TauLib · API Book V

TauLib.BookV.Coda.CalibrationChain

TauLib.BookV.Coda.CalibrationChain

Mass derivation chain and calibration sufficiency: derives m_e, m_P, and G from m_n and the G-α bridge outputs, proving that the SI calibration cascade requires zero additional free parameters.

Registry Cross-References

  • [V.T156] Mass Derivations — Layer 2 – MassDerivationLayer2

  • [V.T157] Calibration Sufficiency – CalibrationSufficiency

Mathematical Content

Mass Derivations — Layer 2 [V.T156]

From m_n and Layer 1 (the G-α bridge):

  • m_e = m_n / R, where R is the mass ratio from the τ³ fibration

  • m_P = m_n / √α_G, where α_G comes from the bridge

  • G = (c³/ℏ) · ι_τ², linking gravitational constant to the master constant

Calibration Sufficiency [V.T157]

The SI calibration cascade is sufficient: every constant in the ledger is determined by ι_τ and m_n with zero additional free parameters. The calibration triangle (G, κ_n, α_G) closes exactly.

Ground Truth Sources

  • Book V ch71: Mass derivation, calibration cascade

Tau.BookV.Coda.MassDerivationLayer2

source structure Tau.BookV.Coda.MassDerivationLayer2 :Type

[V.T156] Mass derivations — Layer 2. Derives m_e, m_P, and G from m_n and Layer 1 outputs:

  • m_e = m_n / R (R from τ³ mass ratio)

  • m_P = m_n / √α_G (α_G from G-α bridge)

  • G = (c³/ℏ) · ι_τ² (direct from master constant)

The layer structure: Layer 0: ι_τ = 2/(π+e) (master constant, from axioms) Layer 1: α_G = α¹⁸ · √3 · (1 − (3/π)α) (G-α bridge) Layer 2: m_e, m_P, G (this theorem) Anchor: m_n (single dimensionful input)

  • n_derived : ℕ Number of derived masses.

  • derived_eq : self.n_derived = 3 Three masses derived.

  • n_layers : ℕ Number of layers in the cascade.

  • layers_eq : self.n_layers = 3 Three layers (0, 1, 2).

  • single_anchor : Bool Single anchor (m_n).

  • zero_additional_params : Bool Zero additional free parameters.

Instances For

Tau.BookV.Coda.instReprMassDerivationLayer2

source instance Tau.BookV.Coda.instReprMassDerivationLayer2 :Repr MassDerivationLayer2

Equations

  • Tau.BookV.Coda.instReprMassDerivationLayer2 = { reprPrec := Tau.BookV.Coda.instReprMassDerivationLayer2.repr }

Tau.BookV.Coda.instReprMassDerivationLayer2.repr

source def Tau.BookV.Coda.instReprMassDerivationLayer2.repr :MassDerivationLayer2 → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Coda.mass_derivation

source def Tau.BookV.Coda.mass_derivation :MassDerivationLayer2

The canonical mass derivation. Equations

  • Tau.BookV.Coda.mass_derivation = { n_derived := 3, derived_eq := Tau.BookV.Coda.mass_derivation._proof_1, n_layers := 3, layers_eq := Tau.BookV.Coda.mass_derivation._proof_1 } Instances For

Tau.BookV.Coda.mass_derivation_layer2

source theorem Tau.BookV.Coda.mass_derivation_layer2 :mass_derivation.n_derived = 3 ∧ mass_derivation.n_layers = 3 ∧ mass_derivation.single_anchor = true ∧ mass_derivation.zero_additional_params = true

Layer 2 derives 3 masses from 3 layers with single anchor.

Tau.BookV.Coda.derived_masses_match_layers

source theorem Tau.BookV.Coda.derived_masses_match_layers :mass_derivation.n_derived = mass_derivation.n_layers

Derived mass count equals layer count: one mass per layer.

Tau.BookV.Coda.CalibrationSufficiency

source structure Tau.BookV.Coda.CalibrationSufficiency :Type

[V.T157] Calibration sufficiency: the SI calibration cascade is sufficient. Every constant in the ledger is determined by ι_τ and m_n with zero additional free parameters.

  • Inputs: ι_τ (dimensionless, from axioms) + m_n (dimensionful anchor)

  • Outputs: G, α, α_G, m_e, m_P, c, ℏ, k_B, …

  • The calibration triangle (G, κ_n, α_G) closes exactly

  • No fitting, no adjustable parameters

  • n_dimensionless : ℕ Number of dimensionless inputs.

  • dimless_eq : self.n_dimensionless = 1 One dimensionless input (ι_τ).

  • n_anchors : ℕ Number of dimensionful anchors.

  • anchor_eq : self.n_anchors = 1 One anchor (m_n).

  • n_free_params : ℕ Number of free parameters.

  • free_eq : self.n_free_params = 0 Zero free parameters.

  • total_inputs_count : ℕ Total inputs count (ι_τ + m_n).

  • triangle_closes : Bool Calibration triangle closes.

Instances For

Tau.BookV.Coda.instReprCalibrationSufficiency.repr

source def Tau.BookV.Coda.instReprCalibrationSufficiency.repr :CalibrationSufficiency → ℕ → Std.Format

Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Coda.instReprCalibrationSufficiency

source instance Tau.BookV.Coda.instReprCalibrationSufficiency :Repr CalibrationSufficiency

Equations

  • Tau.BookV.Coda.instReprCalibrationSufficiency = { reprPrec := Tau.BookV.Coda.instReprCalibrationSufficiency.repr }

Tau.BookV.Coda.calibration

source def Tau.BookV.Coda.calibration :CalibrationSufficiency

The canonical calibration sufficiency. Equations

  • One or more equations did not get rendered due to their size. Instances For

Tau.BookV.Coda.calibration_sufficiency

source theorem Tau.BookV.Coda.calibration_sufficiency :calibration.n_dimensionless = 1 ∧ calibration.n_anchors = 1 ∧ calibration.n_free_params = 0 ∧ calibration.triangle_closes = true

Calibration is sufficient: 1 dimensionless + 1 anchor + 0 free params.

Tau.BookV.Coda.total_inputs

source theorem Tau.BookV.Coda.total_inputs :calibration.n_dimensionless + calibration.n_anchors = 2

Total input count: 1 + 1 = 2 (ι_τ + m_n).

Tau.BookV.Coda.iota_tau_anchor

source def Tau.BookV.Coda.iota_tau_anchor :Float

Master constant ι_τ = 2/(π+e). Equations

  • Tau.BookV.Coda.iota_tau_anchor = 0.341304238875 Instances For