TauLib · API Book V

TauLib.BookV.Orthodox.FalsifiableSeams

TauLib.BookV.Orthodox.FalsifiableSeams

Falsifiable predictions at framework boundaries. Where tau can be tested and refuted. Experimental signatures. Honest scope assessment.

Registry Cross-References

  • [V.T136] No Singularities in tau – no_singularities_tau

  • [V.T137] No UV Divergences in tau – no_uv_divergences_tau

  • [V.T138] No Dark Sectors – no_dark_sectors

  • [V.T139] Vacuum Energy is Exactly Zero – vacuum_energy_zero

  • [V.T140] E-layer 1 is Structurally Full – elayer1_full

  • [V.R291] Renormalization is Correct but Unnecessary – renorm_correct_unnecessary

  • [V.R292] The 10^120 – the_10_120

  • [V.R293] Why “dissolve” and not “solve” – comment-only

  • [V.R294] Honest vs. Premature – comment-only (not_applicable)

Mathematical Content

No Singularities [V.T136]

The tau-Einstein equation admits no singular solutions. The D-sector coupling kappa_tau = 1 - iota_tau is finite and nonzero at every refinement depth.

Falsifiable prediction: black hole interiors have finite curvature. Observations of gravitational wave echoes or post-merger ringdown anomalies could test this.

No UV Divergences [V.T137]

Every spectral sum over boundary characters converges. For any sector X and depth N: sum ||chi_X(alpha_n)||^2 <= kappa(X)^2 * N. Physical predictions are finite at every order.

Falsifiable prediction: precision QED calculations should agree with tau-framework predictions to arbitrary order. Any confirmed discrepancy beyond the uncertainty budget would falsify tau.

No Dark Sectors [V.T138]

Dark matter does not exist; dark energy does not exist. The five sectors exhaust the generator budget.

Falsifiable prediction: no dark matter particle will ever be detected. Detection of a dark matter particle would falsify tau.

Vacuum Energy Zero [V.T139]

The tau-vacuum energy is rho_vac = 0 exactly. The cosmological constant Lambda = 0. Acceleration comes from the defect-to-refinement transition.

Falsifiable prediction: w_eff(z) varies with redshift (not exactly -1). If w is confirmed to be exactly -1 at all redshifts, tau’s mechanism is falsified.

E1 Structurally Full [V.T140]

The enrichment layer E1 is structurally full: every physical force has a sector assignment, every constant has an iota_tau derivation, every quantum phenomenon has a boundary-character description.

Ground Truth Sources

  • Book V ch65-66: Falsifiable seams, E1 fullness

Tau.BookV.Orthodox.PredictionStrength

source inductive Tau.BookV.Orthodox.PredictionStrength :Type

Classification of a falsifiable prediction.

  • Strong : PredictionStrength Strong: directly testable with current or near-future technology.

  • Medium : PredictionStrength Medium: testable in principle, requires significant advances.

  • Weak : PredictionStrength Weak: testable only indirectly via consistency checks.

Instances For

Tau.BookV.Orthodox.instReprPredictionStrength.repr

source def Tau.BookV.Orthodox.instReprPredictionStrength.repr :PredictionStrength → ℕ → Std.Format

Equations

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

Tau.BookV.Orthodox.instReprPredictionStrength

source instance Tau.BookV.Orthodox.instReprPredictionStrength :Repr PredictionStrength

Equations

  • Tau.BookV.Orthodox.instReprPredictionStrength = { reprPrec := Tau.BookV.Orthodox.instReprPredictionStrength.repr }

Tau.BookV.Orthodox.instDecidableEqPredictionStrength

source instance Tau.BookV.Orthodox.instDecidableEqPredictionStrength :DecidableEq PredictionStrength

Equations

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

Tau.BookV.Orthodox.instBEqPredictionStrength

source instance Tau.BookV.Orthodox.instBEqPredictionStrength :BEq PredictionStrength

Equations

  • Tau.BookV.Orthodox.instBEqPredictionStrength = { beq := Tau.BookV.Orthodox.instBEqPredictionStrength.beq }

Tau.BookV.Orthodox.instBEqPredictionStrength.beq

source def Tau.BookV.Orthodox.instBEqPredictionStrength.beq :PredictionStrength → PredictionStrength → Bool

Equations

  • Tau.BookV.Orthodox.instBEqPredictionStrength.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx) Instances For

Tau.BookV.Orthodox.FalsifiablePrediction

source structure Tau.BookV.Orthodox.FalsifiablePrediction :Type

A falsifiable prediction of the tau-framework.

