Independently audit the PR5627 interface and complete recursive invoice

research/pr5627-interface-invoice-audit/PROOF.md

@@ -0,0 +1,91 @@
+# Separate replay of the PR5627 interface and invoice
+
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+
+## Result
+
+The emitted word at ed4dc88a09a7d201971f6603b8c2074e95dd9c32 has the stated
+complete normalized linear action. A new interpreter checks all 565504
+coefficients, every chart transition, every public input and every owned
+output. It imports no predecessor constructor, local verifier, native
+compiler or pricing engine. It reads the frozen word and controller as data.
+This is separate implementation evidence. It is not independent human review.
+
+The audit reproduces 743 public inputs, 535 productive helpers, nine owned
+roles, eleven owned lifetimes, peak occupancy two and 25448 events. The
+local paid histogram is {1:2200,2:456,3:494,4:91,5:163,6:18,7:15}.
+The helper histogram is {1:2,2:4,4:91,5:6,7:5,8:16,9:411}.
+In particular, the removed rank-two helper target is not still credited.
+
+The literal caller adds all eighteen full calls, fifteen query shears,
+and fifteen whole idle jobs, each on 208 fields. Its diagonal gives all
+3328 main targets. The complete bill has 66546 paid calls, 12958 targets
+and rank-mass surplus 760. These are exactly the source counts.
+
+## Exact interface interpretation
+
+Each row is an integer vector divided by a power of two. Initially the
+full matrix is the identity, including formal coordinates for owned roles.
+ADD and SCALE use exact integer arithmetic with a common binary denominator.
+COPY requires a live, zero owned destination in the source chart. INIT
+and CLEAR replace an owned row by zero under the inherited erasure contract.
+MOVE preserves normalized values and changes the chart. Every public move
+must strictly increase its binary span; every owned move must strictly
+decrease it. All scalar operations require equal physical charts.
+
+Induction on events proves that these rows are the exact normalized action.
+The final public row is e_r, with e_(r-112) added for the declared main
+output roles. Every owned row is zero. All helper inputs are independent
+coordinates in this check. The proof therefore covers the combined effect
+of the source's boundaries, splits and preparation without assuming their
+intermediate witness equations. It does not separately certify their
+constructor or their discovery search.
+
+A zero final owned row is not restoration of its initial dirty coordinate.
+INIT and CLEAR use the source's owned-erasure assumption. The receipt counts
+the nonzero rows discarded by CLEAR. No weaker erasure contract is asserted.
+
+## Separate complete invoice and raw ceiling
+
+The invoice is accumulated from the literal controller event types and its
+output diagonal. Source receipt counts are comparison values, not inputs
+to the computation. The native rank assigned to each strict nested chart
+move is the absolute chart-dimension change. This is the source native
+contract; its phase and implementation proof are not replayed here.
+
+The rational power engine is separate from both source engines. For
+r=2^k m with 1<=m<2, it evaluates log(r)=k log(2)+log(m). With
+ y=(m-1)/(m+1), the first 48 terms of
+
+    log(m)=2 sum_(j>=0) y^(2j+1)/(2j+1)
+
+have a nonnegative remainder at most
+
+    2*y^97 / (97*(1-y^2)).
+
+The same formula at y=1/3 encloses log(2). For every tested kappa, the
+argument x=kappa*log(r) is in [0,1). The degree-17 and degree-16 alternating
+Taylor sums enclose exp(-x) from below and above. Monotonicity in log(r)
+gives exact bounds on r^(1-kappa). All calculations use rational numbers.
+Only the final displayed intervals are rounded outward to denominator 10^24.
+
+The resulting target-minus-paid moment is positive at the claimed and
+tested savings, positive at 0.00310440547057 and negative at
+0.00310440547058. A separate termwise derivative bound is strictly negative
+on [0,0.0034]: for positive signed counts use the lower value of
+r^(1-kappa)*log(r) at the right endpoint; for negative counts use the upper
+value at zero. Thus this interval contains the unique raw crossing in the
+retained BIT range. This validates the raw ceiling of this fixed invoice,
+not a compiler or multiplication theorem.
+
+## Controls and exclusions
+
+The verifier rejects a missing input ADD, a wrong SCALE, erasure of a public
+input, a missing owned CLEAR, retention of the removed H2 target, and a
+missing whole idle. Normal and optimized execution use the same explicit
+checks; no Python assert statement carries a scientific condition.
+
+Native phases, actual physical caller execution, the finite compiler,
+outer predicates, precision, tape bounds and all-width admission remain
+inherited or unchecked by this package. No source file or selected result
+is changed. No new kappa is claimed.

