0491a802699`) and #4635
+(κ = 0.0030217754, head `898b0c8e2ca23897c312230988515c2553154f30`). The question:
+what changes between them? And does the +0.0000016099 step come from the paid profile
+and critical root, or from a native transfer/absorption term?
+
+## Result
+
+**The step comes entirely from the changed paid profile, which #4610 supplies. No transfer or absorption term changes.**
+
+1. **Changed ledger.** The targets (10,928 fields), the helper census {4:28, 7:7, 8:47, 9:326} and the controller are byte-identical across the two PRs. The controller blob `49a2f067…` equals main's `research/joint-helper-lattice/CONTROLLER.json` and has 18 LOCAL calls. #4635's `ARITHMETIC.json` is byte-identical to the one in #4610's round-three package at head `1eb8da6c`. The only change is the local paid profile, by {1:−36, 2:+24, 3:+16, 4:−20, 5:+4} per LOCAL call. That is 18× this change globally: {1:−648, 2:+432, 3:+288, 4:−360, 5:+72}. The local rank mass stays 5,327 and the surplus stays 752. #4630's profile equals main's p16 profile in `compact-joint-compiler/arithmetic/RESULT.json`.
+2. **Critical roots.** These were recomputed by an independent method: Decimal ln/exp at 60 digits with bisection, rather than the 2^-128 outward grid of Dillon's engine. The root solves Σ targets·k^θ = Σ paid·r^θ, with one sign change on a grid of (0, 1].
+   - #4630 (p16 profile): 1−θ = 0.00302016597701562…
+   - #4635 (#4610 profile): 1−θ = 0.00302177587077658…
+   - The raw step is 1.60989376e-6. Both stated brackets are confirmed.
+3. **Decomposition.** The κ step 1.6099e-6 exceeds the raw step by only 6.24e-12. The gap between raw saving and κ is 4.770e-10 for #4630 and 4.708e-10 for #4635. The 6.24e-12 is paid from #4630's slightly larger slack. The native lift in NATIVE-LIFT.md is lossless: every κ < min(q_C, 3/32). It therefore contributes nothing numerically. #4635's README already says it does not rediscover the profile or the root. This check confirms that nothing else changes the number.
+4. **Finite absorption at N = 2^(10^12).** The proof needs log-margin > 0. Using the true root:
+   - #4630: margin ≥ 236.8 (stated 646/3)
+   - #4635: margin ≥ 232.5 (stated 164)
+   - The largest q_C this N supports is ≈ 0.0030217758354 for #4635 and ≈ 0.0030201659416 for #4630. The stated q_C values are conservative.
+5. **Mirror and capacity at the #4635 root.** The worst mirror ratio is 0.56281093, below the stated 0.562811 and below β = 0.564. The capacity is η = 0.98209726, above the stated 0.982097.
+6. **#4635 nine-row ledger.** I re-implemented NATIVE-LIFT.md's parameter formulas with Fraction. All of PARAMETERS.json reproduces exactly: q, stop, δ, ε, β, r, layout, ξ, all nine savings and all guards/excesses. The minimum excess is in the main-transform row: 80181306527/1604834840720000000000 ≈ 5.0e-11. Four controls reject:
+   - κ = q_C
+   - κ ≥ 3/32
+   - #4635's κ on #4630's provider
+   - an unfused O(Td) Gaussian row, whose saving δ ≈ 1.2e-11 is below κ
+7. **#4630 nine-row ledger.** It reproduces: the minimum excess is 1.97983445e-11, in the main row. Each of the five rejecting controls fails for its stated reason:
+   - `epsilon_one` breaks ε < 1.
+   - `unfunded_outer_target` breaks the main row.
+   - `membership_at_edge` breaks the membership guard.
+   - `normalization_at_edge` breaks the global γ guard.
+   - `key_fills_whole_word_power` breaks the key guard.
+
+   **Observation:** the group-key guard 1−(β+1−ε) is the same expression as `beta_below_epsilon` (ε−β). It is also strictly weaker than the membership guard (ε−β) − (1−ε). So the key control is implied by the membership control, and the five controls test four independent conditions. This is redundancy, not an error.
+8. **Selected frontier.** The selected κ = 0.00302015 (#4470) lies below the p16 raw root 0.0030201659770. This is consistent with #4630's statement that it does not change the p16 root.
+
+## What is NOT covered
+
+- Whether #4610's changed word is an admitted canonical provider. This includes the all-fiber identity, the 20 changed native maps, the 26 helper interfaces and absolute phases. #4610 is open and unselected, so #4635's number depends on it.
