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Proof vault for Gaussian random fields and persistent homology: full arguments, exact computations, source-bound reviews, and explicit open obligations.

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Universal Law — mathematics, evidence and verification

Mathematics — proofs, calculations, and open reviews

Research home · Topic guide · Run the checks · How to cite · Claim manifest · Proof availability · Work queue (closed downstream record; not a live queue) · Active coordination (historical #475 board) (historical #419 board) (historical #307 board) (historical #229 board; working guidance)

Read a result

Topic Proof or entry point Review and scope
Gaussian lifetime coefficient SIDE24 dimensions 2 and 3 main #65 verifies the calculation; its reading as the parent Theorem C coefficient is reconciled at existential scope; no finite-radius band
Quantitative lifetime density Bounded unrestricted remainder main #67 accepts Theorem R at its existential O(1) scope; its parent interfaces are reconciled; no numerical constants
RN critical-point counting Probability-to-count interface Exact implications and counterexamples; the Gaussian triple integral is not evaluated
RN fixed-remote height window Cubic count and contact kernel Actual count bound on a fixed remote region; shrinking spatial cutoffs and witness collisions remain outside scope
RN reviewed fixed-annulus height window Fixed scaled-annulus theorem Source-bound nonauthor review accepts the fixed d=2 annulus / compact positive-gap / between-pin-window scope only; no global D5/RN/JETMOD closure
P15 obstruction covers Original-coordinate realization Specified family and cover; 816 versus whole-ground 818
P15 failed extension Price-range counterexample Unrestricted same-palette transformed-price extension is false
P15 valid price extension Low-probability transformed-price budget New sufficient hypotheses: demand at least 2 and probabilities at most 1/4
P15 full probability range Full transformed-price budget and sharp constant Source-bound nonauthor review accepts Theorem F on the realized family only: demands at least 2; every independent probability vector; same palette; sharp uniform factor 1/[3-log(3e-2)]
Downstream hard gate Fail-closed promotion control main #90 / #86; integrity only; lemma_closed stays false

Each row is governed by its exact statement, source identity, domain, dependencies, and review object in claims/LANDING_CLAIMS.json. Some rows remain author-side; the two lifetime rows, the fixed-annulus height-window row and the P15 full-range row have scoped nonauthor reviews. A merge or green test never broadens a claim beyond that recorded scope. The counterexample and the restricted successor concern different hypotheses. The full-range successor removes the probability cutoff, not the demand or realized-family hypotheses; the older 16/27 factor remains better on its smaller domain.

These rows are the 24–25 September 2026 landing set, not the newest results. For later work, use proof availability and the proof-reachability record, which inventories the one-level frontier proofs at its 2–3 October 2026 cuts. Frontier folders merged after that cut are not yet in either index; open them in the frontier directory, where folder names carry their dates, or from the merged pull requests. A merge or a listing is not acceptance; each packet's README and review records state its scope.

Run a calculation

All commands below use the Python standard library and run from this repository root.

python -B -S coefficients/side24_v1/coefficient.py
python -B -S -m unittest discover -s coefficients/side24_v1 -p 'test_*.py' -v
python -B -S -m unittest discover -s frontiers/three_fronts_20260924 -p 'test_*.py' -v
python -B -S frontiers/remote_window_20260924/remote_window.py
python -B -S -m unittest discover -s frontiers/remote_window_20260924 -p 'test_*.py' -v
python -B -S frontiers/price_budget_20260924/price_budget.py
python -B -S -m unittest discover -s frontiers/price_budget_20260924 -p 'test_*.py' -v
python -B -S frontiers/full_price_20260924/full_price.py
python -B -S -m unittest discover -s frontiers/full_price_20260924 -p 'test_*.py' -v
python -B -S frontiers/downstream_gate_20260925/hard_gate.py
python -B -S -m unittest discover -s frontiers/downstream_gate_20260925 -p 'test_*.py' -v

The full-price package has 36 distinct tests and seven semantic mutation controls. Run python -B -S frontiers/full_price_20260924/run_validation.py --output /tmp/full-price-new-run for both modes; choose a new output directory outside the source tree. --mode normal or --mode optimized permits bounded split runs. Finite probability grids are checks, not the proof of the full-cube statement.

Full reproduction guide explains normal/optimized runs, mutation controls, and pinned versus current-source replay. Frontier directory groups the packages. Older dated source files are retained unchanged; use the review links for subsequent corrections.

Where the other work lives

main holds the campaign, reviews and legacy research-branch links. meta-framework holds exact source identities; query- looks them up; trial is the historical integration lab; google-drive carries selected public replicas with exact source identities, not a Drive backup. Both stay public under the 6 October surface decision; as of 7 October 2026 neither is archived, and archiving is an owner action. Private experiments are not exported through those public routes.

Byte copies of eight hardening-branch lemma proofs and the P15-B proof, plus a transcription of closed main #59, are in the custody ledger. That ledger is source availability only. It does not adopt source labels and does not change lemma_closed, prizes, premises, or the claim manifest.

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