research/pr5627-interface-invoice-audit/README.md

@@ -0,0 +1,31 @@
+# PR5627 interface and invoice audit
+
+The separate exact implementation in verify.py confirms the final emitted
+PR5627 local interface, all its chart and owned-state transitions, the
+complete recursive invoice and its unique raw crossing. It imports no
+source verification code. PROOF.md states the scope and the rational-series
+error bounds. RESULT.json records the exact evidence and six controls.
+
+Run `python3 -B scripts/research_package.py --package research/pr5627-interface-invoice-audit`.
+Python 3.12 and the standard library suffice.
+
+## Sources and credit
+
+PR5627 at ed4dc88a09a7d201971f6603b8c2074e95dd9c32 supplies the emitted word
+and the claim under audit. Exact source bytes, paths and hashes are retained
+in inputs/ and SOURCE-CONTEXT.json. The controller comes from the pinned
+main package. Ali Romman supplies the helper split and basis composition;
+flyingviper supplies the shared and delayed relay; Scratch-net supplies the
+preparation; Pierre-Loic Doulcet supplies the PR5565 cascade. Retain Cinna
+Davis, David Arias, Gareth Davidson, Jacob Alan Sussman, zxv, Cao Yifan and
+the complete source notices. This audit does not claim these constructions.
+
+## Open next questions
+
+Independently check the final word's native phase inventory and physical
+caller, then the complete compiler and outer conditions at this exact head.
+Do not transfer this audit to a successor word without checking its bytes.
+The five framework assumptions and helper-endpoint contract remain.
+Separate code is not independent human or proof-kernel acceptance.
+
+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.

research/pr5627-interface-invoice-audit/RESULT.json

@@ -0,0 +1,111 @@
+{
+  "complete_bill": {
+    "paid": {
+      "1": 41160,
+      "16": 416,
+      "2": 8208,
+      "24": 416,
+      "3": 8892,
+      "32": 416,
+      "4": 1638,
+      "40": 416,
+      "48": 416,
+      "5": 2934,
+      "56": 416,
+      "6": 324,
+      "64": 416,
+      "7": 270,
+      "72": 208
+    },
+    "paid_calls": 66546,
+    "productive_fields": 12958,
+    "rank_mass_surplus": 760,
+    "targets": {
+      "1": 36,
+      "145": 208,
+      "17": 416,
+      "2": 72,
+      "25": 416,
+      "33": 416,
+      "4": 1638,
+      "41": 416,
+      "49": 416,
+      "5": 108,
+      "57": 416,
+      "65": 416,
+      "7": 90,
+      "73": 208,
+      "8": 288,
+      "9": 7398
+    }
+  },
+  "limits": [
+    "Native phases, physical caller execution, compiler and outer conditions are not replayed.",
+    "Owned CLEAR is the inherited erasure operation, not restoration of an arbitrary dirty input.",
+    "This is a separate implementation check, not independent human or formal acceptance.",
+    "No new kappa and no selected-frontier change."
+  ],
+  "local": {
+    "endpoint_coefficients": 565504,
+    "helpers": {
+      "1": 2,
+      "2": 4,
+      "4": 91,
+      "5": 6,
+      "7": 5,
+      "8": 16,
+      "9": 411
+    },
+    "nonzero_owned_clears": 10,
+    "operations": {
+      "ADD": 21234,
+      "CLEAR": 11,
+      "COPY": 10,
+      "INIT": 11,
+      "MOVE": 3437,
+      "SCALE": 745
+    },
+    "owned_fields": 9,
+    "owned_lifetimes": 11,
+    "paid": {
+      "1": 2200,
+      "2": 456,
+      "3": 494,
+      "4": 91,
+      "5": 163,
+      "6": 18,
+      "7": 15
+    },
+    "paid_rank_mass": 5986,
+    "peak_owned_fields": 2,
+    "public_inputs": 743,
+    "real_scalar_allowance": 220154
+  },
+  "raw_derivative_denominator": 1000000000000,
+  "raw_derivative_upper_numerator": -235999800675475316,
+  "raw_intervals": {
+    "claim": {
+      "denominator": 1000000000000000000000000,
+      "lower_numerator": 2571624799184360834,
+      "upper_numerator": 2571624799184360835
+    },
+    "root_lower": {
+      "denominator": 1000000000000000000000000,
+      "lower_numerator": 1115959290001074,
+      "upper_numerator": 1115959290001075
+    },
+    "root_upper": {
+      "denominator": 1000000000000000000000000,
+      "lower_numerator": -1315931759985787,
+      "upper_numerator": -1315931759985786
+    },
+    "tested": {
+      "denominator": 1000000000000000000000000,
+      "lower_numerator": 1355679274148871187,
+      "upper_numerator": 1355679274148871188
+    }
+  },
+  "rejection_controls": 6,
+  "source_code_imports": 0,
+  "status": "PASS_PR5627_INTERFACE_INVOICE_AUDIT"
+}