+- The shifted-logarithmic majorant guards U, V, Q, d and the recurrence funding (.048546 > .04282).
+- The retained analytic, compiler and recovery proofs, and the native algorithms themselves (fused Gaussian circuits, record products, boundary solver).
+- #4635's frame-bridge and transporter lemmas. #4635 attributes no gain to them.
+
+## Reproduce
+
+From the repository root (Python 3.12, stdlib only, under 1 s):
+
+```sh
+python3.12 -B research/native-lift-4635-delta-check/verify.py
+python3.12 scripts/research_package.py --package research/native-lift-4635-delta-check
+```
+
+PR-head inputs are vendored under `vendor/` and pinned as `head:<sha>:<path>` provenance rows in SOURCES.json. The verifier checks every vendored byte against those SHA256 pins. Its four negative controls reject:
+
+- the #4630 profile against #4635's q_C
+- a q_C above the raw root
+- a one-byte tamper of the vendored profile
+- the #4630 bracket applied to the #4635 profile
+
+Metadata validation of head pins needs the PR-head commits to be present locally, for example via `git fetch origin pull/4630/head pull/4635/head pull/4610/head`.
+
+## Open next questions
+
+The structured list is in [TASK.json](TASK.json).
+
+1. Is #4610 head `1eb8da6c`'s round-three word an admitted canonical provider? A first step is an independent replay of its 20 changed native maps and 26 helper interfaces on all 632 columns.
+2. Do the funded-majorant guards hold for the changed profile under an independent enclosure?
+
+## Credit
+
+Credit goes to the predecessors who did the work:
+
+- Dugongue, for #4630, #4635 and the #4554 native assembly
+- Cao Yifan, for the #4610 round-three joint-helper and native-map profile, which supplies the whole numerical step
+- Cinna Davis and the #4470 joint-helper/controller lineage
+- Dillon (#4532/#4535), for the critical-root criterion and engine
+- zxv and Jacob Alan Sussman, for the compiler and integer matching
+- Ryanson Jonathan, for mirror windows and the #4614–#4616 checks of an earlier #4610 head
+- Vlado Vojdanovski (#1673), the #1758 gauge-free authors, Chafik Boukhalfa (#1786) and Tim Trudgian
+- Harvey and van der Hoeven
+
+No predecessor code is imported or executed. Vendored files are read as data, and the two `.py.txt` files only to bind stated constants.
+
+Prepared by lm1909 with Claude Code (Claude Opus 5.5) assistance. New code is Apache-2.0. Vendored files keep their original Apache-2.0 notices and authorship.
diff --git a/research/native-lift-4635-delta-check/SOURCES.json b/research/native-lift-4635-delta-check/SOURCES.json
@@ -0,0 +1,93 @@
+{
+  "schema_version": 1,
+  "base_commit": "fbc9ea0249746acca4f504d4fda2b84e0e36cf0d",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/compact-joint-compiler/arithmetic/RESULT.json",
+      "usage": "input",
+      "git_blob": "514d12ce4d2d824a4e0a418022bba610c8aed8ff",
+      "sha256": "a6caaa2a6d6460a8c1ef7e48c4853bb27976be33a52b96a4216dfa90d96c9091"
+    },
+    {
+      "path": "research/joint-helper-lattice/CONTROLLER.json",
+      "usage": "input",
+      "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5",
+      "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f"
+    },
+    {
+      "path": "research/native-kappa-30201655/raw-profile.json",
+      "usage": "provenance",
+      "pin": "head:f4b974db1f651250a252721cf127d0491a802699:research/native-kappa-30201655/raw-profile.json",
+      "git_blob": "edf41a49a0350862c23378f837c7397fc5dc7596",
+      "sha256": "c7b2388f6511c19976b337d8c8ac374610af616866a249d75dace704eb5d9e21"
+    },
+    {
+      "path": "research/native-kappa-30201655/native_ledger.py",
+      "usage": "provenance",
+      "pin": "head:f4b974db1f651250a252721cf127d0491a802699:research/native-kappa-30201655/native_ledger.py",
+      "git_blob": "e1faa0cf22d82d55ce76ee13acc3793fd9ee4b47",