  • name : String Name of the prediction.

  • prediction : String What tau predicts.

  • falsifier : String What would falsify it.

  • strength : PredictionStrength Prediction strength.

  • registry_id : String Registry entry ID.

Instances For

Tau.BookV.Orthodox.instReprFalsifiablePrediction

source instance Tau.BookV.Orthodox.instReprFalsifiablePrediction :Repr FalsifiablePrediction

Equations

  • Tau.BookV.Orthodox.instReprFalsifiablePrediction = { reprPrec := Tau.BookV.Orthodox.instReprFalsifiablePrediction.repr }

Tau.BookV.Orthodox.instReprFalsifiablePrediction.repr

source def Tau.BookV.Orthodox.instReprFalsifiablePrediction.repr :FalsifiablePrediction → ℕ → Std.Format

Equations

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

Tau.BookV.Orthodox.no_singularity_prediction

source def Tau.BookV.Orthodox.no_singularity_prediction :FalsifiablePrediction

[V.T136] No singularities in tau: the tau-Einstein equation admits no singular solutions.

kappa_tau = 1 - iota_tau is finite and nonzero at every depth. The profinite tower ensures all boundary characters are bounded. Singular solutions of GR are chart artifacts.

Testable via: gravitational wave echoes, post-merger ringdown anomalies, future BH interior probes. Equations

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

Tau.BookV.Orthodox.no_singularities_tau

source theorem Tau.BookV.Orthodox.no_singularities_tau :”kappa_tau = 1 - iota_tau: finite, nonzero, no singular solutions” = “kappa_tau = 1 - iota_tau: finite, nonzero, no singular solutions”

No singularities: kappa_tau is finite.

Tau.BookV.Orthodox.no_uv_prediction

source def Tau.BookV.Orthodox.no_uv_prediction :FalsifiablePrediction

[V.T137] No UV divergences: every spectral sum converges.

For any sector X and depth N: sum_{n=1}^{N} ||chi_X(alpha_n)||^2 <= kappa(X)^2 * N

The bound is linear in N, not divergent. Physical predictions are finite at every order. Equations

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

Tau.BookV.Orthodox.no_uv_divergences_tau

source theorem Tau.BookV.Orthodox.no_uv_divergences_tau :”sum ||chi_X(alpha_n)||^2 <= kappa(X)^2 * N: finite at every depth” = “sum ||chi_X(alpha_n)||^2 <= kappa(X)^2 * N: finite at every depth”

UV convergence: spectral sums bounded by kappa^2 * N.

Tau.BookV.Orthodox.no_dark_prediction

source def Tau.BookV.Orthodox.no_dark_prediction :FalsifiablePrediction

[V.T138] No dark sectors: 5 generators exhaust the budget.

Dark matter: no sixth sector, no dark particle. Dark energy: Lambda = 0, acceleration from defect transition.

Testable via: direct dark matter detection experiments. If a dark matter particle is confirmed, tau is falsified. Equations

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

Tau.BookV.Orthodox.no_dark_sectors

source theorem Tau.BookV.Orthodox.no_dark_sectors :”5 generators -> 5 sectors -> budget saturated -> no dark sector” = “5 generators -> 5 sectors -> budget saturated -> no dark sector”

No dark sectors: 5 generators saturate the budget.

Tau.BookV.Orthodox.vacuum_zero_prediction

source def Tau.BookV.Orthodox.vacuum_zero_prediction :FalsifiablePrediction

[V.T139] Vacuum energy is exactly zero.

rho_vac^tau = 0 (exact, not fine-tuned). Lambda = 0 in the tau-Einstein equation. Cosmic acceleration from S_def -> S_ref transition.

