yangMillsCertifiedDisplayAudit
plain-language theorem explainer
Specializes the certified-display Δ-audit to the Yang-Mills mass-gap problem. Continuum display objects (connection, excitation, zero-mode tags) each carry an explicit finite certificate from the YM inventory (plaquette ledger, excitation-gap witness, zero-mode obstruction). Cited by anyone using the hard-problem Delta bridge for YM. One-line instantiation of the generic certified-display audit.
Claim. The Yang-Mills mass-gap problem admits a $\Delta$-audit whose native certificates are the finite inventory $\{\text{finite plaquette ledger},\ \text{excitation gap witness},\ \text{zero-mode obstruction}\}$, whose display objects pair those certificates with continuum tags $\{\text{connection},\ \text{excitation},\ \text{zero-mode}\}$, and whose legitimacy and pathology predicates are conservative for the certified-display completion.
background
In the Primitive Recognition Calculus, a problem audit packages a completion from native finite certificates to continuum display objects, plus legitimacy and pathology predicates that are conservative for that completion. The $\Delta$-audit is the bridge from finite witnesses to continuum-facing statements; it does not claim a full solution.
For Yang-Mills the finite certificate inventory has three constructors: finite plaquette ledger, excitation-gap witness, and zero-mode obstruction witness. Display payloads tag the continuum side as connection, excitation, or zero-mode. A certified display pairs a certificate with a payload so every admissible display carries an explicit finite witness.
The generic certified-display audit builds such a problem audit for any certificate type and inhabited payload type, wiring completion and the standard legitimacy/pathology predicates with their conservativity proofs.
proof idea
One-line wrapper: instantiate the generic certified-display audit at the Yang-Mills certificate inventory and the Yang-Mills display-payload type. No extra obligations. The generic construction already supplies completion, legitimacy, pathology, and both conservativity proofs; the payload type is inhabited via the default connection-display tag.
why it matters
Feeds the certified-display audits headline, which asserts finite reduction for all four hard-problem certified-display audits (prime critical line, Navier-Stokes energy, Yang-Mills gap, Hodge algebraic). The headline states this is "still not a solution of the four problems; it is the correct Delta bridge shape for later analytic interfaces."
Places the Yang-Mills mass gap inside the Recognition Science quantized-proof and finite-reduction pipeline: continuum claims are only as strong as the finite certificates they carry. Infrastructure for hard-problem audits rather than a step in the T0–T8 forcing chain; the physics content arrives later when analytic interfaces attach to these certified displays.
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