Research: averaged cyclotomic heights give O(r² log² r) precision (no new kappa)

.github/workflows/averaged-cyclotomic-height.yml

@@ -0,0 +1,43 @@
+name: Averaged cyclotomic height
+
+on:
+  workflow_dispatch:
+  pull_request:
+    paths:
+      - 'research/averaged-cyclotomic-height/**'
+      - '.github/workflows/averaged-cyclotomic-height.yml'
+  push:
+    branches: ['codex/averaged-cyclotomic-height-20261013']
+    paths:
+      - 'research/averaged-cyclotomic-height/**'
+      - '.github/workflows/averaged-cyclotomic-height.yml'
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    timeout-minutes: 30
+    strategy:
+      fail-fast: false
+      matrix:
+        python: ['3.11', '3.14']
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Install exact-algebra dependency
+        run: python -m pip install -r research/averaged-cyclotomic-height/requirements.txt
+      - name: Rational intervals, exact resultants and integer budgets
+        run: python -I -O -B research/averaged-cyclotomic-height/verify.py --out /tmp/averaged-height-math.json
+      - name: Package rejection controls and full read-only relocation
+        run: python -I -O -B research/averaged-cyclotomic-height/test_package.py --out /tmp/averaged-height-package.json
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: averaged-height-python-${{ matrix.python }}
+          path: |
+            /tmp/averaged-height-math.json
+            /tmp/averaged-height-package.json

research/averaged-cyclotomic-height-validation/LINUX314-PACKAGE.json

@@ -0,0 +1,66 @@
+{
+  "controls": [
+    {
+      "name": "missing manifest",
+      "rejected": true,
+      "terminal": "ValueError: missing package manifest"
+    },
+    {
+      "name": "altered implementation",
+      "rejected": true,
+      "terminal": "ValueError: package hash: budgets.py"
+    },
+    {
+      "name": "extra file",
+      "rejected": true,
+      "terminal": "ValueError: package file coverage"
+    },
+    {
+      "name": "missing source",
+      "rejected": true,
+      "terminal": "ValueError: package file coverage"
+    },
+    {
+      "name": "source hash independent of manifest",
+      "rejected": true,
+      "terminal": "ValueError: source SHA256: vendor/pr621/PROOF.md"
+    },
+    {
+      "name": "source Git object independent of manifest",
+      "rejected": true,
+      "terminal": "ValueError: source Git blob: vendor/pr621/PROOF.md"
+    },
+    {
+      "name": "duplicate manifest key",
+      "rejected": true,
+      "terminal": "ValueError: duplicate JSON key: files"
+    },
+    {
+      "name": "symlink injection",
+      "rejected": true,
+      "terminal": "ValueError: package symlink"
+    },
+    {
+      "name": "preloaded module substitution",
+      "rejected": true,
+      "terminal": "ValueError: local module binding: budgets"
+    },
+    {
+      "name": "false receipt boolean integer confusion",
+      "rejected": true,
+      "terminal": "ValueError: mathematical receipt mismatch"
+    },
+    {
+      "name": "existing output preserved",
+      "rejected": true
+    },
+    {
+      "name": "full read-only isolated optimized relocation",
+      "passed": true,
+      "receipt_sha256": "b25ae109654d2e3ac16e6348c982b86d8c07fca80d8cff600205511b9d2617bf"
+    }
+  ],
+  "full_readonly_replay": true,
+  "rejected": 11,
+  "status": "PASS_AVERAGED_HEIGHT_PACKAGE"
+}

research/averaged-cyclotomic-height-validation/LINUX314-PLATFORM.json

@@ -0,0 +1,11 @@
+{
+  "bytecode_disabled": true,
+  "isolated": true,
+  "machine": "aarch64",
+  "manifest_sha256": "7844dd0039723d9a955a2d0961ff1cb0f710f21277c0b2905577ad7b2b5c2f2a",
+  "mpmath": "1.3.0",
+  "optimized": true,
+  "platform": "Linux-6.17.0-1032-nvidia-aarch64-with-glibc2.39",
+  "python": "3.14.8",
+  "sympy": "1.14.0"
+}

research/averaged-cyclotomic-height-validation/LINUX314-TERMINAL.json

@@ -0,0 +1,6 @@
+{
+  "full_package_controls": true,
+  "manifest_sha256": "7844dd0039723d9a955a2d0961ff1cb0f710f21277c0b2905577ad7b2b5c2f2a",
+  "math_sha256": "b25ae109654d2e3ac16e6348c982b86d8c07fca80d8cff600205511b9d2617bf",
+  "status": "PASS_FROZEN_AVERAGED_HEIGHT_PACKAGE"
+}

