IndisputableMonolith.Measurement.RSNative.Calibration.SingleAnchor

   1import Mathlib
   2import IndisputableMonolith.Measurement.RSNative.Core
   3import IndisputableMonolith.Measurement.RSNative.Calibration.SI
   4import IndisputableMonolith.Constants.RSNativeUnits
   5
   6/-!
   7# Single-Anchor SI Calibration (RS-native Measurement Framework)
   8
   9This module provides a **concrete single-anchor calibration protocol** for reporting
  10RS-native measurements in SI without introducing any *fit parameters*.
  11
  12## Idea
  13
  14- RS-native theory runs in tick/voxel/coh/act with \(c=1\) and no SI numerals.
  15- If one wants SI reporting, one must provide a calibration seam.
  16- We choose a **single scalar anchor**: `seconds_per_tick` (τ₀ in seconds).
  17
  18Then we *derive* the full `ExternalCalibration`:
  19
  20- meters_per_voxel is fixed by the SI definition of \(c\): 299792458 m/s
  21- joules_per_coh is fixed by the SI definition of Planck's constant \(h\) (exact),
  22  hence \(\hbar = h/(2\pi)\), together with the RS identity `1 act = 1 coh * 1 tick`
  23
  24So, **only one empirical scalar** is supplied; everything else is derived or definitional.
  25-/
  26
  27namespace IndisputableMonolith
  28namespace Measurement
  29namespace RSNative
  30namespace Calibration
  31namespace SingleAnchor
  32
  33open IndisputableMonolith.Constants.RSNativeUnits
  34open IndisputableMonolith.Measurement.RSNative
  35
  36noncomputable section
  37
  38/-! ## SI definitional constants (not fit parameters) -/
  39
  40/-- SI-definitional speed of light in meters per second (exact). -/
  41def c_SI : ℝ := 299792458
  42
  43lemma c_SI_pos : 0 < c_SI := by
  44  norm_num [c_SI]
  45
  46/-- SI-definitional Planck constant \(h\) (exact, 2019 SI): 6.62607015×10⁻³⁴ J·s.
  47
  48We write this exactly as a rational: 662607015 / 10^42. -/
  49noncomputable def h_SI : ℝ :=
  50  (662607015 : ℝ) / ((10 : ℝ) ^ (42 : ℕ))
  51
  52lemma h_SI_pos : 0 < h_SI := by
  53  unfold h_SI
  54  have hnum : (0 : ℝ) < (662607015 : ℝ) := by norm_num
  55  have hden : (0 : ℝ) < (10 : ℝ) ^ (42 : ℕ) := by
  56    exact pow_pos (by norm_num : (0 : ℝ) < 10) 42
  57  exact div_pos hnum hden
  58
  59/-- Reduced Planck constant \(\hbar = h/(2\pi)\) (exact given SI definition of \(h\)). -/
  60noncomputable def hbar_SI : ℝ :=
  61  h_SI / (2 * Real.pi)
  62
  63lemma hbar_SI_pos : 0 < hbar_SI := by
  64  unfold hbar_SI
  65  have hden : (0 : ℝ) < 2 * Real.pi := by
  66    have h2 : (0 : ℝ) < 2 := by norm_num
  67    exact mul_pos h2 Real.pi_pos
  68  exact div_pos h_SI_pos hden
  69
  70/-! ## Calibration protocol (measurement framework) -/
  71
  72/-- Single-anchor SI calibration protocol: provide τ₀ in seconds.
  73
  74This is an *explicit* seam. It does not tune any dimensionless RS predictions;
  75it only fixes the SI reporting scale. -/
  76def tau0_seconds_protocol : Protocol :=
  77  { name := "calibration.single_anchor.tau0_seconds"
  78    summary :=
  79      "Single-anchor SI calibration. Supply τ0 (seconds per tick) as the only empirical scalar. " ++
  80      "Derive meters_per_voxel via SI-defined c=299792458 and derive joules_per_coh via SI-defined h (hbar=h/(2π)) " ++
  81      "together with RS identity 1 act = 1 coh * 1 tick. No mass-data fitting; this is a reporting seam only."
  82    status := .hypothesis
  83    assumptions :=
  84      [ "A1: τ0 (one RS tick) corresponds to a stable physical duration that can be measured in SI seconds using a declared lab protocol."
  85      , "A2: SI definitional constants (c and h) are treated as exact conventions; they introduce no fit freedom."
  86      ]
  87    falsifiers :=
  88      [ "F1: Two independent anchors for τ0 (e.g. time-first vs length-first) disagree beyond stated uncertainties."
  89      , "F2: Under the derived calibration, the SI speed consistency check fails beyond uncertainty."
