TauLib · API Book V

TauLib.BookV.Cosmology.FalsificationPack

TauLib.BookV.Cosmology.FalsificationPack

Falsification package. Three falsification levels with specific testable predictions. Experimental program for the τ-framework.

Registry Cross-References

  • [V.R243] Scope note: CMB predictions C2, C5, C6 – structural remark

  • [V.D184] Falsification Levels – FalsificationLevels

Mathematical Content

Three Falsification Levels

Level 1 (Structural): fundamental predictions that, if falsified, would refute the τ-framework entirely:

  • A sixth force

  • Dark matter particle

  • c_gw ≠ c (gravitational wave speed ≠ light speed)

  • GW echoes (would indicate S² instead of T² horizon)

Level 2 (Quantitative): precise numerical predictions:

  • m_e = 0.510999 MeV (0.025 ppm from R formula)

  • G to 3 ppm (from closing identity with c₁ = 3/π)

  • r ι_τ⁴ 0.014 (tensor-to-scalar ratio)

  • sin²θ_W from sector coupling ratios

Level 3 (Observational frontier): predictions that require future technology to test:

  • T²-topology BH shadows (vs. S²)

  • Profinite discreteness at Planck scale

  • No trans-Planckian modes in CMB

CMB Predictions (Scope Note)

CMB predictions C2, C5, C6 involve mapping τ-native quantities to standard CMB observables. The mapping itself is tau-effective, but the numerical calibration carries observational uncertainties.

Ground Truth Sources

  • Book V ch55: Falsification Package

Tau.BookV.Cosmology.FalsificationLevel

source inductive Tau.BookV.Cosmology.FalsificationLevel :Type

Falsification level classification.

  • Structural : FalsificationLevel Level 1: structural (refutes framework).

  • Quantitative : FalsificationLevel Level 2: quantitative (tests specific numbers).

  • ObservationalFrontier : FalsificationLevel Level 3: observational frontier (needs future tech).

Instances For

Tau.BookV.Cosmology.instReprFalsificationLevel.repr

source def Tau.BookV.Cosmology.instReprFalsificationLevel.repr :FalsificationLevel → ℕ → Std.Format

Equations

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

Tau.BookV.Cosmology.instReprFalsificationLevel

source instance Tau.BookV.Cosmology.instReprFalsificationLevel :Repr FalsificationLevel

Equations

  • Tau.BookV.Cosmology.instReprFalsificationLevel = { reprPrec := Tau.BookV.Cosmology.instReprFalsificationLevel.repr }

Tau.BookV.Cosmology.instDecidableEqFalsificationLevel

source instance Tau.BookV.Cosmology.instDecidableEqFalsificationLevel :DecidableEq FalsificationLevel

Equations

  • Tau.BookV.Cosmology.instDecidableEqFalsificationLevel x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

Tau.BookV.Cosmology.instBEqFalsificationLevel

source instance Tau.BookV.Cosmology.instBEqFalsificationLevel :BEq FalsificationLevel

Equations

  • Tau.BookV.Cosmology.instBEqFalsificationLevel = { beq := Tau.BookV.Cosmology.instBEqFalsificationLevel.beq }

Tau.BookV.Cosmology.instBEqFalsificationLevel.beq

source def Tau.BookV.Cosmology.instBEqFalsificationLevel.beq :FalsificationLevel → FalsificationLevel → Bool

Equations

  • Tau.BookV.Cosmology.instBEqFalsificationLevel.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx) Instances For

Tau.BookV.Cosmology.TestablePrediction

source structure Tau.BookV.Cosmology.TestablePrediction :Type

A single testable prediction.

  • name : String Prediction identifier.

  • level : FalsificationLevel Falsification level.

  • description : String Description of the prediction.

  • status : String Current experimental status.

  • currently_testable : Bool Whether currently testable.

Instances For

Tau.BookV.Cosmology.instReprTestablePrediction

source instance Tau.BookV.Cosmology.instReprTestablePrediction :Repr TestablePrediction

Equations

  • Tau.BookV.Cosmology.instReprTestablePrediction = { reprPrec := Tau.BookV.Cosmology.instReprTestablePrediction.repr }

Tau.BookV.Cosmology.instReprTestablePrediction.repr

source def Tau.BookV.Cosmology.instReprTestablePrediction.repr :TestablePrediction → ℕ → Std.Format

Equations

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

Tau.BookV.Cosmology.FalsificationLevels

source structure Tau.BookV.Cosmology.FalsificationLevels :Type

[V.D184] Falsification levels: three-tier classification of τ-framework predictions by falsifiability strength and experimental accessibility.