research/averaged-cyclotomic-height-validation/LINUX314.log.txt

@@ -0,0 +1,40 @@
+PASS 752 integer budgets, exact logarithm enclosure and dyadic polynomial
+3 PASS rational interval enclosures
+4 PASS rational interval enclosures
+5 PASS rational interval enclosures
+7 PASS rational interval enclosures
+8 PASS rational interval enclosures
+9 PASS rational interval enclosures
+11 PASS rational interval enclosures
+13 PASS rational interval enclosures
+16 PASS rational interval enclosures
+17 PASS rational interval enclosures
+19 PASS rational interval enclosures
+23 PASS rational interval enclosures
+25 PASS rational interval enclosures
+27 PASS rational interval enclosures
+29 PASS rational interval enclosures
+31 PASS rational interval enclosures
+32 PASS rational interval enclosures
+3 PASS independent exact resultant
+4 PASS independent exact resultant
+5 PASS independent exact resultant
+7 PASS independent exact resultant
+8 PASS independent exact resultant
+9 PASS independent exact resultant
+PASS_AVERAGED_CYCLOTOMIC_HEIGHT interval_radices=17 exact_resultants=6 budgets=752 kappa=unchanged
+PASS package control missing manifest
+PASS package control altered implementation
+PASS package control extra file
+PASS package control missing source
+PASS package control source hash independent of manifest
+PASS package control source Git object independent of manifest
+PASS package control duplicate manifest key
+PASS package control symlink injection
+PASS package control preloaded module substitution
+PASS package control false receipt boolean integer confusion
+PASS package control existing output preserved
+PASS full read-only isolated optimized relocation
+PASS_AVERAGED_HEIGHT_PACKAGE rejected=11 full_readonly_replay=True
+PASS_AVERAGED_HEIGHT_BINDINGS sources=12
+PASS_FROZEN_AVERAGED_HEIGHT_PACKAGE

research/averaged-cyclotomic-height-validation/MACOS311-PACKAGE.json

@@ -0,0 +1,66 @@
+{
+  "controls": [
+    {
+      "name": "missing manifest",
+      "rejected": true,
+      "terminal": "ValueError: missing package manifest"
+    },
+    {
+      "name": "altered implementation",
+      "rejected": true,
+      "terminal": "ValueError: package hash: budgets.py"
+    },
+    {
+      "name": "extra file",
+      "rejected": true,
+      "terminal": "ValueError: package file coverage"
+    },
+    {
+      "name": "missing source",
+      "rejected": true,
+      "terminal": "ValueError: package file coverage"
+    },
+    {
+      "name": "source hash independent of manifest",
+      "rejected": true,
+      "terminal": "ValueError: source SHA256: vendor/pr621/PROOF.md"
+    },
+    {
+      "name": "source Git object independent of manifest",
+      "rejected": true,
+      "terminal": "ValueError: source Git blob: vendor/pr621/PROOF.md"
+    },
+    {
+      "name": "duplicate manifest key",
+      "rejected": true,
+      "terminal": "ValueError: duplicate JSON key: files"
+    },
+    {
+      "name": "symlink injection",
+      "rejected": true,
+      "terminal": "ValueError: package symlink"
+    },
+    {
+      "name": "preloaded module substitution",
+      "rejected": true,
+      "terminal": "ValueError: local module binding: budgets"
+    },
+    {
+      "name": "false receipt boolean integer confusion",
+      "rejected": true,
+      "terminal": "ValueError: mathematical receipt mismatch"
+    },
+    {
+      "name": "existing output preserved",
+      "rejected": true
+    },
+    {
+      "name": "full read-only isolated optimized relocation",
+      "passed": true,
+      "receipt_sha256": "b25ae109654d2e3ac16e6348c982b86d8c07fca80d8cff600205511b9d2617bf"
+    }
+  ],
+  "full_readonly_replay": true,
+  "rejected": 11,
+  "status": "PASS_AVERAGED_HEIGHT_PACKAGE"
+}

research/averaged-cyclotomic-height-validation/MACOS311-PLATFORM.json

@@ -0,0 +1,11 @@
+{
+  "bytecode_disabled": true,
+  "isolated": true,
+  "machine": "arm64",
+  "manifest_sha256": "7844dd0039723d9a955a2d0961ff1cb0f710f21277c0b2905577ad7b2b5c2f2a",
+  "mpmath": "1.3.0",
+  "optimized": true,
+  "platform": "macOS-27.0.1-arm64-arm-64bit",
+  "python": "3.11.15",
+  "sympy": "1.14.0"
+}

research/averaged-cyclotomic-height-validation/MACOS311-TERMINAL.json

@@ -0,0 +1,6 @@
+{
+  "full_package_controls": true,
+  "manifest_sha256": "7844dd0039723d9a955a2d0961ff1cb0f710f21277c0b2905577ad7b2b5c2f2a",
+  "math_sha256": "b25ae109654d2e3ac16e6348c982b86d8c07fca80d8cff600205511b9d2617bf",
+  "status": "PASS_FROZEN_AVERAGED_HEIGHT_PACKAGE"
+}