+      "sha256": "cf3ededf5c980e272deb4647bdae76b1132aa1aa164c89af92eb58ac2597f3c2"
+    },
+    {
+      "path": "research/native-kappa-30201655/critical_check.py",
+      "usage": "provenance",
+      "pin": "head:f4b974db1f651250a252721cf127d0491a802699:research/native-kappa-30201655/critical_check.py",
+      "git_blob": "fe6cb22e2f634eb06efafd565e97c451e4ea2f26",
+      "sha256": "41fa69948c5e20faa7245f441c7487e0a7f89ccaffc778849d80187ba012eb28"
+    },
+    {
+      "path": "research/native-provider-lift/ARITHMETIC.json",
+      "usage": "provenance",
+      "pin": "head:898b0c8e2ca23897c312230988515c2553154f30:research/native-provider-lift/ARITHMETIC.json",
+      "git_blob": "c89e009ca4a5ad316c69f0371d885d72045ba415",
+      "sha256": "ab10f6a4a8a4f589d4b094aac663e002c43ec44774e6bd181c51915c7fa7e521"
+    },
+    {
+      "path": "research/native-provider-lift/PARAMETERS.json",
+      "usage": "provenance",
+      "pin": "head:898b0c8e2ca23897c312230988515c2553154f30:research/native-provider-lift/PARAMETERS.json",
+      "git_blob": "0ec8027ed7cb6a2213e0513d177bb84ad8a1c246",
+      "sha256": "95bb0399057fd1c83687c8f51e47799cced99e0a112575bca486fb922a606a9e"
+    },
+    {
+      "path": "research/native-provider-lift/critical_provider_check.py",
+      "usage": "provenance",
+      "pin": "head:898b0c8e2ca23897c312230988515c2553154f30:research/native-provider-lift/critical_provider_check.py",
+      "git_blob": "76f58548ffc7baf5a5db01b03b6647adae9aecc4",
+      "sha256": "593fbf957e9049bcdfcee198cf4f47f1b4eb4cc40f05f216f983a9c4d8486faa"
+    },
+    {
+      "path": "research/native-provider-lift/NATIVE-LIFT.md",
+      "usage": "provenance",
+      "pin": "head:898b0c8e2ca23897c312230988515c2553154f30:research/native-provider-lift/NATIVE-LIFT.md",
+      "git_blob": "a900a66392f6486d439234a858c8127af56d138c",
+      "sha256": "66188d374905361062d30710b2cd0510defcf50d3786c1e54323847c3d9f9d08"
+    },
+    {
+      "path": "research/native-provider-lift/CONTROLLER.json",
+      "usage": "provenance",
+      "pin": "head:898b0c8e2ca23897c312230988515c2553154f30:research/native-provider-lift/CONTROLLER.json",
+      "git_blob": "49a2f0675819f9deeea27ed77be2c2b6ff2e87e5",
+      "sha256": "1f5d6aa267e4e66048818714b5d3b5eae17a58abe91d15deeaa34574f7391a5f"
+    },
+    {
+      "path": "research/kappa-round3-warp-20261022/ARITHMETIC.json",
+      "usage": "provenance",
+      "pin": "head:1eb8da6cfb35512c0cc2533413e5ca42f48e13c6:research/kappa-round3-warp-20261022/ARITHMETIC.json",
+      "git_blob": "c89e009ca4a5ad316c69f0371d885d72045ba415",
+      "sha256": "ab10f6a4a8a4f589d4b094aac663e002c43ec44774e6bd181c51915c7fa7e521"
+    }
+  ]
+}
diff --git a/research/native-lift-4635-delta-check/TASK.json b/research/native-lift-4635-delta-check/TASK.json
@@ -0,0 +1,106 @@
+{
+  "schema_version": 1,
+  "task_id": "independent-moment",
+  "priority_revision": 7,
+  "base_commit": "fbc9ea0249746acca4f504d4fda2b84e0e36cf0d",
+  "original_card": {
+    "id": "independent-moment",
+    "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-mixed-fourth-entry/README.md",
+      "research/staged-fourth-mixture-ceiling/README.md",
+      "research/r437-two-window-carrier/README.md"
+    ],
+    "methods": [
+      "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.",
+      "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls."
+    ],
+    "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.",
+    "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.",
+    "allowed_variations": [
+      "Reconstruct either a source ledger or a numeric enclosure with a different method."
+    ],
+    "scope_change_triggers": [
+      "Importing the primary function and calling its output independent verification.",
+      "Calling an aggregate histogram or source archive an independently accepted physical supplier."
