An invitation to review
Help us find what we’ve missed.
A missing hypothesis. An earlier theorem. A step that needs a stronger argument. Focused feedback is welcome.
Three questions for specialists
The analytic questions below refer to the current unreviewed v1.2 preprint, revised 27 October 2026 (CDT), published here 28 October 2026 (UTC). October finite formalization progress is recorded separately on the research note.
Source-check priority: the exact original Montgomery–Vaughan Brun–Titchmarsh theorem number and real-endpoint range/convention remain unchecked. The estimate is retained as a named input; no human peer review or full analytic Lean verification is claimed.
Does the density estimate support the stated tail bound?
Check the moving-parameter uniformity, the once-integrated explicit formula and the use of the exact decreasing envelope. The target is an absolute bound on a signed integral, not an integral of the absolute error.
Do the four links use compatible hypotheses?
Trace the same budget through centered inclusion, near-pattern counting and shell aggregation. Check eventual thresholds, endpoint conventions and the distinction between analytic and combinatorial constants.
Is the result already implied by an earlier theorem?
We particularly welcome precise mappings to existing integrated-tail or Robin-counting results. The classical benefit and partition methods are credited. Whether the combined argument yields a new result remains to be established.
Review the October 25 finite statement
Start with the canonical finite-certification summary. Check whether the quantifiers describe every real cutoff y rather than every integer N; whether event completeness includes the repeated-prime increment; and whether exact and coincident ties retain the smaller exponents. Examine the distinction between certificate soundness, sufficient budgets and inconclusive outcomes.
The proof sources, generated certificates and logs remain private. This public summary supports scrutiny of the stated scope, but does not provide enough material to independently reproduce the kernel checks. No independent human review is claimed.
Shell/profile statements
A separate review can check whether a formal statement matches its intended mathematics: profile distinctness, unit-shell placement, or the padding-cost hypotheses. Those finite checks do not settle the manuscript’s analytic argument. Public source release is not part of this update; the private repository is not public reproduction evidence.
Make your feedback traceable
Please identify the manuscript version and section or equation, give the objection or reference, and say which steps you checked. A short, reproducible finding is more useful than a general verdict.
Send focused feedback to research@arithmeticconnectome.com. Please include the manuscript version and the section or equation you checked. The downloadable template helps organize your comments; it does not submit them.
About review and attribution
Reviewers will be credited only with their permission. Reviewing an argument does not imply endorsement. The existing audits used AI tools; human specialist review is still being sought.