Foundation Primitive Recognition Calculus Physical One Act Calibration Physical

The one-act instrument

In any measurement science, calibration is the act of fixing the unit. Recognition Science formalizes this with a ledger, a discrete record of recognition events, and a cost, the forced price of each recognition. The framework's library, a machine-checked collection of formal theorems, proves a calibration statement: any instrument that reads exactly one unit of curvature forces that unit to be the canonical unit, which is simply 1.

The declaration physical_one_act_calibration_headline bundles three facts. First, every such instrument has unit equal to 1. Second, such an instrument exists: the canonical instrument with unit 1 and readout 1 is a consistency witness. Third, the instrument's interface preserves the unit. The proof is short: the instrument's readout equals its curvature, and since the readout is locked to 1, the curvature is 1, which by the normalization theorem forces the unit to be 1.

This is not a claim about building hardware. The canonical instrument is a mathematical witness, not a lab apparatus. The theorem does not construct a physical device; it shows that if one existed, its unit would be forced. Nor does it define what a recognition event is in physical terms. The bridge from the abstract ledger to physical events remains open. The theorem's force is conditional: given a one-act instrument, the unit is 1.

What the theorem changes is the status of the unit. In the framework, the unit of cost is not a free parameter. It is forced by the calibration condition. This is the sense in which the framework claims its constants are derived rather than chosen: the unit is locked by the structure of the instrument, not selected by convention.

/-- The physical one-act instrument forces the canonical cost unit. -/
theorem instrument_forces_canonical_unit (I : OneActInstrument) :
    I.unit = 1 :=
  normalized_interface_forces_J I.toInterface

/-- The canonical instrument exists at the canonical unit. This is a consistency
witness, not a construction of lab hardware. -/
def canonicalInstrument : OneActInstrument where
  unit := 1
  positive := by norm_num
  readout := 1
  reads_curvature := by
    rw [oneActCurvature_eq]
    norm_num
  locked_to_one := rfl

What this page does not claim

The theorem does not construct a physical device. It does not define what a recognition event is in physical terms. It does not claim the unit is one in any conventional physical system without the one-act condition.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Foundation/PrimitiveRecognitionCalculus/PhysicalOneActCalibration.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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