+    ],
+    "overlap_terms": [
+      "independent moment",
+      "rank histogram",
+      "exact enclosure",
+      "2979",
+      "rank7 joint endframes",
+      "paired extraction",
+      "joint lowering",
+      "4088",
+      "4091",
+      "4067",
+      "staged544-mixed-fourth-entry",
+      "staged-fourth-mixture-ceiling",
+      "r437-two-window-carrier"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.",
+        "evidence": "research/staged544-mixed-fourth-entry/README.md",
+        "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.",
+        "status": "author-checked",
+        "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.",
+        "evidence": "research/staged-fourth-mixture-ceiling/README.md",
+        "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.",
+        "status": "author-checked",
+        "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.",
+        "evidence": "research/r437-two-window-carrier/README.md",
+        "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.",
+        "status": "author-checked",
+        "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "For Dugongue's native Word RAM line, independently determine what changes between #4630 (kappa 0.0030201655, head f4b974db) and #4635 (kappa 0.0030217754, head 898b0c8e): bind the changed paid ledger to its #4610 source and the unchanged main controller, recompute both critical roots with a different enclosure method, recompute the finite-absorption margins, and recompute both nine-row native cost ledgers and their rejecting controls exactly.",
+  "scope_change_reason": "The card asks for independent coverage of a changed paid ledger; the changed ledger here is #4610's round-three local profile as consumed by the #4635 native lift, so the check is refined to that ledger plus the native transfer terms that could otherwise explain the +1.6099e-6 step.",
+  "bottleneck_link": "Separates a machine-model transfer contribution from a paid-profile contribution, so the #4635 headline is attributed to the right (still unselected) #4610 profile and not counted as an independent Word RAM advance.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after the #4630->#4635 delta is fully attributed and both nine-row ledgers and the five #4630 controls are recomputed; do not review the inherited all-fiber/analytic proofs.",
+  "outcome": "completed",
+  "evidence": "python3.12 -B research/native-lift-4635-delta-check/verify.py prints PASS_4635_DELTA_IS_PROFILE_ONLY: only the 18x local paid profile changes ({1:-36,2:+24,3:+16,4:-20,5:+4} per LOCAL call); raw savings 0.00302016597702 -> 0.00302177587078 (step 1.60989376e-6); kappa step 1.6099e-6 exceeds raw step by 6.24e-12, paid from #4630's larger transfer slack; nine-row ledgers reproduce exactly; four negative controls reject.",
+  "author": "lm1909",
+  "ai_assistance": "Prepared by lm1909 with Claude Code (Claude Opus 5.5) assistance.",
+  "open_questions": [
+    {
+      "question": "Is #4610's round-three word (local paid profile {1:2201,2:412,3:510,4:127,5:40,8:8}) an admitted canonical provider under the all-fiber identity and absolute-phase contracts that #4635's NATIVE-LIFT.md requires?",
+      "why_it_matters": "The entire +1.6099e-6 of #4635 rests on this profile; the native lift adds no saving of its own.",
+      "first_step": "Independently replay #4610 head 1eb8da6c's changed 20 native maps and 26 helper interfaces on the 632 formal columns in both orientations, without importing its interpreters.",
+      "blocked_by": "#4610 is open and not maintainer-reviewed; #4614-#4616 covered an earlier head."
+    },
+    {
+      "question": "Do the funded critical-majorant guards (U, V, Q, d, recurrence funding .048546 > .04282) hold for the changed profile under an independent enclosure?",
+      "why_it_matters": "This package recomputes the root, mirror ratio and capacity, but not the shifted-logarithmic majorant that turns the root into L(N) < N^(1-q_C).",
+      "first_step": "Re-implement the critical_guards inequalities of PR #4532/#4535 from their PROOF.md with Decimal intervals and evaluate them on the #4610 profile.",
+      "blocked_by": "None; needs a careful reading of the #4532 majorant statement."
+    }
+  ]
+}
diff --git a/research/native-lift-4635-delta-check/VERIFY.json b/research/native-lift-4635-delta-check/VERIFY.json
@@ -0,0 +1,22 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "certificates/selected-result.json",
+    "research/compact-joint-compiler/arithmetic/RESULT.json",
+    "research/joint-helper-lattice/CONTROLLER.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Head-pinned vendored bytes and main inputs; #4630->#4635 changed paid ledger bound to #4610 and the unchanged main controller; Decimal critical roots for both profiles; finite absorption; both nine-row native ledgers and #4630 five controls; four negative controls (old profile vs new q_C, q_C above root, tampered vendored byte, wrong bracket)."
+    }
+  ]
+}