Source · Paper

Sendov conjecture: original proof

PreprintPublication date Aug 5, 2026
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Overview

A directed AI workflow reports a proof of Sendov for every degree at least two; the original proof and formalization preceded Tao’s exposition.

Public manuscript or exposition; publication does not imply independent OpenMath review.

Passages

The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.

Passage 1 · OpenMath paraphrasePermalink

Original proof dated 5 August 2026

A directed AI workflow reports a proof of Sendov for every degree at least two; the original proof and formalization preceded Tao’s exposition.

Passage details

Passage ID: sendov-conjecture:entry:mazur:v1

Source item: mazur

Source record: sendov-conjecture:source:mazur:v1

Used in

Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.

Sendov’s conjecture →

Problem publication v8

Problem context · 4 citations

Research activity

Discovery, exposition and formalization

Mazur and GPT-5.6 Pro supplied the original result; Tao digested its mathematics and directed the second formalization, whose project credits Claude Opus 5.

Two formalizations of a descended argument do not automatically constitute two independent mathematical proofs.

History

Mazur’s AI-assisted all-degree proof

Further reading

Read the mathematical argument; inspect its Claim for assessment and scope.

Files

Linked manuscripts, code and data. External proof reports, statement correspondence and OpenMath execution are separate checks.

Formal declarations

Lean: Sendov for every degree ↗

Complete formal proof reported externally

Source-reported complete. The separate Challenge file contains deliberate statement placeholders; the project reports no holes in the proof endpoint.

Statement match: Linked by OpenMath · independent review separate · checked Oct 13, 2026

Declaration & revision

Credits

Recorded authorship

Lech Mazur

AI involvement reported by the source

Lech Mazur directed GPT-5.6 Pro discovery and formal work; mathematical direction, model work and later exposition are distinct contributions.

Versions

OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.

  1. 2026-08-05 · selectedObserved Oct 13, 2026 · used in current publications

    Sendov conjecture: original proof

Record details
Source ID
sendov-conjecture-mazur
Record ID
sendov-conjecture:source:mazur:v1
Recorded title
Sendov conjecture: original proof
Revision
2026-08-05
Observed
Oct 13, 2026
Source updated
Aug 5, 2026
Content SHA-256
Not recorded
Update method
Source comparison followed by a new immutable curation revision.
Identifier policy
Stable source and entry identities; changed wording receives a new version.
Check interval
90 days
Rights
metadata-link
License
Original document rights remain with its authors.

OpenMath supplies original paraphrases and links; no proof text is republished.

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