P versus NP

Structural Challenge

This response is paired with its canonical Structural Challenge: P versus NP (CB-PVSNP) in the Mathematics Structural Challenge Ledger.

τ response

Evidence route

This response is supported by 7 canonical registry items in the τ Corpus.

• III.D33 — NP Witness as Canonical Address (v1) direct problem account confidence: high
• III.D34 — τ-CDCL Architecture direct problem account confidence: high
• III.D78 — τ-Native Abstract Turing Machine direct problem account confidence: high
• III.P38 — P vs NP as Polynomial Translation Obstruction direct problem account confidence: high
• III.T30 — TTM τ-Nativity direct problem account confidence: high
• III.T31 — Interface Width Principle direct problem account confidence: high
• III.T34 — No Barrier Theorem direct problem account confidence: high

Notes

Verification

• Verification routeformal_proof_checking
• Verification statuspending_external_review
• External statusexternally_open

External-review boundary

External mathematical review of the τ formulation, comparison against orthodox proofs/disproofs, and assessment of the bridge between τ-internal results and standard mathematical statements.

Provenance

• v1 predecessormath-p-vs-np (promoted one to one)
• v1 mapping recovered fromf534b3fb^

Status disclaimer

A Challenge Response reports the program's current internal stance against a canonical Structural Challenge. It does not imply external verification, scientific consensus, philosophical settlement, or final proof. Read it together with its evidence route, registry references, verification status, and external-review boundary.