Foundation Primitive Recognition Calculus Physical One Act Calibration Canonical

The canonical instrument

In Recognition Science, a ledger is a discrete record of events, and the cost of recording an event is not chosen freely but forced by the framework's axioms. The declaration canonicalInstrument is a formal object that packages the simplest possible calibration: it takes a positive unit, a real-valued readout, a proof that the readout equals the one-act curvature of that unit, and a lock showing the readout equals one. In plain terms, it is a consistency witness: it shows that a self-consistent calibration exists at the canonical unit, without constructing any laboratory hardware.

The structure OneActInstrument is defined with four fields: a unit (a positive real number), a readout (a real number), a proof that the readout equals the one-act curvature of the unit, and a proof that the readout is locked to one. The canonicalInstrument is the specific instance where both unit and readout are 1. The theorem instrument_forces_canonical_unit then proves that any such instrument must have unit equal to 1, and the headline theorem physical_one_act_calibration_headline bundles three facts: every instrument forces unit = 1, at least one such instrument exists, and the interface preserves the unit.

The one-act curvature is the framework's term for the cost of a single recognition event at a given unit. The theorem that any instrument forces unit = 1 is the key result: it says the calibration is not a choice but a consequence. If you have any positive unit, a readout that correctly reports its curvature, and a lock that pins the readout to one, then the unit itself must be 1. This is a forcing result, not an empirical measurement.

What the declaration does not claim is equally important. It does not claim that any physical device has been built or measured. It does not claim that the one-act curvature has been observed in a laboratory. It is a formal consistency witness: it shows that the framework's axioms admit a self-consistent calibration at unit 1, nothing more. The framework's library is a machine-checked collection of formal theorems, and this declaration is one small piece of that collection.

/-- 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

/-- 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

/-- **Physical calibration headline.** The abstract one-act normalization is
exactly the datum supplied by a physical one-act instrument: any such instrument
produces the normalized interface and forces `unit = 1`, and the canonical unit
carries a consistent instrument witness. -/
theorem physical_one_act_calibration_headline :
    (∀ I : OneActInstrument, I.unit = 1)
      ∧ (∃ I : OneActInstrument, I.unit = 1)
      ∧ (∀ I : OneActInstrument, (OneActInstrument.toInterface I).unit = I.unit) :=
  ⟨instrument_forces_canonical_unit, ⟨canonicalInstrument, rfl⟩, fun _ => rfl⟩

What this page does not claim

No physical laboratory device is constructed or measured by this declaration. The one-act curvature is not observed empirically; it is a formal construct. The declaration does not derive the value of any physical constant beyond the unit 1.

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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