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Ostmann's inverse Goldbach conjecture

Theorem 1.1: if $A,B\subseteq\mathbb N_0$ have $|A|,|B|\ge2$ , then $(A+B)\triangle\mathcal P$ is infinite. After the Laffer-Mann reduction to two infinite summands, the proof combines residue restrictions at every prime, decorrelation from translated multiplicative characters, prime coverage and a positive statistic averaged over arrangements; it does not use Green and Harper's conditional inverse-sieve route. In particular, if $A+B$ contains every large prime it contains infinitely many composites. No quantitative version is claimed.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Ostmann's inverse Goldbach conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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Attribution

VibeMathed
registry · event recorded by

Unreleased internal OpenAI model
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Ostmann's inverse Goldbach conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the introduction and Theorem 1.1 were read against Ostmann's conjecture. lean/docs/013.md lists OstmannPrimes.json (OAI.Ostmann.main, module OAI.NumberTheory.Ostmann.Main) and OstmannComplete.json (OAI.Ostmann.inverseGoldbach and OAI.Ostmann.twoInfiniteSummandsImpossible, module OAI.NumberTheory.Ostmann.Complete). Both solution files exist at the pinned commit; neither challenge is in the formalization catalogue formalization.yaml. The statement was read here: for all sets A, B of natural numbers with at least two elements each, the symmetric difference of A+B and the primes is infinite. That is exactly the conjecture. Not rebuilt here.

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Ostmann's inverse Goldbach conjecture

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Lean proof (OAI.Ostmann.main)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Lean proof (OAI.Ostmann.inverseGoldbach)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.