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IndisputableMonolith.Foundation.PrimitiveRecognitionCalculus.PRCShrunkCertificate

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Packages the four load-bearing statements of the δ (delta) program into one small certificate object. Anyone auditing the Primitive Recognition Calculus chain cites this as the shrunk interface that the rest of the foundation can import without pulling the full sub-development. The module is structural: it re-exports and bundles results already proved in the six PRC imports.

claimThere is a single certificate object assembling the four load-bearing claims of the $\delta$ program: one-primitive recognition, the calibration target, the minimal field structure (with exp/log), the chain bridge, and the distinction dichotomy, presented as one compact interface rather than six separate modules.

background

Primitive Recognition Calculus (PRC) is the foundation layer that forces the recognition cost and the discrete ladder before the T0–T8 forcing chain is stated in full. The $\delta$ program is the local development that isolates the minimal algebraic and order-theoretic facts needed so that recognition is unique up to the J-cost $J(x)=(x+x^{-1})/2-1$ and the self-similar scale $\varphi$.

This module sits above six PRC pieces: one-primitive recognition, the calibration target, the minimal field, the exp/log field, the chain bridge into the unified forcing development, and the distinction dichotomy. Each of those modules carries part of the $\delta$ argument; none is meant to be the public face of the package.

The certificate is the small object that names those four load-bearing statements together so downstream foundation code can depend on one import rather than the whole PRC tree.

proof idea

This is a certificate/aggregation module, not a proof module. It defines a structure (or analogous bundle) PRCShrunkCertificate and a witness prc_shrunk_certificate that packages theorems already established in the imported PRC modules. No new mathematical argument is carried here; the work is wiring and interface shrinkage.

why it matters in Recognition Science

In the Recognition Science foundation, large intermediate developments are collapsed into shrunk certificates so the forcing chain and later physics extractions stay readable. This module is that collapse for the $\delta$ program inside Primitive Recognition Calculus: it is the single object a reader should open when checking that the one-primitive, calibration, minimal-field/exp-log, chain-bridge, and distinction pieces are all present.

It does not itself advance T5–T8 (J-uniqueness, $\varphi$, eight-tick octave, $D=3$), but it is the hygiene layer those steps rely on when they import PRC facts. With used_by currently empty in the graph, its role is still as the intended public face of the $\delta$ bundle rather than as a leaf lemma.

scope and limits

depends on (6)

Lean names referenced from this declaration's body.

declarations in this module (2)