IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.QuantizedProofMethod
Defines the Delta-audit interface for continuum problems: a problem is audited when it admits a finite reduction to a certificate that can be checked by the primitive recognition calculus. Analysts working on hard continuum claims in RS cite this module for the audit and stub-obligation types. The module is mostly definitional scaffolding plus a headline linking audits to finite reductions from FiniteCertificateTransfer.
claimA continuum problem $P$ has a Delta audit when there exists a finite reduction of $P$ to a checkable certificate. The module packages the audit record, the finite-reduction predicate, application stubs, and stub obligations that later native-analysis modules discharge.
background
In the Primitive Recognition Calculus, continuum statements are not accepted raw. They must pass through a quantized proof path: reduce the claim to a finite certificate, then transfer that certificate via the FiniteCertificateTransfer layer. The present module sits on that import and names the audit objects used downstream.
The central notions are a problem audit (the structured record that a continuum problem has been reduced), the finite-reduction property, and lightweight application stubs with explicit stub obligations. These are bookkeeping types rather than physical laws: they record that a continuum claim has been cut down to something the discrete recognition machinery can verify.
The local setting is Foundation, not the forcing chain T0–T8 itself. The module prepares continuum side-claims (for example native Delta analysis) so they can inherit finite-certificate discipline rather than open-ended analytic arguments.
proof idea
This is primarily a definition and interface module, not a deep proof development. It introduces the audit and stub structures, states the finite-reduction link (problemAudit_finiteReduction), and exposes a headline declaration for the quantized proof method. Substantive work is deferred to importers that fill stubs and run native Delta analysis against the audit interface.
why it matters in Recognition Science
Without a shared audit type, continuum claims in RS would bypass the finite-certificate discipline that keeps the foundation machine-checkable. This module supplies that shared interface.
It is imported by DeltaNativeAnalysis, DeltaNativeStrongClosure, and HardProblemCertificateAudits. Those modules turn the audit stubs into concrete native bounds and hard-problem certificate checks. In the broader framework the pattern supports treating continuum side-results as quantized obligations rather than free analytic hypotheses, consistent with the discrete, certificate-first style of the recognition calculus.
scope and limits
- Does not prove any specific continuum identity or bound by itself.
- Does not construct concrete certificates; only names audit and stub interfaces.
- Does not replace FiniteCertificateTransfer; it depends on that module.
- Does not assert physical constants, mass ladders, or forcing-chain steps T0–T8.
- Does not discharge ApplicationStub obligations; downstream modules must.