Reduce conditional κ = 0.0023 template ranks to 2^465000 and 2^7100

research/log-potential-template-ranks/.gitattributes

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+vendor/** -text -whitespace

research/log-potential-template-ranks/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65",
+      "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96"
+    }
+  ]
+}

research/log-potential-template-ranks/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "supplier-boundary-audit",
+  "priority_revision": 7,
+  "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "original_card": {
+    "id": "supplier-boundary-audit",
+    "question": "Can the #4088 four-provider dispatch satisfy the complete ordinary/outer admission contract?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-mixed-fourth-entry/README.md",
+      "research/scatter-boundary-decision/README.md"
+    ],
+    "methods": [
+      "Trace one hypothesis through the source, checker and complete caller.",
+      "Construct one semantically invalid but superficially well-formed fixture and test rejection."
+    ],
+    "acceptance_gate": "Pin the current sources and one obligation; the historical owner audit is an example, not evidence of a current bug.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read #4088 Scope and Open next questions: local words, native receipts and literal fill do not include a rerun of the mixed four-provider ordinary/outer engine. #3801 is the newer scatter-boundary decision; do not restart #2977 as if untouched.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Pin the provider registry, four native source closures and dispatch. Make a bounded acceptance coverage map or one registry adapter preserving every inherited admission predicate and rejection control (including an omitted fourth provider). Record remaining ordinary/outer obligations and a resource estimate before heavy execution. Stop at unresolved source/caller dependencies; no selected-result promotion from a local pass.",
+    "bottleneck_link": "Closing a current acceptance gap or proof obligation strengthens reliability even without changing kappa.",
+    "allowed_variations": [
+      "One provider-registry, dispatch, native-closure or admission-predicate obligation; separate branches must name distinct coverage."
+    ],
+    "scope_change_triggers": [
+      "Reporting the historical timing-only diagnostic as a new current acceptance bug.",
+      "Calling a malformed mutant a failure of the selected construction, or importing an opt-in repair without testing the exporter boundary.",
+      "Running another root enclosure instead of validating dispatch or weakening an inherited predicate to make mixed admission pass."
+    ],
+    "overlap_terms": [
+      "owner boundary",
+      "bridge omission",
+      "hosting",
+      "2977",
+      "scatter export",
+      "duplicate index",
+      "parity semantics",
+      "4088",
+      "3801",
+      "staged544-mixed-fourth-entry",
+      "scatter-boundary-decision"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4088: author-checked local words, native receipts, owner/phase fill and exact moment.",
+        "evidence": "research/staged544-mixed-fourth-entry/README.md",
+        "remaining": "Rebind and validate ordinary/outer admission with all four providers; full mixed release not established.",
+        "status": "author-checked",
+        "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #3801: successor scatter-boundary decision package.",
+        "evidence": "research/scatter-boundary-decision/README.md",
+        "remaining": "Consult its exact acceptance scope before any new exporter audit; not proof of a selected failure.",
+        "status": "author-checked",
+        "source_commit": "911f8800ba7a4b03603ef62c5ffc6240e53cb5fd",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Prove a logarithmic majorant for PR4359 leaf counts, certify smaller ranks at unchanged supplier savings, and retune the complete cover/atom/outer consumer to retain kappa 0.0023 at ranks 2^465000 and 2^7100.",
