TauLib · API Book IV

TauLib.BookIV.Calibration.DimensionlessCouplings2

TauLib.BookIV.Calibration.DimensionlessCouplings2

Cross-couplings (ch10 second half), temporal complement, multiplicative closure, and power hierarchy — all wrapping existing CouplingFormulas proofs.

Registry Cross-References

  • [IV.D281] Electroweak cross-coupling — ew_cross

  • [IV.D282] Weak-strong cross-coupling — weak_strong_cross

  • [IV.D283] EM-strong cross-coupling — em_strong_cross

  • [IV.D284] EM-gravity cross-coupling — em_grav_cross

  • [IV.D285] Strong-gravity cross-coupling — strong_grav_cross

  • [IV.R250] Lean verification — (structural remark)

  • [IV.T104] Temporal Complement — temporal_complement_ch10

  • [IV.T105] Temporal Multiplicative Closure — temporal_mult_ch10

  • [IV.R252] Lean formalization — (structural remark)

  • [IV.T106] Power Hierarchy — power_hierarchy_ch10

  • [IV.P165] Hierarchy Resolution — hierarchy_resolution

  • [IV.R254] No landscape — (structural remark)

Ground Truth Sources

  • Chapter 10 of Book IV (2nd Edition), second half

Tau.BookIV.Calibration.ew_cross

source@[reducible, inline]

abbrev Tau.BookIV.Calibration.ew_cross :Sectors.CouplingFormula

[IV.D281] Electroweak cross-coupling κ(A,B) = ι_τ³ ≈ 0.03982. Connects weak (base) to EM (fiber). Equations

  • Tau.BookIV.Calibration.ew_cross = Tau.BookIV.Sectors.kappa_AB Instances For

Tau.BookIV.Calibration.weak_strong_cross

source@[reducible, inline]

abbrev Tau.BookIV.Calibration.weak_strong_cross :Sectors.CouplingFormula

[IV.D282] Weak-strong cross-coupling κ(A,C) = ι_τ⁴/(1−ι_τ) ≈ 0.02063. Note: kappa_AC is ι_τ⁴/(1−ι_τ) = κ(A)·κ(C), the Weak-Strong = beta decay channel. Equations

  • Tau.BookIV.Calibration.weak_strong_cross = Tau.BookIV.Sectors.kappa_AC Instances For

Tau.BookIV.Calibration.em_strong_cross

source@[reducible, inline]

abbrev Tau.BookIV.Calibration.em_strong_cross :Sectors.CouplingFormula

[IV.D283] EM-strong cross-coupling κ(B,C) = ι_τ³/(1+ι_τ) ≈ 0.02968. The weakest primitive cross-coupling. Equations

  • Tau.BookIV.Calibration.em_strong_cross = Tau.BookIV.Sectors.kappa_BC Instances For

Tau.BookIV.Calibration.em_grav_cross

source@[reducible, inline]

abbrev Tau.BookIV.Calibration.em_grav_cross :Sectors.CouplingFormula

[IV.D284] EM-gravity cross-coupling κ(B,D) = ι_τ²(1−ι_τ)² ≈ 0.05061. Gravitational lensing channel. Equations

  • Tau.BookIV.Calibration.em_grav_cross = Tau.BookIV.Sectors.kappa_BD Instances For

Tau.BookIV.Calibration.strong_grav_cross

source@[reducible, inline]

abbrev Tau.BookIV.Calibration.strong_grav_cross :Sectors.CouplingFormula

[IV.D285] Strong-gravity cross-coupling κ(C,D) = ι_τ³(1−ι_τ) ≈ 0.02623. Mass curves time. Equations

  • Tau.BookIV.Calibration.strong_grav_cross = Tau.BookIV.Sectors.kappa_CD Instances For

Tau.BookIV.Calibration.temporal_complement_ch10

source theorem Tau.BookIV.Calibration.temporal_complement_ch10 :Sectors.kappa_AA.numer + Sectors.kappa_DD.numer = Sectors.kappa_AA.denom

[IV.T104] Temporal complement: κ(A;1) + κ(D;1) = 1. Wraps CouplingFormulas.temporal_complement.

Tau.BookIV.Calibration.temporal_mult_ch10

source theorem Tau.BookIV.Calibration.temporal_mult_ch10 :Sectors.kappa_AD.numer * (Sectors.kappa_AA.denom * Sectors.kappa_DD.denom) = Sectors.kappa_AA.numer * Sectors.kappa_DD.numer * Sectors.kappa_AD.denom

[IV.T105] Temporal multiplicative closure: κ(A,D) = κ(A;1)·κ(D;1). Wraps CouplingFormulas.temporal_multiplicative.

Tau.BookIV.Calibration.power_hierarchy_ch10

source theorem Tau.BookIV.Calibration.power_hierarchy_ch10 :Sectors.kappa_BB.numer * (Sectors.kappa_AA.denom * Sectors.kappa_AA.denom) = Sectors.kappa_AA.numer * Sectors.kappa_AA.numer * Sectors.kappa_BB.denom ∧ Sectors.kappa_AC.numer * (Sectors.kappa_AA.denom * Sectors.kappa_CC.denom) = Sectors.kappa_AA.numer * Sectors.kappa_CC.numer * Sectors.kappa_AC.denom

[IV.T106] Power hierarchy: κ(B;2) = κ(A;1)² and κ(A,C) = κ(A;1)·κ(C;3). The EM coupling is the square of the weak coupling; weak-strong is the multiplicative closure of weak × strong.

Tau.BookIV.Calibration.hierarchy_resolution

source theorem Tau.BookIV.Calibration.hierarchy_resolution :Sectors.kappa_DD.numer > Sectors.kappa_AA.numer

[IV.P165] The gravitational self-coupling κ(D;1) = 1−ι_τ is the LARGEST primitive coupling. The apparent weakness of gravity is a readout artifact: G involves ι_τ² from the torus vacuum.