Combine T37 and T8 chronology: conditional κ > 0.00173004755209

research/staged-width-t450/CLAIM.json

@@ -0,0 +1,27 @@
+{
+  "replicas": 450,
+  "calls": 4050,
+  "roles": 1652400,
+  "physical": 403709,
+  "profile": {
+    "1": 9983580,
+    "2": 2940300,
+    "3": 936579,
+    "4": 413100,
+    "5": 87495,
+    "8": 32400,
+    "48": 172221
+  },
+  "root_interval": [
+    "0.001730047552093344159584",
+    "0.001730047552093344159585"
+  ],
+  "candidate_endpoint": "17300475520933441595839999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "frontier_pr": 3605,
+  "frontier_head": "3efbb5de06a49ffeea6684482f2d3fe48cdca3fb",
+  "frontier_sha256": "2e721209f626d5111142951b1f26383d6746b4f230a4625244b5e5c84d6079d5",
+  "scope": "Complete source-bound conditional release with authenticated same-session native reuse; inherited mathematical premises remain.",
+  "status": "PASS_COMPLETE_CONDITIONAL_RELEASE",
+  "kappa": "17300475520933441595839999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "evidence": "evidence/EVIDENCE-PINS.json"
+}

research/staged-width-t450/CREDITS.md

@@ -0,0 +1,11 @@
+# Credits and provenance
+
+Ross Richardson’s PR3605 (`3efbb5de06a49ffeea6684482f2d3fe48cdca3fb`) supplies the staged-width words, predecessor T740 release and integral-network allocation machinery. The supplier artifacts and owner machinery retain their original notices and source pins.
+
+Our PR3494 (`5c139955cc707b4a362cd20779ef361a930648f4`) supplies the retained T8 chronology. Earlier T16/T8 investigations informed the combination and allocation method. Their numerical gains are not counted twice.
+
+The contribution here is the combined chronology, its exact allocation on 450 replicas, deterministic literal construction, and completed source-bound admission. The private optimizer, integer-repair tools and journal are excluded.
+
+The retained `research/t8-rank7-two-swaps` materializer preserves the earlier rank-seven supplier, compiler, controller and conditional-release chain, including the PR3133 contributor notices. Exact sources are recorded in the accompanying provenance manifests in this package.
+
+Prepared for the hexapode account with substantial OpenAI Codex assistance in mathematics, implementation, independent same-session checks and prose. New material is Apache-2.0. No independent human acceptance or formal verification of the complete multiplication theorem is claimed.