research/averaged-cyclotomic-height-validation/MACOS311.log.txt

@@ -0,0 +1,40 @@
+PASS 752 integer budgets, exact logarithm enclosure and dyadic polynomial
+3 PASS rational interval enclosures
+4 PASS rational interval enclosures
+5 PASS rational interval enclosures
+7 PASS rational interval enclosures
+8 PASS rational interval enclosures
+9 PASS rational interval enclosures
+11 PASS rational interval enclosures
+13 PASS rational interval enclosures
+16 PASS rational interval enclosures
+17 PASS rational interval enclosures
+19 PASS rational interval enclosures
+23 PASS rational interval enclosures
+25 PASS rational interval enclosures
+27 PASS rational interval enclosures
+29 PASS rational interval enclosures
+31 PASS rational interval enclosures
+32 PASS rational interval enclosures
+3 PASS independent exact resultant
+4 PASS independent exact resultant
+5 PASS independent exact resultant
+7 PASS independent exact resultant
+8 PASS independent exact resultant
+9 PASS independent exact resultant
+PASS_AVERAGED_CYCLOTOMIC_HEIGHT interval_radices=17 exact_resultants=6 budgets=752 kappa=unchanged
+PASS package control missing manifest
+PASS package control altered implementation
+PASS package control extra file
+PASS package control missing source
+PASS package control source hash independent of manifest
+PASS package control source Git object independent of manifest
+PASS package control duplicate manifest key
+PASS package control symlink injection
+PASS package control preloaded module substitution
+PASS package control false receipt boolean integer confusion
+PASS package control existing output preserved
+PASS full read-only isolated optimized relocation
+PASS_AVERAGED_HEIGHT_PACKAGE rejected=11 full_readonly_replay=True
+PASS_AVERAGED_HEIGHT_BINDINGS sources=12
+PASS_FROZEN_AVERAGED_HEIGHT_PACKAGE

research/averaged-cyclotomic-height-validation/README.md

@@ -0,0 +1,38 @@
+# Frozen averaged-height validation
+
+The complete package in `../averaged-cyclotomic-height` passed on macOS
+arm64 / Python 3.11.15 and Linux aarch64 / Python 3.14.8, both with
+SymPy 1.14.0 and mpmath 1.3.0. Each replay used `-I -O -B`.
+
+Each platform ran all 17 rational interval cases, six exact resultants and
+752 integer budgets three times: the ordinary verifier, the deliberately
+altered-receipt rejection, and the full read-only relocation. Each package
+harness rejected eleven faults. The full mathematical receipts are byte
+identical after decompression, including all rational endpoints and integer
+budget rows. The Linux source tree was read-only and outside Git; its
+supervisor recorded exit code zero.
+
+- Mathematical receipt SHA256:
+  `b25ae109654d2e3ac16e6348c982b86d8c07fca80d8cff600205511b9d2617bf`.
+- Source manifest SHA256:
+  `7844dd0039723d9a955a2d0961ff1cb0f710f21277c0b2905577ad7b2b5c2f2a`.
+- `SOURCE-GIT-CHECK.json` records the twelve retained files checked against
+  immutable original Git objects before replay.
+- `MACOS311-*` and `LINUX314-*` contain the complete math, package-control,
+  platform and terminal receipts. The logs record successful completion.
+- `REPOSITORY-CHECKS.log.txt` records the selected-record check and all
+  25 selected-record/inventory/proof-binding tests at the publication base.
+
+The preparation base recorded in the frozen source pins is
+`8bddbee377e2f3ce1f1247196c4b290d55767d20`. The isolated publication branch
+was subsequently advanced to main
+`2921874911956718fcaaaf9396fe8267b3cfa9f0` without changing any frozen
+package byte. Main still selects PR942 at
+`1661960547713947/10^18`. This contribution does not change that selection.
+
+The all-size claim comes from the written proof. The large-radix rows test
+exact exponent arithmetic; no inverse at those enormous word sizes was
+executed. The full repository suite, selected construction's cold replay
+and full multiplication theorem were not verified here. No independent
+human/delegated-agent review or practical speedup is claimed. Hosted CI is
+separate from these retained local platform results.

research/averaged-cyclotomic-height-validation/REPOSITORY-CHECKS.log.txt

@@ -0,0 +1,12 @@
+Publication base: 2921874911956718fcaaaf9396fe8267b3cfa9f0
+COMMAND ['make', 'selected-record-check']
+python3 -B scripts/verify_selected_result.py
+PASS selected record, exact kappa, original source inventory and proof supplement: 1661960547713947/1000000000000000000
+EXIT 0
+COMMAND ['python3', '-B', '-m', 'unittest', 'discover', '-s', 'tests', '-p', 'test_selected*.py']
+.........................
+----------------------------------------------------------------------
+Ran 25 tests in 0.327s
+
+OK
+EXIT 0