+  "scope_change_reason": "Explicit user assignment to build on conditional-kappa-0023, followed by a request to shrink ranks further. The catalogue four-provider audit is replaced by a changed majorant and complete consumer-parameter retuning; no new kappa is claimed.",
+  "bottleneck_link": "The majorant removes a squared inverse-gap loss; the complete consumer ledger allows the surplus supplier saving to be exchanged for smaller ambient ranks.",
+  "budget_minutes": 60,
+  "stop_rule": "One proved majorant, two exact sufficient ranks and negative controls; no template materialization, H decoder campaign or full outer replay.",
+  "outcome": "completed",
+  "evidence": "README.md proof and complete retuned consumer bill; RESULT.json exact checks; VENDOR.json immutable predecessor subset.",
+  "author": "zxv, with substantial OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance in proof development, code, verification and writing. No subagents or independent human review.",
+  "open_questions": [
+    {
+      "question": "Can the logarithmic exponent be sharpened using the actual source and exit distributions?",
+      "why_it_matters": "Further lowers the sufficient rank while testing the coarse worst-case source-band estimate.",
+      "first_step": "Bound the complete weighted source complement and exit logarithm ratios before changing t or q.",
+      "blocked_by": "A uniform distribution-sensitive inequality, beyond the present eta/theta bound."
+    },
+    {
+      "question": "Can one construct a materially smaller supplier or rigorously bound its productive width and instruction count?",
+      "why_it_matters": "Reduced ambient rank alone does not make the finite program practical.",
+      "first_step": "Build compressed count recurrences for B_N, P_N and owned-unit counts with denominator clearing.",
+      "blocked_by": "Huge integer batch widths and no materialized winning template."
+    },
+    {
+      "question": "Does the inherited compiler and native/outer transfer pass independent mathematical review?",
+      "why_it_matters": "These remain premises of the conditional rank improvement and proposed kappa.",
+      "first_step": "Follow pinterbanget’s announced source/exit audit, then separately audit native closure and delayed BIT cover.",
+      "blocked_by": "Independent acceptance is not supplied by this package."
+    },
+    {
+      "question": "Can the logarithmic majorant reduce ranks at PR4405’s higher proposed kappa point?",
+      "why_it_matters": "Combines this structural quantitative improvement with a distinct endpoint refinement.",
+      "first_step": "Pin PR4405’s exact endpoint parameters and choose a rational tested t strictly below its uniform exponent; then recheck the complete consumer and final integer powers.",
+      "blocked_by": "Independent acceptance of PR4405 and exact source binding for that additional parameter point; not tested here."
+    }
+  ],
+  "upstream_checkpoint": {
+    "commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+    "priority_revision": 7,
+    "checked_at_utc": "2026-10-21T17:02:27.623597+00:00"
+  },
+  "overlap": {
+    "checked_at_utc": "2026-10-21T17:02:27.623597+00:00",
+    "open_pr_records": 513,
+    "discussion_records": 3250,
+    "cache_pagination_complete": true,
+    "scope": "Open PR bodies and discussions; local READMEs/TASKs/ledger. No remote closed PR bodies or code-diff search.",
+    "nearest": "PR4359; pinterbanget PR4404 at 77f20afb7c24286937c75cb65a7f19e24e7a567f audits the original chain; parallel PR4405 at 873d1b3c96a83b701a5c0bba8e37a861e6672fef sharpens the old power majorant and increases the proposed kappa. This package instead replaces the power majorant by a logarithmic factor and reprices the smaller-rank kappa=0.0023 consumer."
+  }
+}

