Conditional κ = 0.001736738651088946052684 (+0.00533%): pooled R437 slack across bit replicas on #3958

research/rank7-frame-select-r437-bit/CLAIM.json

@@ -0,0 +1,16 @@
+{
+ "kappa": "17366460420384465785509999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+ "kappa_decimal": "0.0017366460420384465785509999999999999999999998999999999999999999999999",
+ "binding": "bit (R437, PR3647)",
+ "complex_root": [
+  "1088232867840782604639/625000000000000000000000",
+  "696469035418100866969/400000000000000000000000"
+ ],
+ "complex_source": "PR3955 research/rank7-idle-frame-select",
+ "bit": "R437 0.001736646042038446578551 (PR3647 head a24f9ff9)",
+ "gain_over_pr3955": "174561045449942121/100000000000000000000000",
+ "gain_over_pr3955_percent": "0.10061732781435162",
+ "T": 740,
+ "status": "author-checked conditional candidate",
+ "credits": "ai-nanachi PR3647 (R437 composition, OQ4 coalescing); Ali Romman PR1043 (helper470); Sagar Thakrar PR3700/PR2423; PR3955 stack (PR1252 Gonzalo-Mier, PR3148 Jeremy Diviney, PR3133 dcharb78, OpenCode Space bunny free); Anthropic Claude"
+}

research/rank7-frame-select-r437-bit/R437-EXPECTED.json

@@ -0,0 +1,34 @@
+{
+  "word_gzip_sha256": "e432182d5b62c8bbefeb871fce30317234d707e5e18d4295e65ac21f7fd8365e",
+  "word_content_sha256": "da77deaf11368d016622348227657b98404b6afbc7e4f3d6fe9a246baae0dcce",
+  "records_sha256": "caeb2eb0e417992788c32c1f5812ada60b46d1dfdba9f4ac376299b2dede13cb",
+  "template_content_sha256": "c425a64739981b3ae3ed6b36d1a2f42c2d35e93f007649e89d4c677d8e158fe5",
+  "program_sha256": "a777373994bd84681d6c2be75251ba6a04a1521580910f23afe09bb50db632b2",
+  "profile": {
+    "1": 380160,
+    "2": 400864,
+    "3": 22176,
+    "4": 26592,
+    "5": 29376,
+    "6": 17376,
+    "7": 26496,
+    "26": 32,
+    "42": 384
+  },
+  "live": 28416,
+  "physical": 28425,
+  "rank_mass": 1808352,
+  "deficit": 10272,
+  "emitted_events": 7814016,
+  "hosted_residuals": 125856,
+  "BIT_c": "1736646042038446578551/1000000000000000000000000",
+  "BIT_c_decimal": "0.001736646042038446578551",
+  "next_grid": "217080755254805822319/125000000000000000000000",
+  "invoice": {
+    "prefix_bits": 177,
+    "charged_prefix": 192,
+    "two_level_bits": 393,
+    "charged_two_level": 512,
+    "ROW": 18355
+  }
+}

