Foundation Primitive Recognition Calculus Physical One Act Calibration Instrumen

The one-act instrument

A one-act instrument is the framework's name for a single, self-contained measurement: it takes one positive candidate unit, reads one real number from it, and certifies that the number is exactly the curvature of that unit. The structure demands three things at once: the unit is positive, the readout equals the one-act curvature of that unit, and the readout equals one. This is not a proposal for lab hardware; it is a mathematical shape that any such measurement must fit.

The theorem instrument_forces_canonical_unit proves that any one-act instrument must have unit equal to one. The proof runs through a normalized interface: the instrument supplies the same data that the abstract normalization requires, and a prior theorem forces that interface to the canonical unit. The result is a forcing statement, not an observation: if you have a measurement that reads exactly one, the unit it measures is the canonical unit, no other.

The framework also provides a consistency witness, a canonical instrument with unit one and readout one, showing the structure is not empty. The headline theorem packages both directions: every instrument forces unit one, and an instrument at unit one exists. This is the calibration result that ties the abstract cost calculus to a physical reading.

What the declaration does not claim is equally sharp. It does not construct or describe any physical apparatus; the canonical instrument is a witness in the logic, not a blueprint. It does not say that any real measurement will read one, only that if a measurement fits the one-act shape and reads one, its unit is forced. It says nothing about how such an instrument would be built, calibrated, or read in practice.

/-- 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

/-- **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

The declaration does not construct or describe any physical apparatus. It does not say that any real measurement will read one, only that if a measurement fits the one-act shape and reads one, its unit is forced. It says nothing about how such an instrument would be built, calibrated, or read in practice.

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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