Paper Integrity Record · LEDGER

Maximal-Hull z-Ideals, Congruence Closures, and Coherent Frames of Commutative Semirings

As of 20 July 2026, Pith completed 6 of 6 listed checks against arXiv:2607.07319. The completed checks produced 1 public finding within their stated scope.

This is a record of named checks, not a clean-status claim or a paper verdict.

pith.integrity.v1
2607.07319 v1
pith:2026:OFECVLAT23IJSNSNHNW6E6JNLS

Coverage vector

completed 6 of 6 listed checks

Counted as completed checks in the claim sentence numerator.

Listed checks

doi_title_agreement

completed

v1.0.0, observed 2026-07-20 22:35:21.927049+00:00

Scope: Cited titles compared with titles resolved from their DOI or arXiv identifier.
Completed surface: Checked 8 references.

ai_meta_artifact

completed

v1.0.0, observed 2026-07-16 08:59:06.640421+00:00

Scope: Paper body text scanned for literal AI-assistant artifacts.
Completed surface: Checked 1 reference.

doi_compliance

completed

v1.0.0, observed 2026-07-15 15:27:04.822452+00:00

Scope: DOI and arXiv identifiers listed in the bibliography checked against named registries.
Completed surface: Checked 18 references. Recorded 1 finding from this run.

claim_evidence

completed

v1.0.0, observed 2026-07-15 14:24:41.611572+00:00

Scope: Recorded paper claims checked for the evidence artifacts they name.
Completed surface: Completed within the stated scope.

citation_quote_validity

completed

v0.1.0, observed 2026-07-09 15:57:41.254500+00:00

Scope: Specific factual attributions checked against cited-paper text available in Pith.
Completed surface: Completed within the stated scope.

cited_work_retraction

completed

v1.0.0, observed 2026-07-09 13:18:30.688382+00:00

Scope: Cited references checked for source-reported retractions or expressions of concern.
Completed surface: Completed within the stated scope.

Observations

Methods and limits

Each listed check names the surface it examined. A skipped, failed, partial, unavailable, not collected, not requested, or withheld check says nothing about what a completed check would have returned.

Only checks with status completed enter the claim sentence numerator.
Findings appear only from completed checks and only within the scope printed for that check.
Severity labels describe one observation row. They do not roll up into a paper judgment.