research/log-potential-template-ranks/VENDOR.json

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+{
+  "schema": "pinned-predecessor-subset/1",
+  "repository": "https://github.com/zxv/integer-mult-bounds",
+  "source_pr": "https://github.com/CrocSwap/integer-mult-bounds/pull/4359",
+  "source_commit": "da637c87c89482bc4c86be36bd0071b3d400dbed",
+  "scope": "Ten byte-identical inputs for the conditional leaf-count, cover/atom and outer-parameter arguments only; native programs and full outer admission are not reproduced.",
+  "files": [
+    {
+      "original_path": "research/kappa-rebuild/architecture/FINITE-PRECOMPILATION.md",
+      "path": "research/log-potential-template-ranks/vendor/FINITE-PRECOMPILATION.md",
+      "git_blob": "4badb40f0919c515823cb07e44c6470d4d6469ca",
+      "sha256": "4cb32f6b8e388ecf6ed41b5bbdeeb4539cb40c8424f194974afea58f7e0921e8"
+    },
+    {
+      "original_path": "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json",
+      "path": "research/log-potential-template-ranks/vendor/MIXED-PRODUCTIVE-BIT.json",
+      "git_blob": "6a139eedbc1015c13df6f2a4333e1a89b5edd18d",
+      "sha256": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf"
+    },
+    {
+      "original_path": "research/kappa-rebuild/controller/EXPLICIT-TEMPLATE-BOUNDS.json",
+      "path": "research/log-potential-template-ranks/vendor/EXPLICIT-TEMPLATE-BOUNDS.json",
+      "git_blob": "19b27c6e40a7bf20822ec35b7a4159cc7e89be2e",
+      "sha256": "3f1abfafa6f1bb192aafdf342a33ef60fd469fb0764be3eb1516984fc3c22c3f"
+    },
+    {
+      "original_path": "research/kappa-rebuild/controller/EXPLICIT-TEMPLATE-BOUNDS.md",
+      "path": "research/log-potential-template-ranks/vendor/EXPLICIT-TEMPLATE-BOUNDS.md",
+      "git_blob": "b00acfbe8bf0fb540e90eebd0d1fe0b094b1880d",
+      "sha256": "e54345bfdbceda1e41a68682c6902899372252d36d16ca914c1207f0bf03f8b0"
+    },
+    {
+      "original_path": "research/kappa-rebuild/controller/P3-NATIVE-COVER.json.gz",
+      "path": "research/log-potential-template-ranks/vendor/P3-NATIVE-COVER.json.gz",
+      "git_blob": "51a09b3952a491f06780bf6ce5f69b385f026b21",
+      "sha256": "facfc6d6ecde151afb7e6a167776f3fdaac1c816e785a21a39f7f0bfd9140f3f"
+    },
+    {
+      "original_path": "research/kappa-rebuild/controller/OUTER-PARAMETERS.json",
+      "path": "research/log-potential-template-ranks/vendor/OUTER-PARAMETERS.json",
+      "git_blob": "956853dcd169c71ac69fff5d2c213d2ebb89c22e",
+      "sha256": "15818c10c41ac2ea650e503de830795f6c88830a7f9be9553dd938bb1d76717a"
+    },
+    {
+      "original_path": "research/kappa-rebuild/transfer-audit/OUTER-TRANSFER-AUDIT.md",
+      "path": "research/log-potential-template-ranks/vendor/OUTER-TRANSFER-AUDIT.md",
+      "git_blob": "e8b7ef8956ece5bd493cbf52113916e5dc288535",
+      "sha256": "67569961d068633c6ff3ac9dfde47a0c17f0da6d20432799dcc920cff92b5779"
+    },
+    {
+      "original_path": "research/kappa-rebuild/bit/BIT-ALLSIZE-PARAMETERS.json",
+      "path": "research/log-potential-template-ranks/vendor/BIT-ALLSIZE-PARAMETERS.json",
+      "git_blob": "fbe6da7241357d89cf5c55b2e7ce2d0d046be32a",
+      "sha256": "edb273f59a27356ad89f38791590c3c806b228c3510eb508e01e89f2caba95ef"
+    },
+    {
+      "original_path": "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md",
+      "path": "research/log-potential-template-ranks/vendor/DELAYED-COVER-BRIDGE.md",
+      "git_blob": "a58774e237c9362869a60a22bda35be09fb85872",
+      "sha256": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443"
+    },
+    {
+      "original_path": "research/kappa-observation-integration/release-work/current/package/outer/check_ledger.py",
+      "path": "research/log-potential-template-ranks/vendor/check_ledger.py",
+      "git_blob": "d3b6149c5c1cca84c7c305f6e2e32c814e30777e",
+      "sha256": "1dd56009986eb14dd6603c9193c7ad71dd45c7d005bf71c9cd3f916e66f54d98"
+    }
+  ]
+}

research/log-potential-template-ranks/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/log-potential-template-ranks/vendor/FINITE-PRECOMPILATION.md",
+    "research/log-potential-template-ranks/vendor/MIXED-PRODUCTIVE-BIT.json",
+    "research/log-potential-template-ranks/vendor/EXPLICIT-TEMPLATE-BOUNDS.json",
+    "research/log-potential-template-ranks/vendor/EXPLICIT-TEMPLATE-BOUNDS.md",
+    "research/log-potential-template-ranks/vendor/P3-NATIVE-COVER.json.gz",
+    "research/log-potential-template-ranks/vendor/OUTER-PARAMETERS.json",
+    "research/log-potential-template-ranks/vendor/OUTER-TRANSFER-AUDIT.md",
+    "research/log-potential-template-ranks/vendor/BIT-ALLSIZE-PARAMETERS.json",
+    "research/log-potential-template-ranks/vendor/DELAYED-COVER-BRIDGE.md",
+    "research/log-potential-template-ranks/vendor/check_ledger.py",
+    "research/log-potential-template-ranks/VENDOR.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Four logarithmic-majorant rank certificates, 12 rejecting scientific mutations, four failing previous grid points, complete BIT cover/atom chain, nine outer cost rows, 63 inherited predicates, 22 added interface inequalities and four rejecting outer controls."
+    }
+  ]
+}

