Integrate P33 cross-size covariance diagnostics

.github/workflows/threshold-rank-covariance-audit.yml

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+name: Threshold-rank covariance audit
+
+on:
+  push:
+    branches:
+      - research/threshold-rank-covariance-audit-20260828
+    paths:
+      - .github/workflows/threshold-rank-covariance-audit.yml
+      - scripts/audit_threshold_rank_covariance.py
+      - scripts/score_threshold_rank_root_doubling.py
+      - tests/test_threshold_rank_cross_size_covariance.py
+      - tests/test_threshold_rank_root_doubling.py
+  workflow_dispatch:
+
+permissions:
+  contents: write
+
+concurrency:
+  group: threshold-rank-covariance-audit
+  cancel-in-progress: false
+
+jobs:
+  audit:
+    runs-on: ubuntu-latest
+    timeout-minutes: 45
+    steps:
+      - name: Check out audit branch
+        uses: actions/checkout@v4
+        with:
+          ref: ${{ github.ref_name }}
+          fetch-depth: 0
+
+      - name: Set up Python 3.9
+        uses: actions/setup-python@v5
+        with:
+          python-version: '3.9'
+          cache: pip
+
+      - name: Install dependencies
+        run: python -m pip install --upgrade pip && python -m pip install -r requirements.txt
+
+      - name: Run covariance regression tests
+        run: >-
+          python -m unittest
+          tests.test_threshold_rank_cross_size_covariance
+          tests.test_threshold_rank_root_doubling
+          -v
+
+      - name: Reconstruct aligned cross-size covariance
+        run: |
+          rm -rf results/server-20260828/P33-cross-size-covariance
+          python scripts/audit_threshold_rank_covariance.py \
+            --histograms results/server-20260828/P33/p33_all_sizes_arm_10m.hist.csv \
+            --p 0.592746050790 \
+            --training-sizes 65,85,130 \
+            --heldout-sizes 145,170 \
+            --seed-label p33-working-tree-10m \
+            --output-dir results/server-20260828/P33-cross-size-covariance
+
+      - name: Score no-fit root-gap doubling relation
+        run: |
+          python scripts/score_threshold_rank_root_doubling.py \
+            --summary results/server-20260828/P33-cross-size-covariance/summary.json \
+            --json results/server-20260828/P33-cross-size-covariance/root_doubling.json \
+            --csv results/server-20260828/P33-cross-size-covariance/root_doubling.csv \
+            --report results/server-20260828/P33-cross-size-covariance/ROOT_DOUBLING_REPORT.md
+
+      - name: Record commands and source state
+        run: |
+          {
+            echo "source_commit=$(git rev-parse HEAD)"
+            echo "python=$(python --version 2>&1)"
+            echo "mpmath=$(python -c 'import mpmath; print(mpmath.__version__)')"
+            echo
+            echo "python scripts/audit_threshold_rank_covariance.py --histograms results/server-20260828/P33/p33_all_sizes_arm_10m.hist.csv --p 0.592746050790 --training-sizes 65,85,130 --heldout-sizes 145,170 --seed-label p33-working-tree-10m --output-dir results/server-20260828/P33-cross-size-covariance"
+            echo "python scripts/score_threshold_rank_root_doubling.py --summary results/server-20260828/P33-cross-size-covariance/summary.json --json results/server-20260828/P33-cross-size-covariance/root_doubling.json --csv results/server-20260828/P33-cross-size-covariance/root_doubling.csv --report results/server-20260828/P33-cross-size-covariance/ROOT_DOUBLING_REPORT.md"
+          } > results/server-20260828/P33-cross-size-covariance/provenance.txt
+          sha256sum \
+            results/server-20260828/P33-cross-size-covariance/* \
+            > results/server-20260828/P33-cross-size-covariance/checksums.sha256
+
+      - name: Commit generated audit outputs
+        env:
+          BRANCH_NAME: ${{ github.ref_name }}
+        run: |
+          git config user.name "github-actions[bot]"
+          git config user.email "41898282+github-actions[bot]@users.noreply.github.com"
+          git add results/server-20260828/P33-cross-size-covariance
+          if git diff --cached --quiet; then
+            echo "Audit outputs are already current."
+            exit 0
+          fi
+          git commit -m "analysis: record P33 cross-size covariance audit [skip ci]"
+          git push origin "HEAD:${BRANCH_NAME}"

results/server-20260828/P33-cross-size-covariance/ROOT_DOUBLING_REPORT.md

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+# Threshold-rank Gaussian root-gap doubling audit
+
+Frozen lineage prediction: `Delta p*(2N) / Delta p*(N) = -1/4`.
+Child signs follow multiplication by `1+i`, not stored display order.
+
+| lineage | observed ratio | ratio SE | full-cov residual z | diagonal residual z |
+|---|---:|---:|---:|---:|
+| 65->130 | -0.48492843 | 0.262 | 0.942 | 0.889 |
+| 85->170 | -0.61670569 | 0.268 | 1.649 | 1.628 |
+
+Full-covariance joint residual chi-square: **3.46246 / 2**.
+Diagonal diagnostic chi-square: **3.44173 / 2**.