Multi-advance 20260913: spatial-source Hessian, invisible marks, annealed/quenched roots, rank-source zero-free strip, conditional-odds integration, limit-order audit (do not merge)

[LightChainr]

Deliverable: a validated multi-advance analysis package (2026-09-13)

Pure additive contribution stacked on #710 (analysis/width4-parametric-onsets-20260912), which itself stacks on #708. All new files live under delivery/, source_inputs/, execution/ plus root VALIDATION.json / HIGH_PRECISION.json / REMOTE_ACTIONS.json. The official root README.md is untouched; STATUS is unchanged; do not merge.

Contents (8 notes + 5 scripts + 3 tests + 5 result JSONs)

1. Spatial-source Hessian — complete finite 4x4 torus Hessian with exact Bernstein coefficients, Fourier diagonalization (six D4 orbits), root Hessian inertia (9,6,1), and a logit-vs-additive coordinate caveat. (notes/spatial-source-hessian-20260913.md, scripts/torus_source_hessian.py, scripts/verify_source_hessian.py, results/.../full-site-hessian*.json)
2. Invisible spatial marks — L/T marks with identical uniform-p joint law of (r,K) but independent nonzero spatial-source distinctions; determinant 131072. (notes/invisible-spatial-marks-20260913.md, scripts/invisible_spatial_marks.py, results/.../invisible-spatial-marks.json)
3. Annealed/quenched roots — finite quenched order, no infinite-volume annealing claim. (notes/annealed-quenched-root-20260913.md)
4. Rank-source zero-free strip — Re Z(x+iy)>0 for |y|<pi/2; extensive-source controls approach the limiting max 0.1. (notes/rank-source-zero-free-strip-20260913.md, scripts/topological_source_zeros.py, results/.../topological-source-zeros.json)
5. Conditional-odds integration — finite-sum differentiation with exact controls. (notes/conditional-odds-integration-20260913.md, scripts/conditional_odds_integration.py, results/.../conditional-odds-integration.json)
6. Limit-order readout audit — audit of the limit-order readout in the existing corpus. (notes/limit-order-readout-audit-20260913.md)

Validation

• 27 applied tests, all passed (0.538 s; python 3.13.5, mpmath 1.3.0) — execution/applied-tests.log.
• All 5 scripts re-run; outputs byte-identical except elapsed_seconds — recorded in VALIDATION.json and execution/high-precision.log.
• VALIDATION.json records sha256 + bytes for all 21 files with applied_byte_identical: true; pinned input hashes match source_inputs/.
• Patch stat: 21 files, 6127 insertions — execution/patch-stat.log.
• No Monte Carlo; finite numerical roots are diagnostics, additive Hessian signs and mark determinants have exact rational/integer certificates.

Inputs (unchanged copies for reproduction)

• source_inputs/width4-rank-closure-certificate.json — unchanged PR708 certificate (Git blob 50b7297deefe7c50215aea2ed534ca5810461af3).
• source_inputs/width4-parametric-definition.json — sha256 5edc6243…, hard-checked by topological_source_zeros.py.

Known gap (open)

Three large raw artifacts from the zip are NOT committed here because the remote file-push channel cannot carry their content: results/research-control-20260912/full-site-hessian.json (118,841 B), source_inputs/width4-rank-closure-certificate.json (242,514 B) and matching-one-multi-advance-20260913.patch (285,334 B). Mitigations: full-site-hessian.json is regenerated deterministically by torus_source_hessian.py (~1 s) and cross-checked by verify_source_hessian.py; the certificate already exists on this branch's ancestors (#708); the patch is the same diff that delivery/ already materializes. VALIDATION.json still lists all 21 files with their pinned hashes so a later full sync can be verified.