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Paper Integrity Record · LEDGER

Geometric--Nongeometric Optimizer Calculus: A Modular Language for Reachable Gradient Methods

As of 10 July 2026, Pith completed 5 of 6 listed checks against arXiv:2607.07206. The completed checks produced 1 public finding within their stated scope. 1 check was skipped and produced no result.

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

pith.integrity.v1
2607.07206 v1
pith:2026:GBXMSZ43FCMC3ULTTVIO75CDOW

Coverage vector

completed 5 of 6 listed checks

Counted as completed checks in the claim sentence numerator.

skipped 1 of 6 listed checks

Skipped checks produced no result and say nothing about absence.

Listed checks

doi_title_agreement

completed

v1.0.0, observed 2026-07-10 18:01:37.548523+00:00

Scope
Cited titles compared with titles resolved from their DOI or arXiv identifier.
Completed surface
Checked 68 references.

doi_compliance

completed

v1.0.0, observed 2026-07-10 17:48:46.090883+00:00

Scope
DOI and arXiv identifiers listed in the bibliography checked against named registries.
Completed surface
Checked 21 references. Recorded 1 finding from this run.

claim_evidence

completed

v1.0.0, observed 2026-07-10 08:02:26.133036+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 19:56:54.645591+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 15:18:31.137243+00:00

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

ai_meta_artifact

skipped

v1.0.0, observed 2026-07-09 07:54:08.157468+00:00

Scope
Paper body text scanned for literal AI-assistant artifacts.
Reason
Paper body text was unavailable.

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.