research/staged-width-t450/EXECUTION-COVERAGE.json

@@ -0,0 +1,127 @@
+{
+  "status": "PASS_TERMINAL_T450_FULL_ADMISSION",
+  "authoritative_session": 1122,
+  "exit_code": 0,
+  "source_pins": {
+    "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/RESULT.json": "a8f36c25dd0a0615931eebaae5ff4e0288de519585d7e12924b218660a46873a",
+    "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/release/RELEASE-RECEIPT.json": "6cc5ebd42a949ba0d12aac17b6213f84e653f801feba90c3760dd89d35321161",
+    "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/CURRENT-FRONTIER-CHECK.json": "489a7ee9a1acc8ef9dbaef32463c6a25519be0fe34fa1c29b041c74f91dba534",
+    "/private/tmp/integer-mult-experiments/contract/pr3605-t450-admission-command.json": "3ed00ef796cbd23c2f49fbe896da62fa74317de22eae1bed6185d98aa603d74b",
+    "/private/tmp/integer-mult-experiments/contract/pr3605_t450_entry.py": "35ccfb17fcdf019d32eb2b786caede4e7e442966403d70a0b63006d7d90ec20f",
+    "/private/tmp/integer-mult-experiments/contract/pr3605-public-full-replay/changed/native/NATIVE-RECEIPT.json": "411b6fc1ac480263a90d36eca58c109687307e9a2d204af3ed4d002f9f8ff629",
+    "/private/tmp/integer-mult-experiments/contract/pr3605-t450-portable-live-equivalence.json": "b9cdf65cc9f43fd043a1723f2bdccf8067cf961eabaf084fe1644053722dd77b"
+  },
+  "stages": [
+    {
+      "name": "owners",
+      "exit_code": 0,
+      "seconds": 32.495388834009646,
+      "command": [
+        "/private/tmp/integer-mult-experiments/adversarial/cap740-venv/bin/python",
+        "-B",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/package/reconstruct.py",
+        "--out",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/owners"
+      ]
+    },
+    {
+      "name": "parent-lift",
+      "exit_code": 0,
+      "seconds": 69.96427941598813,
+      "command": [
+        "/private/tmp/integer-mult-experiments/adversarial/cap740-venv/bin/python",
+        "-B",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/package/lift_parent.py",
+        "--package",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/package",
+        "--owners",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/owners",
+        "--out",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/parent-data"
+      ]
+    },
+    {
+      "name": "rebind",
+      "exit_code": 0,
+      "seconds": 6.081565125001362,
+      "command": [
+        "/private/tmp/integer-mult-experiments/adversarial/cap740-venv/bin/python",
+        "-B",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/package/new/rebind.py",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/package",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-public-full-replay/changed/native/native-cache/735c540b1fe29d0ceeb4d2f304ec941e5f2bd3bc92bafc8cce2b4f9a67a3b653/local",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-public-full-replay/changed/native/native-cache/886338fc32da14f3389a82c8120a1bcf9c5e2f0ec3e9b2d377fdae809e1d977f/local",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/rebound"
+      ]
+    },
+    {
+      "name": "discovery",
+      "exit_code": 0,
+      "seconds": 545.0851802910038,
+      "command": [
+        "/private/tmp/integer-mult-experiments/adversarial/cap740-venv/bin/python",
+        "-B",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/layout/packing74/replay.py",
+        "--data",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/layout/packing74/candidate",
+        "--work",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/discovery",
+        "--local",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-public-full-replay/changed/native/native-cache/735c540b1fe29d0ceeb4d2f304ec941e5f2bd3bc92bafc8cce2b4f9a67a3b653/local",
+        "--discover"
+      ]
+    },
+    {
+      "name": "outer-check_ledger.py",
+      "exit_code": 0,
+      "seconds": 0.12613950000377372,
+      "command": [
+        "/private/tmp/integer-mult-experiments/adversarial/cap740-venv/bin/python",
+        "-B",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/package/outer/check_ledger.py"
+      ]
+    },
+    {
+      "name": "outer-independent_check.py",
+      "exit_code": 0,
+      "seconds": 0.034549625008367,
+      "command": [
+        "/private/tmp/integer-mult-experiments/adversarial/cap740-venv/bin/python",
+        "-B",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/package/outer/independent_check.py"
+      ]
+    },
+    {
+      "name": "release",
+      "exit_code": 0,
+      "seconds": 836.9905952500121,
+      "command": [
+        "/private/tmp/integer-mult-experiments/adversarial/cap740-venv/bin/python",
+        "-B",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/package/verify_release.py",
+        "--main",
+        "/private/tmp/integer-mult-experiments/contract",
+        "--work",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-t450-full-admission/release",
+        "--native-cache",
+        "/private/tmp/integer-mult-experiments/contract/pr3605-public-full-replay/changed/native/native-cache",
+        "--jobs",
+        "2"
+      ]
+    }
+  ],
+  "kappa": "17300475520933441595839999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "profile": {
+    "1": 9983580,
+    "2": 2940300,
+    "3": 936579,
+    "4": 413100,
+    "48": 172221,
+    "5": 87495,
+    "8": 32400
+  },
+  "native_coverage": "Fresh both-current-provider five-stage cache authenticated and reused; retained parent evidence separately authenticated. T450 did not rerun cold native providers.",
+  "portable_coverage": "Exact portable/live source and driver equivalence; no completed T450 portable CLI claimed.",
+  "admission_scope": "Conditional inherited all-size/compiler/precision assumptions remain. Internal supplier endpoint differs from global outer headline.",
+  "scientific_source_mutations_during_run": false
+}

research/staged-width-t450/EXPECTED.json

@@ -0,0 +1,24 @@
+{
+  "replicas": 450,
+  "calls": 4050,
+  "roles": 1652400,
+  "physical": 403709,
+  "profile": {
+    "1": 9983580,
+    "2": 2940300,
+    "3": 936579,
+    "4": 413100,
+    "5": 87495,
+    "8": 32400,
+    "48": 172221
+  },
+  "root_interval": [
+    "0.001730047552093344159584",
+    "0.001730047552093344159585"
+  ],
+  "candidate_endpoint": "17300475520933441595839999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "frontier_pr": 3605,
+  "frontier_head": "3efbb5de06a49ffeea6684482f2d3fe48cdca3fb",
+  "frontier_sha256": "2e721209f626d5111142951b1f26383d6746b4f230a4625244b5e5c84d6079d5",
+  "scope": "Finite profile expectation; complete admission checked separately."
+}