research/pr5627-interface-invoice-audit/SOURCE-CONTEXT.json

@@ -0,0 +1,44 @@
+[
+  {
+    "file": "inputs/PR5627-WORD.json.gz",
+    "commit": "ed4dc88a09a7d201971f6603b8c2074e95dd9c32",
+    "path": "research/p104-helper-subspace-splits/WORD.json.gz",
+    "sha256": "162e6f13a6e3805517946309bd6247eaa45b337ab9c39621806b254b415075ec",
+    "git_blob": "b60955f312f76d08ee4f86ac2ad664e3ab4e46ea"
+  },
+  {
+    "file": "inputs/PR5627-RESULT.json",
+    "commit": "ed4dc88a09a7d201971f6603b8c2074e95dd9c32",
+    "path": "research/p104-helper-subspace-splits/RESULT.json",
+    "sha256": "f24925b2f549dce6ff404bd9d35fb0a19e5ebc5fa5cbf67996fd4064e450137b",
+    "git_blob": "1e90afdd0372980c68c1a444a6c0fe5f1e7da7c2"
+  },
+  {
+    "file": "inputs/PR5627-PROOF.md",
+    "commit": "ed4dc88a09a7d201971f6603b8c2074e95dd9c32",
+    "path": "research/p104-helper-subspace-splits/PROOF.md",
+    "sha256": "85c2fc0e87c129b3f5cb9b3c6ee6a0ad64b35f04cd58af912d500b37c2913da2",
+    "git_blob": "594b26982f6f81037e8649ba30da01221ee3bd58"
+  },
+  {
+    "file": "inputs/PR5627-PREPARATION.json",
+    "commit": "ed4dc88a09a7d201971f6603b8c2074e95dd9c32",
+    "path": "research/p104-helper-subspace-splits/PREPARATION.json",
+    "sha256": "72aebe0407f7e1566ccf50d8a6e971cb05d53c82e1cab2e8303fef49bac4d6f9",
+    "git_blob": "663e1f2bcbe9d9da566a7e4c3cb1201beebe3cd8"
+  },
+  {
+    "file": "inputs/PR5627-SPLITS.json",
+    "commit": "ed4dc88a09a7d201971f6603b8c2074e95dd9c32",
+    "path": "research/p104-helper-subspace-splits/SPLITS.json",
+    "sha256": "adc590f754105902cf11f4695a0d167de2d832fb75417745a725ecd3b89af396",
+    "git_blob": "9a9aa0c46013c63a58f456fc4e4deebc61925775"
+  },
+  {
+    "file": "inputs/PR5627-BOUNDARIES.json",
+    "commit": "ed4dc88a09a7d201971f6603b8c2074e95dd9c32",
+    "path": "research/p104-helper-subspace-splits/BOUNDARIES.json",
+    "sha256": "e5dc3ff85d6c7a104c0f02c03a9f873b3e5a8df46d240141024cb505390274e4",
+    "git_blob": "c6ce5174bd7d6908e47f7fa72b8eeee5185d7091"
+  }
+]

research/pr5627-interface-invoice-audit/SOURCES.json

@@ -0,0 +1,24 @@
+{
+  "schema_version": 1,
+  "base_commit": "6cf7a683f447b9f1e2333791907fd92be5009a63",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446",
+      "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/p104-productive-controller/CONTROLLER.json",
+      "usage": "input",
+      "git_blob": "cc539db709cf7a6c42872c4380902736ad453af3",
+      "sha256": "a84f6bbd547379597464e56c420cc665f96bc43a9a1351eed4b7cd0fce3cc4b9"
+    }
+  ]
+}