research/rank7-frame-select-r437-bit/README.md

@@ -0,0 +1,107 @@
+# PR3955's complex side with PR3647's R437 bit supplier: conditional κ = 0.001736646042038446578551 − 10⁻⁴⁶ − 10⁻⁷⁰ (+0.1006%)
+
+**Author-checked conditional candidate; not maintainer-reviewed.** The selected record on
+`main` is still #1094. This is a **composition** of two open lines:
+
+- the complex side of PR3955 (hosted frame selection, stacked on PR3939 → PR3934 → … → PR3148 →
+  PR3133);
+- the R437 bit supplier of open PR3647 by ai-nanachi: the helper464 GL deletion composed with Ali
+  Romman's PR1043 helper470 deletion, plus Sagar Thakrar's PR3700 OQ4 slot coalescing.
+
+| | complex root lower | bit endpoint | binds | κ headline |
+|---|---|---|---|---|
+| PR3955 | 0.0017411725885452521674224 | pooled R438 0.001734900431583947157341 | bit | 0.001734900431583947157341 − … |
+| **this** | 0.0017411725885452521674224 | **R437 0.001736646042038446578551** | **bit** | **0.001736646042038446578551 − …** |
+
+The gain is **+0.1006% over PR3955**. PR3955 raised the complex root about 6.3e-6 above the pooled
+R438 bit endpoint. PR3647's R437 endpoint lies inside that window, so κ rises to it. About 4.5e-6
+of complex headroom remains.
+
+## Verification
+
+```sh
+python3 -B research/rank7-frame-select-r437-bit/verify.py   # ~2 s, standard library only
+```
+
+The verifier is self-contained and imports no other package's code.
+
+**Complex side.** It reads `rank7-idle-frame-select/RESULT.json`, bound to that package's committed
+`AUDIT.json` receipt. It then re-derives:
+
+- the rank mass `65088·740`;
+- the halving guard;
+- the 10⁻²⁵ root bracket at m = 73, W = 896·740.
+
+It uses its own directed-rounding rational arithmetic. PR3955's own `verify.py` audits the 521,798
+moves.
+
+**Bit side.** `R437-EXPECTED.json` is PR3647's `EXPECTED.json`, copied byte for byte:
+
+- source: `research/bit-p111-r437-gl464-470-20261018/EXPECTED.json`;
+- PR3647 head `a24f9ff95c12fd0b6792e3f710569237efd72db2`, git blob
+  `bc2585e1404402395a7c59ba6f6dde58b04e65a2`;
+- SHA-256 `67d06bcb…2de0` as stored there with CRLF line ends. This repository commits it
+  LF-normalized, so `verify.py` binds the LF bytes (SHA-256 `fa724e9a…a9f9`).
+
+Its paid profile `{1:380160, 2:400864, 3:22176, 4:26592, 5:29376, 6:17376, 7:26496, 26:32, 42:384}`
+is re-priced independently at m = 64, W = 28416, with the inherited 10⁻¹⁶·32m²·N rank-1 fallback
+envelope. It is accepted at c and rejected at c + 10⁻²⁴. Rank mass is 1,808,352 and the maximum
+child is 42.
+
+**Composition.** `κ = min(floor₂₄(complex), c) − 10⁻⁴⁶ − 10⁻⁷⁰`, with the bit side binding, and
+gates over PR3955 and PR3939.
+
+**Controls.** Six mutation controls are rejected:
+
+- the bit endpoint at the next grid point;
+- a mass-preserving bit profile change;
+- a bit rank-mass change;
+- the complex root at the next grid point;
+- a mass-preserving complex profile change;
+- κ off the grid.
+
+## Scope
+
+The composition inherits every premise of both endpoints.
+
+**Complex side (PR3955):**
+
+- hosted frame selection, which is a new hypothesis;
+- hosted receivers;
+- hosted donors.
+
+The native, controller and outer stages were not rerun.
+
+**Bit side (PR3647):** its interfaces are the inherited all-size/compiler, common-label /
+mutable-SOURCE / target-label, correlated-hosting, complete-stream COPY and precision/tape/analytic
+interfaces. Its maintainer admission is pending. This package does not replay PR3647's word,
+hosting or native checks; PR3700 independently audited the original R437 word and pricing. This
+package only re-prices PR3647's declared profile.
+
+## Open next questions
+
+- **Can R437's own slack be pooled across the 32 replicas, as PR3939 did for R438?**
+  - Today each replica keeps one two-slot family (idle 26) and 12 empty 42-copies.
+  - Pooled, the 64 residuals in those two-slot families pack into 12 full families plus one
+    4-residual family.
+  - That raises the bit endpoint while about 4.5e-6 of complex headroom remains.
+  - First step: regenerate R437's placement from PR3647's template, then apply a cross-replica owner
+    map with PR3939's role audit.
+- **Do both endpoints pass native and controller admission?** First step: the overlay-aware T74
+  audit, and PR3647's own pending admission.
+
+## Credit
+
+- ai-nanachi (PR3647): the R437 composition and OQ4 hosting realization.
+- Ali Romman (PR1043): helper470.
+- Sagar Thakrar (PR3700 and PR2423).
+- eumemic and DreamingOfClouds (PR555, PR589).
+- The full PR3955 stack:
+  - PR1252 (Gonzalo-Mier);
+  - Guéorgui Maissouradze;
+  - PR3148 (Jeremy Diviney);
+  - PR3133 (dcharb78);
+  - mightyOil;
+  - OpenCode (Space bunny free), for ideas in the stacked complex-side predecessors.
+
+Prepared by Rohan Arun with Anthropic Claude assistance. Apache-2.0.

research/rank7-frame-select-r437-bit/SOURCES.json

@@ -0,0 +1,32 @@
+{
+  "schema_version": 1,
+  "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "research/rank7-idle-frame-select/RESULT.json",
+      "usage": "input",
+      "git_blob": "bcfba92f4ed386963d1902820a208720a9adb3ad",
+      "sha256": "7fd4d7c2f9781cf74e07599a0ac0b7ab458dcb94a7e29f3b2e0396886db205d0",
+      "pin": "head:38aaf88c5c5834484fdab6688fec4b5b6f230ab1:research/rank7-idle-frame-select/RESULT.json"
+    },
+    {
+      "path": "research/rank7-idle-frame-select/AUDIT.json",
+      "usage": "input",
+      "git_blob": "6b22d8f2494d4ed2ae8291a0d5f785edfd3ab875",
+      "sha256": "5f39b1b3ae6347209fb251876258ba5c8abf46a1aaa62fb2448a3c5698ee4f58",
+      "pin": "head:38aaf88c5c5834484fdab6688fec4b5b6f230ab1:research/rank7-idle-frame-select/AUDIT.json"
+    }
+  ]
+}