research/staged-width-t450/FRONTIER.json

@@ -0,0 +1,33 @@
+{
+  "calls": 6660,
+  "dimension": 73,
+  "generated_package_manifest_sha256": "d516ed4734f0d10d99fd157db769d72fe372ca09947e1d2c5ac93a27f0142dda",
+  "kappa": "17300065495388418470049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa_decimal": "0.0017300065495388418470049999999999999999999998999999999999999999999999",
+  "live": 663040,
+  "local_publication_head": "ac92a027c78b0c9bb0ada739b26959afda489d0e",
+  "owner_payload_sha256": "653085641ff2e9470e25aedfc92861ec34e5cf594d52123e8b28b6f0ec20b9f8",
+  "physical": 663549,
+  "profile": {
+    "1": 16417896,
+    "2": 4835160,
+    "3": 1540174,
+    "4": 679321,
+    "48": 283185,
+    "5": 143992,
+    "6": 3,
+    "8": 53280
+  },
+  "release_receipt_sha256": "ce1ce9d9ad3ac9440057534d19e06b7cb4fb8da98ba5e72e01ce538b59eb2f40",
+  "replicas": 740,
+  "roles": 2717280,
+  "root_interval": [
+    "346001309907768369401/200000000000000000000000",
+    "865003274769420923503/500000000000000000000000"
+  ],
+  "scope": "Complete fixed T740 source/native/owner/physical/prefix/outer release bound to the stated exact endpoint. All inherited all-size/compiler/uniform-cost/hosting/bootstrap-time/PR559/rounding/tape/recovery/analytic/BIT H1-H5 hypotheses remain. No unconditional or formal-kernel theorem or selected-record update.",
+  "source_manifest_sha256": "adb145b4f36ca330c34c0dbdb847351dafdc4ca9cd7bb4e1de01ed634d96bfe1",
+  "status": "CONDITIONAL_RELEASE_BOUND",
+  "unchanged_bit_endpoint": "0.001733427039589844234749",
+  "validation_binding": "evidence/FINAL-BINDING.json"
+}

research/staged-width-t450/PROOF.md

@@ -0,0 +1,47 @@
+# T450 construction argument and conditional release
+
+## Sources and chronology
+
+Use the two unchanged staged-width suppliers of PR3605, with their preserved source pins and native programs. Concatenate the inherited 37-replica order with the retained T8 order from PR3494, renumbering the eight replicas as 37 through 44. Preserve each constituent’s provider dispatch. Recompute every physical source window from the actual parent geometry and the combined order; do not merely shift a declared window. In particular, the initial lower boundary stays global rather than becoming the join between the two blocks.
+
+The aggregate certificate uses ten copies of this 45-replica chronology. There are 4,050 calls, each with 408 helper roles, hence 1,652,400 individual assignments. Both providers have the same paid local profile and width inventory, but the dispatch and both actual native words remain separately authenticated.
+
+## Exact cost and comparison
+
+The paid profile is
+
+`9983580 H(1) + 2940300 H(2) + 936579 H(3) + 413100 H(4) + 87495 H(5) + 32400 H(8) + 172221 H(48)`,
+
+where `H(r)=r^(1−κ)`. Its rank mass is exactly `65088*450`. The normalized cost is
+
+`F(κ)=sum_r n_r*(r/73)^(1−κ)/(896*450)`.
+
+Every occupied rank is positive and less than 73, so F is strictly increasing. Since `F(0)=65088/65408<1`, the two rational sign enclosures in `verify_price.py` certify the unique positive crossing between `0.001730047552093344159584` and `0.001730047552093344159585`.
+
+Different replica counts must be normalized. The checker compares `740*profile_T450 − 450*profile_T740`, whose nonzero signed coefficients are
+
+`−204000 H(1) − 9840 H(3) − 450 H(4) − 50100 H(5) − 1350 H(6) + 10290 H(48)`.
+
+Its rank mass is zero and its cost is strictly negative at the pinned predecessor root’s upper endpoint. The admitted conditional endpoint is the candidate root’s lower endpoint minus `10^−46 + 10^−70`; the completed source-bound release establishes exactly that endpoint. No earlier T8 or T16 numerical gain is added again.
+
+## Constructive assignment
+
+Integer pattern counts fill the physical groups. Integer role flows obey actual source windows, per-width demand, and per-call group capacity. Every occupied pattern has at most five slots, below the copy count ten.
+
+The retained integral-network decomposition applies to this general copy count. With R copies remaining, assigning each remaining role fraction 1/R satisfies the width quotas, the per-bin unit capacity, and the group bounds needed to preserve feasibility for R−1 copies. Integral lower-bound flow selects the next copy. Sorting bins by their latest required copy at the upper endpoint gives compatible physical owner copies. The actual source-family windows are disjoint, preventing a family collision across different child windows.
+
+A grouped time describes ten successive copied calls, not one physical call. A bin can therefore hold several roles at that grouped time if they occur in distinct actual calls. The builder and independent literal auditor check the actual call times; a one-call capacity inequality imposed on an entire grouped time would be invalid.
+
+The deterministic literal construction and independent native-frame audit have passed for all 1,652,400 roles, including five rejection controls. This does not replace the full release.
+
+## Physical stock and precision
+
+The live stock is `896*450`. The retained private stock is `408+8+91+2`, giving a total of 403,709 physical families. This fits the original `2^20` sufficient ceiling; the larger-stock generalization explored for T2220 is unnecessary here.
+
+Exact stock arithmetic gives norm exponent 1324. The conservative reserve is `128+37+18+1324+1+4=1512<2048`. The completed source-bound admission checks actual prefix 1479, namespaces, arbitrary dirty endpoints, buffer cleanup and the full outer ledger. Stored receipts are authenticated by `verify_evidence.py`; the numerical reserve calculation alone would not establish them.
+
+## Scope and open next questions
+
+All inherited all-size, compiler, uniform-cost, hosting, bootstrap-time, rounding, tape/recovery, analytic and BIT endpoint assumptions remain. Same-session independent checks are not independent human review or formal-kernel verification.
+
+The next construction question is whether another chronology or supplier changes the complete cost. The first step is an exact cost and feasibility screen. The separate theoretical question is how to discharge the inherited all-size premises; this finite allocation does not settle it.