research/log-potential-template-ranks/vendor/BIT-ALLSIZE-PARAMETERS.json

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+{
+  "C0_before_cover": "69/25000",
+  "C0_minus_C1": "1/100000",
+  "C1_after_cover": "11/4000",
+  "atom_power": "3/1000",
+  "finite_constants_to_replace": {
+    "ambient_dimension": "N, not50 or64",
+    "bad_fallback_children": "At most32*N^2 per bad final leaf",
+    "coefficient_data": "Every fixed rational entry, inverse, determinant, prefix descriptor and height",
+    "fixed_row_routes": "R, original port charts and every internal matcher/inverse",
+    "generic_affine_work": "At most4*N^2-2*N basic shears per rank1 normalizer together with its inverse",
+    "owned_storage": "C, bounded by one owned bank per allocated finite unit instance",
+    "paid_leaf_count": "P, including copied-center descendants",
+    "pointwise_and_copy_count": "L, literal compiled scalar/copy/erase records",
+    "productive_roles": "B, not3739 or661"
+  },
+  "finite_template_hypothesis": "Fixed integers N>=2,B>=1,P>=1 and a whole-cover native schematic uniform word, with P/B < N^(1-C0), final paid leaves of rank1, arbitrary productive inputs and separately owned storage.",
+  "mixed_margin_at_C0": {
+    "display": 0.7944031286900184,
+    "lower": "67580344230009584908122845692691165477/85070591730234615865843651857942052864",
+    "strict_negative": false,
+    "strict_positive": true,
+    "upper": "270321376920038339632491382770764742407/340282366920938463463374607431768211456"
+  },
+  "new_kappa": false,
+  "old_ordinary_saving": "384599/10000000000",
+  "ordinary_saving_admitted": "27/10000",
+  "ordinary_saving_before_final_relaxation": "27418653797/10000000000000",
+  "ordinary_saving_display": 0.0027418653797,
+  "prime_rule": {
+    "N_to_d_lower": "200001/200000",
+    "also_required": "Odd prime avoiding every fixed rational denominator, matcher determinant and chosen rank witness of the entire compiled word.",
+    "bound": "q > 25600000 * N^5",
+    "complete_moment_upper": "400001/400002",
+    "fallback_multiplier_upper": "400001/400000",
+    "good_moment_upper": "N^(-d), d=C0-C1",
+    "strict_moment_slack_lower": "1/400002"
+  },
+  "root_cost_terms": [
+    "e^(1-delta)",
+    "e^((1-delta)*(1-C1)+delta*(1-a_old))",
+    "e^delta * log(e)"
+  ],
+  "schema": "conditional-delayed-cover-BIT-allsize-parameters/1",
+  "source_sha256": {
+    "notes/batched-bit-rows.tex": "ef72c0ead19373cbc19c8a3aacb44dd0f75353ee5f4d055f775a986a4878022c",
+    "notes/three-stage-cover-bit.tex": "47123a756f823c83a0d48cca2bf5add6472cd88410b13aed345e70c8834fb511",
+    "notes/three-stage-cover-rows.tex": "6ad97a5cd7d6aecf978a81226e1c2763d37840caca130c61f3bf5c4ac111c5c8",
+    "research/kappa-rebuild/bit/BIT-P3-NATIVE-BINDING.json": "9ece46fdfda6182e757e9a3b1f513fb3d029d730f3bafdcd6ed59180a14175b0",
+    "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.json": "1e1a91871ad8d1098b6851c95d257e8e3fb130222933009b4edfb5e2c2d5c471",
+    "research/kappa-rebuild/bit/DELAYED-COVER-BRIDGE.md": "9731b93026717f5fa15851e3633cbb4bdc76eba2bffb9d6b4a3b69f7dd502443",
+    "research/kappa-rebuild/bit/MIXED-PRODUCTIVE-BIT.json": "2f69a19f417c0e0d141c180f9b2fae3d358391b9a230f5848ee07c45450e70bf",
+    "research/kappa-rebuild/bit/bit_allsize_parameters.py": "59f92cf44019c27bde3db2f4482f2b5fcf25f0c3dcf071319d46b041f7b6a821"
+  },
+  "status": "PASS_EXACT_PARAMETERS_CONDITIONAL_ON_FINITE_UNIFORM_PRECOMPILATION",
+  "stock": {
+    "asymptotic": "Fixed compiled N,B,P: k=O_(N,B,q)(w*log e)=o(e), w=ceil(e^(3/1000)); pad high rows once by factor<2.",
+    "borrowed_digits": "k <= D_N(ceil(e/w))*(N^2*(w-1)+ceil(log_q(B*|GL_N(F_q)|)))+ceil(log_q S_old)+1",
+    "depth_bound": "D_N(n)=floor(log_N n) for rank<=floor(n/N) children; any larger explicit integer bound is safe.",
+    "descendant_weights": "Only final leaves are lowered. This outer cover row and role type become ancestor data; every next ordinary invocation has fresh disjoint role stock.",
+    "reserve": "S(e,w)=W(w)^D_N(ceil(e/w))*S_old(e,w)",
+    "role_divisor": "W(w)=B*|GL_N(F_q)|*q^(N^2*(w-1))"
+  },
+  "strict_power_gaps": {
+    "borrowed_stock_log_absorption": "9942581346203/10000000000000",
+    "final_relaxation": "418653797/10000000000000",
+    "linear_adapter": "2581346203/10000000000000"
+  }
+}