  90      ]
  91  }
  92
  93theorem tau0_seconds_protocol_hygienic : Protocol.hygienic tau0_seconds_protocol := by
  94  simp [Protocol.hygienic, tau0_seconds_protocol]
  95
  96/-! ## Derive the full `ExternalCalibration` from one scalar -/
  97
  98/-- Build a full `ExternalCalibration` from one scalar: τ₀ in seconds. -/
  99noncomputable def externalCalibration_of_tau0_seconds (tau0_s : ℝ) (htau : 0 < tau0_s) :
 100    ExternalCalibration :=
 101  { seconds_per_tick := tau0_s
 102    meters_per_voxel := (c_SI : ℝ) * tau0_s
 103    joules_per_coh := hbar_SI / tau0_s
 104    seconds_pos := htau
 105    meters_pos := mul_pos c_SI_pos htau
 106    joules_pos := div_pos hbar_SI_pos htau
 107    speed_consistent := by
 108      have htau_ne : tau0_s ≠ 0 := ne_of_gt htau
 109      -- (c_SI * tau0_s) / tau0_s = 299792458
 110      simp [c_SI, htau_ne]
 111  }
 112
 113/-! ## Certificate: one-scalar calibration seam (explicit) -/
 114
 115/-- A calibration certificate bundling:
 1161) the single-anchor protocol
 1172) one measured scalar τ₀ in seconds
 1183) the derived full `ExternalCalibration` used for SI reporting
 119
 120Everything beyond τ₀ is derived (or SI-definitional). -/
 121structure CalibrationCert where
 122  /-- The single empirical scalar: τ₀ in seconds (seconds per tick). -/
 123  tau0_seconds : Measurement ℝ
 124  /-- Protocol is the canonical single-anchor protocol. -/
 125  protocol_ok : tau0_seconds.protocol = tau0_seconds_protocol
 126  /-- Positivity: τ₀ must be positive. -/
 127  tau0_pos : 0 < tau0_seconds.value
 128
 129/-- The derived `ExternalCalibration` associated to a certificate. -/
 130noncomputable def calibration (cert : CalibrationCert) : ExternalCalibration :=
 131  externalCalibration_of_tau0_seconds cert.tau0_seconds.value cert.tau0_pos
 132
 133theorem calibration_protocol_hygienic (cert : CalibrationCert) :
 134    Protocol.hygienic cert.tau0_seconds.protocol := by
 135  simpa [cert.protocol_ok] using tau0_seconds_protocol_hygienic
 136
 137/-! ## Consistency checks (derived, not additional parameters) -/
 138
 139/-- Under the derived calibration, 1 voxel/tick reports exactly c_SI in m/s. -/
 140theorem c_reports_exact (cert : CalibrationCert) :
 141    IndisputableMonolith.Constants.RSNativeUnits.to_m_per_s (calibration cert)
 142        IndisputableMonolith.Constants.RSNativeUnits.c = c_SI := by
 143  -- This follows from the `speed_consistent` field plus `c_in_si`.
 144  -- Note: RSNativeUnits.c = 1 (voxel/tick).
 145  have := IndisputableMonolith.Constants.RSNativeUnits.c_in_si (calibration cert)
 146  simpa [c_SI] using this
 147
 148/-- Under the derived calibration, 1 act reports \(\hbar\) in SI \(J·s\). -/
 149theorem one_act_reports_hbar (cert : CalibrationCert) :
 150    IndisputableMonolith.Measurement.RSNative.Calibration.SI.to_joule_seconds
 151        (calibration cert) (⟨(1 : ℝ)⟩ : Act) = hbar_SI := by
 152  -- Expand definitions and cancel τ0_s.
 153  have htau_ne : cert.tau0_seconds.value ≠ 0 := ne_of_gt cert.tau0_pos
 154  -- to_joule_seconds uses: (A:ℝ) * (joules_per_coh * seconds_per_tick)
 155  simp [IndisputableMonolith.Measurement.RSNative.Calibration.SI.to_joule_seconds,
 156    calibration, externalCalibration_of_tau0_seconds, htau_ne, hbar_SI]
 157
 158/-! ## Convenience constructor (for use in examples/tests) -/
 159
 160/-- Build a certificate from a chosen τ₀ (seconds per tick).
 161
 162This is a helper for downstream modules; real usage should supply a `Protocol`d
 163measurement record coming from a declared empirical procedure. -/
 164def mkCert (tau0_s : ℝ) (htau : 0 < tau0_s) : CalibrationCert :=
 165  { tau0_seconds :=
 166      { value := tau0_s
 167        protocol := tau0_seconds_protocol
 168        notes := ["Units: SI seconds per RS tick (single-anchor calibration seam)."] }
 169    protocol_ok := rfl
 170    tau0_pos := htau
 171  }
 172
 173end
 174
 175end SingleAnchor
 176end Calibration
 177end RSNative
 178end Measurement
 179end IndisputableMonolith
 180