Results Challenge Response Canonical mathematics challenge-response, mathematics The Corpus currently constrains, reframes, or materially supports an account of this problem.
Mathematics Challenge Response

Yang–Mills Existence and Mass Gap

CB-YANG-MILLS canonical benchmark canonical benchmarks τ response: Structurally constrained External: externally open Verification: pending external review

The Corpus currently constrains, reframes, or materially supports an account of this problem.

This response is paired with its canonical Structural Challenge: Yang–Mills Existence and Mass Gap (CB-YANG-MILLS) in the Mathematics Structural Challenge Ledger.

τ response

Registry evidence gives a direct Corpus account or constraint.

Evidence route

This response is supported by 5 canonical registry items in the τ Corpus.

  • IV.D176 — YM sector coupling direct problem account confidence: high
  • IV.D177 — Gap quantum direct problem account confidence: high
  • IV.D179 — Orthodox Bridge Conjecture direct problem account confidence: high
  • IV.D579 — Yang--Mills on tau3 direct problem account confidence: high
  • IV.T75 — τ-Yang--Mills Mass Gap Theorem direct problem account confidence: high

Notes

The τ-internal mass-gap theorem IV.T75 closes kernel-only against Mathlib + native_decide alone — no custom-axiom dependency. The reason this Challenge Response carries a Structurally constrained status rather than Internally addressed is the bridge layer: the formal correspondence between the τ-formulation of Yang–Mills and the Clay Yang–Mills statement on ℝ⁴ is treated separately and not yet formally bridged via Lean. This is the same pattern as the Master Schema → classical Riemann Hypothesis split: a τ-internal kernel-only result plus an unproven bridge to the orthodox classical statement. See the Yang–Mills note on the Custom Axiom Inventory for the full split, and IV.T75 for the kernel-only theorem itself. The bridge layer is the program’s open work; IV.T75 is not axiom-dependent.

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-yang-mills-existence-mass-gap (promoted one to one)
  • v1 mapping recovered fromf534b3fb^

Bibliography clusters whose prior art bears on this page. Each cluster links to its representative references and to the broader Deep Comparison briefing.

Source: prior-art cluster index · canonical data lives in corpus/data/bibliography/prior-art-clusters.yml

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.

Save or share this page for inspection

Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.

Email to expert