Level 1: structural — would refute entire framework Level 2: quantitative — tests specific numerical values Level 3: frontier — requires future technology

  • structural : List TestablePrediction Level 1 predictions.

  • quantitative : List TestablePrediction Level 2 predictions.

  • frontier : List TestablePrediction Level 3 predictions.

  • has_structural : self.structural.length > 0 At least one structural prediction.

  • has_quantitative : self.quantitative.length > 0 At least one quantitative prediction.

  • has_frontier : self.frontier.length > 0 At least one frontier prediction.

Instances For

Tau.BookV.Cosmology.instReprFalsificationLevels

source instance Tau.BookV.Cosmology.instReprFalsificationLevels :Repr FalsificationLevels

Equations

  • Tau.BookV.Cosmology.instReprFalsificationLevels = { reprPrec := Tau.BookV.Cosmology.instReprFalsificationLevels.repr }

Tau.BookV.Cosmology.instReprFalsificationLevels.repr

source def Tau.BookV.Cosmology.instReprFalsificationLevels.repr :FalsificationLevels → ℕ → Std.Format

Equations

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

Tau.BookV.Cosmology.pred_no_sixth_force

source def Tau.BookV.Cosmology.pred_no_sixth_force :TestablePrediction

S1: No sixth force. Equations

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

Tau.BookV.Cosmology.pred_no_dm_particle

source def Tau.BookV.Cosmology.pred_no_dm_particle :TestablePrediction

S2: No dark matter particle. Equations

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

Tau.BookV.Cosmology.pred_cgw_equals_c

source def Tau.BookV.Cosmology.pred_cgw_equals_c :TestablePrediction

S3: c_gw = c exactly. Equations

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

Tau.BookV.Cosmology.pred_no_gw_echoes

source def Tau.BookV.Cosmology.pred_no_gw_echoes :TestablePrediction

S4: No GW echoes. Equations

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

Tau.BookV.Cosmology.pred_electron_mass

source def Tau.BookV.Cosmology.pred_electron_mass :TestablePrediction

Q1: Electron mass at 0.025 ppm. Equations

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

Tau.BookV.Cosmology.pred_grav_constant

source def Tau.BookV.Cosmology.pred_grav_constant :TestablePrediction

Q2: Gravitational constant at 3 ppm. Equations

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

Tau.BookV.Cosmology.pred_tensor_scalar

source def Tau.BookV.Cosmology.pred_tensor_scalar :TestablePrediction

Q3: Tensor-to-scalar ratio r ~ 0.014. Equations

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

Tau.BookV.Cosmology.pred_torus_shadow

source def Tau.BookV.Cosmology.pred_torus_shadow :TestablePrediction

F1: T² topology BH shadows. Equations

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

Tau.BookV.Cosmology.pred_discreteness

source def Tau.BookV.Cosmology.pred_discreteness :TestablePrediction

F2: Profinite discreteness at Planck scale. Equations

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

Tau.BookV.Cosmology.pred_no_transplanckian

source def Tau.BookV.Cosmology.pred_no_transplanckian :TestablePrediction

F3: No trans-Planckian modes in CMB. Equations

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

Tau.BookV.Cosmology.falsification_package

source def Tau.BookV.Cosmology.falsification_package :FalsificationLevels

The complete falsification package. Equations

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

Tau.BookV.Cosmology.structural_count

source theorem Tau.BookV.Cosmology.structural_count :falsification_package.structural.length = 4

4 structural predictions.

Tau.BookV.Cosmology.quantitative_count

source theorem Tau.BookV.Cosmology.quantitative_count :falsification_package.quantitative.length = 3

3 quantitative predictions.

Tau.BookV.Cosmology.frontier_count

source theorem Tau.BookV.Cosmology.frontier_count :falsification_package.frontier.length = 3

3 frontier predictions.

Tau.BookV.Cosmology.total_predictions

source theorem Tau.BookV.Cosmology.total_predictions :falsification_package.structural.length + falsification_package.quantitative.length + falsification_package.frontier.length = 10

Total: 10 testable predictions.

Tau.BookV.Cosmology.cmb_scope_note

source def Tau.BookV.Cosmology.cmb_scope_note :Prop

[V.R243] Scope note: CMB predictions C2, C5, C6 involve mapping τ-native quantities to standard CMB observables (angular power spectrum, polarization). The mapping is tau-effective, but numerical calibration carries observational uncertainties. Equations

  • Tau.BookV.Cosmology.cmb_scope_note = (“CMB predictions: tau-effective mapping, observational calibration” = “CMB predictions: tau-effective mapping, observational calibration”) Instances For

Tau.BookV.Cosmology.cmb_scope_holds

source theorem Tau.BookV.Cosmology.cmb_scope_holds :cmb_scope_note