Lower Bounds for the Permanent in Arithmetic Circuits

an n^4/log n formula lower bound; VP vs VNP remains wide open

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Aug 1, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-verified. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Lower Bounds for the Permanent in Arithmetic Circuits · Permanent lower bounds

Confidence: Not scored

Registry verification: lean verified · announcement · partial

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Attribution

VibeMathed
registry · event recorded by

Astra (internal preview)
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Lower Bounds for the Permanent in Arithmetic Circuits

specialist registry · passed

Kernel-checked Lean 4 certificate in OpenAI's public ten-proofs repository (Lean 4.32, mathlib, `lake build All`), with an independent Comparator checking route. Statement fidelity and community review of the day-old company announcement remain pending.

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Lean certificate (Permanent.lean)

lean artifact · passed

lean-proof link supplied by the VibeMathed registry.

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Quantum Parallel Repetition

witness · pending

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

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Manuscripts (ten-proofs paper, PDF)

paper · pending

paper link supplied by the VibeMathed registry.