research/staged-width-t450/README.md

@@ -0,0 +1,39 @@
+# Combining T37 and T8 chronology with the staged-width suppliers
+
+**Complete source-bound T450 admission passes, with conditional κ = `0.001730047552093344159584 − 10^−46 − 10^−70`.**
+
+This candidate combines the 37-replica chronology underlying Ross Richardson’s PR3605 with our retained eight-replica chronology from PR3494. A new integer allocation uses ten copies of the combined 45-replica order, for 450 replicas in total. It preserves both staged-width suppliers from PR3605.
+
+The complete finite profile has its root between `0.001730047552093344159584` and `0.001730047552093344159585`, above the T740 profile at PR3605 commit `3efbb5de06a49ffeea6684482f2d3fe48cdca3fb`. All 1,652,400 individual assignments passed an independent native-frame owner audit. The full physical, precision and outer release passes.
+
+The package contains the integer certificate, deterministic builder and verification code. Private optimization tools and the research journal are excluded. From the repository root, run the bounded finite checks with Python 3.12 and the dependencies declared in `VERIFY.json`:
+
+```sh
+python3 -B research/staged-width-t450/verify.py
+```
+
+This authenticates declared source inputs, reconstructs the actual aggregate profile, checks its rational root and predecessor comparison, and runs semantic and import-authentication rejection controls. It does not rerun every literal role or full admission. The separate `verify_price.py` convenience command prices the pinned expected profile only.
+
+For deterministic literal reconstruction, choose a fresh output directory:
+
+```sh
+OWNER_SOURCE_REPO="$PWD" python3 -B research/staged-width-t450/owners/portable_expand.py --out /tmp/t450-owners
+```
+
+For complete source/native/physical/precision/outer replay, use another fresh output directory:
+
+```sh
+python3 -B research/staged-width-t450/replay.py --t8-package research/t8-rank7-two-swaps --main-files . --allocation /tmp/t450-owners --work /tmp/t450-release
+```
+
+The portable command explicitly authenticates retained parent-cache reuse, reconstructs the changed supplier sources, runs both changed native suppliers freshly, and invokes full admission with the original stock checker. The completed separate admission run instead reused those same-session freshly checked changed native caches with exact source and word bindings. The complete portable T450 command has not been run end to end with fresh changed-native execution; the completed admission used authenticated same-session native caches. Stored evidence, finite checks and full replay have different coverage; `VALIDATION.json` records the exact coverage. The finite command also authenticates the stored completed release receipts; that is not a fresh complete replay.
+
+Independent native-frame literal-audit instructions are in `owners/README.txt`. That audit checks every assignment but does not replace the complete release.
+
+See `PROOF.md` for the construction argument and `CREDITS.md` for attribution. All inherited conditional premises remain; this is not an unconditional multiplication theorem or a change to the selected result.
+
+## Open next questions
+
+Can a different combined chronology improve the profile further? Start with source-derived windows and an exact integer certificate before literal expansion. For this fixed 45-replica chronology and proportional profile, ten copies are the minimum permitted by integer profile counts; that is not a lower bound for other profiles or orders.
+
+Can a changed supplier or recursive interface improve the underlying cost? Estimate source acquisition, delivery, restoration and the full physical bill before a large search.