Foundation Primitive Recognition Calculus Physical One Act Calibration

One-act calibration

In Recognition Science, a ledger (a discrete record of events) assigns a cost to each recognition event. The framework's central theorem states that any cost function satisfying five plain conditions must equal J(x) = (x + 1/x)/2 - 1. A natural question follows: what fixes the unit in which that cost is measured? The answer in the framework is a one-act calibration: a single physical act of measurement forces the canonical unit to be exactly 1.

The module defines a one-act instrument as a positive candidate 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 1. In plain words, the instrument reads out the curvature of its own unit, and that readout is locked to one. The framework's library, a machine-checked collection of formal theorems, proves that any such instrument forces its unit to equal 1. The canonical instrument, with unit 1 and readout 1, exists as a consistency witness, not as a construction of lab hardware.

The headline theorem states three things together: every one-act instrument has unit equal to 1, there exists at least one such instrument, and the interface conversion preserves the unit. This is a proved theorem in Lean 4, axiom-clean, with no RS-specific axioms. The physical calibration headline is the abstract one-act normalization made concrete: any physical one-act instrument produces the normalized interface and forces unit = 1.

What this changes: the framework does not leave the unit of cost as a free parameter. A single measurement act, modeled as a one-act instrument, fixes the unit. The cost function is unique, and now its unit is forced too. The reader can see that the framework's claims about cost are not just about shape but about scale.

/-- 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

This does not claim that a physical one-act instrument has been built in a laboratory. This does not claim that the one-act calibration derives the value of any other physical constant. This does not claim that the unit of cost is the only unit the framework forces.

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)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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