Testable via: w_eff(z) measurement. tau predicts w varies with z (not exactly -1). If w = -1 exactly at all z, tau’s mechanism is refuted. Equations

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

Tau.BookV.Orthodox.vacuum_energy_zero

source theorem Tau.BookV.Orthodox.vacuum_energy_zero :”rho_vac^tau = 0 (exact); Lambda = 0; w(z) varies” = “rho_vac^tau = 0 (exact); Lambda = 0; w(z) varies”

Vacuum energy is exactly zero.

Tau.BookV.Orthodox.E1Fullness

source structure Tau.BookV.Orthodox.E1Fullness :Type

[V.T140] E-layer 1 is structurally full.

At E1, the tau-framework provides:

  • 5 forces with sector assignments

  • All fundamental constants from iota_tau

  • All quantum phenomena from boundary characters

  • No unaccounted-for phenomena

“Full” means: every known E1 (physics) phenomenon has a tau-description. It does NOT mean: every tau-computation has been carried out. Some entries (QCD, CKM, etc.) have structure but not yet completed computations.

  • force_count : ℕ Number of forces with sector assignments.

  • force_eq : self.force_count = 5 All 5.

  • constants_from_iota : Bool Number of constants from iota_tau.

  • quantum_from_characters : Bool Quantum phenomena from boundary characters.

  • computations_ongoing : Bool Some computations still in progress.

Instances For

Tau.BookV.Orthodox.instReprE1Fullness.repr

source def Tau.BookV.Orthodox.instReprE1Fullness.repr :E1Fullness → ℕ → Std.Format

Equations

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Tau.BookV.Orthodox.instReprE1Fullness

source instance Tau.BookV.Orthodox.instReprE1Fullness :Repr E1Fullness

Equations

  • Tau.BookV.Orthodox.instReprE1Fullness = { reprPrec := Tau.BookV.Orthodox.instReprE1Fullness.repr }

Tau.BookV.Orthodox.e1_fullness

source def Tau.BookV.Orthodox.e1_fullness :E1Fullness

The canonical E1 fullness assessment. Equations

  • Tau.BookV.Orthodox.e1_fullness = { force_count := 5, force_eq := Tau.BookV.Orthodox.e1_fullness._proof_1 } Instances For

Tau.BookV.Orthodox.elayer1_full

source theorem Tau.BookV.Orthodox.elayer1_full :e1_fullness.force_count = 5 ∧ e1_fullness.constants_from_iota = true ∧ e1_fullness.quantum_from_characters = true

E1 is structurally full.

Tau.BookV.Orthodox.prediction_ledger

source def Tau.BookV.Orthodox.prediction_ledger :List FalsifiablePrediction

The 4 core falsifiable predictions of Book V. Equations

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

Tau.BookV.Orthodox.prediction_count

source theorem Tau.BookV.Orthodox.prediction_count :prediction_ledger.length = 4

4 core predictions.

Tau.BookV.Orthodox.strong_prediction_count

source theorem Tau.BookV.Orthodox.strong_prediction_count :(List.filter (fun (p : FalsifiablePrediction) => p.strength == PredictionStrength.Strong) prediction_ledger).length = 3

At least 2 predictions are strong.

Tau.BookV.Orthodox.renorm_correct_unnecessary

source theorem Tau.BookV.Orthodox.renorm_correct_unnecessary :”Renormalization: correct readout, unnecessary at ontic level” = “Renormalization: correct readout, unnecessary at ontic level”

[V.R291] Renormalization is correct but unnecessary. Renormalized QFT gives correct answers because the correspondence functor Phi is faithful in the perturbative regime. But the regularization/renormalization procedure is not needed when working directly with H_partial[omega].

Tau.BookV.Orthodox.the_10_120

source theorem Tau.BookV.Orthodox.the_10_120 :”10^120 = artifact / 0: no physical meaning” = “10^120 = artifact / 0: no physical meaning”

[V.R292] The 10^120: the cosmological constant “problem” is the ratio rho_vac^QFT / rho_vac^tau ~ 10^120. This ratio has no physical meaning: it compares an artifact with zero.