Integration proof bundle

The ledger is a 14 October 2026 development. It is not an amendment of Paper VII, and it does not certify an external mathematics release. Each record states assumptions, a conclusion, a written argument, and a limit. The statuses in the table below are the bundle’s labels.

$G=a\varphi$ and $C=a\pi$ are selected readouts. $C$ is not the retained major-arc length. $q=339949771344778/10^{15}$ is not $\lambda=\varphi/(\varphi+\pi)$. The canonical sine is not evaluated. An auxiliary rational seed such as $s=1/2$ is not that sine. The cyclotomic check is the order 2,592,000 and the ambient real degree 345,600. It is not an expansion in that basis.

Pi transcendence and the cyclotomic degree formula are named classical dependencies. They are not reproved here.

The certificate file is 1,722,817 bytes, SHA-256 daaee23b3c27bbb320d0f8db2c8d00a4a077f08e5fe0056864323873ddf71b19. That is the digest named by the checker and by the ledger. This archive ran verify.py on those bytes with Python 3.10.21. Both modes exited 0. The two logs are byte-identical.

The supplied report is Python 3.13.5. Its file is 2,820 bytes, SHA-256 eb4dab39fc196a2f1f09b9cac36f94ec0d28fae6595b07a349f28fc02dfbed91, the digest named in the supplied status. This archive’s report matches that report except the runtime string. Matching mathematical fields supports execution agreement. The logs are not byte-identical across the two interpreters.

The 2,314 algebra checks split into two kinds. An eq check with free variables is a polynomial identity under the program’s construction, not one numerical example. A constant positivity check is an inequality of one exact constant. Some groups are finite fixed cases. The checker’s own limit says that normalizing a polynomial does not prove an analytic limit, a quantifier over arbitrary functions, or positivity under a variable inequality.

The finite audit is separate: 32,768 seeds, horizon 23, 753,664 transitions, maximum extinction step 10, and 8 rejected malformed inputs. The floor maps agree for integers $0\le d<42189065$ by the stated floor-sum certificate. That threshold was not enumerated state by state. At 42,189,065 the certified floors are 14,342,163 and 14,342,162. This is a different program from the transition checker and the 13 October recovery checker. The later 15 October thesis prints a different checker. Its JSON grammar is not this bundle’s grammar. Its written arguments have not been reviewed here either.

The supplied status also reports an adversarial script, a SymPy cross-check, a historical verifier, and states that Julia and Rust were not run. Those source files were not in this upload. This archive did not run them, and it does not treat the status summary as a substitute.

The hosted logs have recorded SHA-256 digests. Matching those digests checks the logs’ byte integrity. The logs document the archive’s reported executions. Rerunning the checker tests whether those results are reproducible.

A matching hash does not itself verify that the recorded execution occurred or that the checker is mathematically correct.