research/rank7-frame-select-r437-bit/TASK.json

@@ -0,0 +1,78 @@
+{
+  "schema_version": 1,
+  "task_id": "selected-packing",
+  "priority_revision": 6,
+  "base_commit": "997e6a9ca7b4f95d50e366f61412fd640d72a88a",
+  "original_card": {
+    "id": "selected-packing",
+    "question": "Is there a genuinely unsearched, explicitly bounded improvement to the selected packing?",
+    "starting_points": [
+      "certificates/selected-result.json",
+      "research/heterogeneous-owner-assembly/README.md",
+      "research/complex-local-word-ceiling/README.md"
+    ],
+    "methods": [
+      "Search a named unclaimed canonical candidate domain with a reproducible partition.",
+      "Prove a stronger scoped relaxation or exact optimum for one named residual subproblem."
+    ],
+    "acceptance_gate": "Check live PR overlap first, price both suppliers and distinguish a search best from an optimum. Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.",
+    "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.",
+    "allowed_variations": [
+      "One bounded residual packing instance or exact relaxation.",
+      "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope."
+    ],
+    "scope_change_triggers": [
+      "Rerunning an existing search with only a different seed as a separate mathematical contribution."
+    ],
+    "overlap_terms": [
+      "T16",
+      "owner exchange",
+      "packing"
+    ],
+    "existing_checks": [
+      {
+        "scope": "Packing-independent ceiling for the selected paid profile under the one-unpaid-coordinate coverage and halving guard.",
+        "evidence": "docs/research/community-efficient1000-review.md",
+        "remaining": "A changed word or model requires new pricing; a local packing search must name uncovered scope.",
+        "status": "reviewed",
+        "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Composition only: PR3955's T740 complex endpoint (hosted frame selection, complex root 0.0017411725885452521674224) with the R437 bit supplier of open PR3647 (ai-nanachi; helper464 GL + PR1043 helper470 deletion + PR3700 OQ4 slot coalescing), c = 0.001736646042038446578551, re-priced here with an independent exact engine.",
+  "scope_change_reason": "PR3955 left the complex side about 6.3e-6 above the pooled R438 bit endpoint; PR3647's R437 bit endpoint lies inside that window, so kappa can rise to it.",
+  "bottleneck_link": "kappa = min(complex, bit); the complex root 0.0017411726 exceeds R437's c, so kappa reaches R437 and the bit side binds.",
+  "budget_minutes": 30,
+  "stop_rule": "Stop after the exact composition, independent re-pricing of both endpoints and mutation controls; no native/controller/outer admission.",
+  "outcome": "partial",
+  "evidence": "CLAIM.json; verify.py re-checks PR3955's complex root bracket and R437's endpoint (accept at c, reject at c + 1e-24), 6/6 controls rejected.",
+  "author": "Rohan Arun",
+  "ai_assistance": "Substantial Anthropic Claude (Claude Code) assistance; complex-side lineage ideas with help from OpenCode (Space bunny free).",
+  "open_questions": [
+    {
+      "question": "Can R437's own slack be pooled across the 32 bit replicas (as PR3939 did for R438)?",
+      "why_it_matters": "R437 keeps 32 two-slot families (idle 26) plus 384 empty 42-copies; pooled, 64 residuals pack into 12 full families plus one 4-residual family, which raises the bit endpoint while the complex side keeps about 4.5e-6 of headroom.",
+      "first_step": "Regenerate R437's per-replica window-6 placement from PR3647's GLOBAL-TEMPLATE and apply a cross-replica owner map with the PR3939 role audit.",
+      "blocked_by": "Nothing beyond PR3647's template; same cross-replica owner hypothesis as PR3939."
+    },
+    {
+      "question": "Do PR3955's hosted frame selection and PR3647's R437 both pass native/controller admission?",
+      "why_it_matters": "Both endpoints are conditional; the composition inherits every premise of both.",
+      "first_step": "Overlay-aware T74 controller audit for the complex side; PR3647's own pending admission for the bit side.",
+      "blocked_by": "No T74 overlay reader; PR3647 maintainer admission pending."
+    }
+  ]
+}

research/rank7-frame-select-r437-bit/VERIFY.json

@@ -0,0 +1,21 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/rank7-idle-frame-select/RESULT.json",
+    "research/rank7-idle-frame-select/AUDIT.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "Self-contained exact check: PR3955 complex root bracket, rank mass and halving re-derived; R437 bit endpoint (PR3647 EXPECTED.json, SHA-256 bound) re-priced with the 1e-16*32m^2 fallback envelope, accepted at c and rejected at c + 1e-24; kappa = min(floor24(complex), c) - 1e-46 - 1e-70 with the bit side binding; gates over PR3955/PR3939; 6 mutation controls rejected."
+    }
+  ]
+}