TauLib · API Book IV

TauLib.BookIV.Calibration.DimensionlessCouplings

TauLib.BookIV.Calibration.DimensionlessCouplings

The 5 self-couplings + 1 cross-coupling from Chapter 10, with their numerical values presented as the Dimensionless Cascade.

Registry Cross-References

  • [IV.R247] Origin of the No Knobs Principle — (structural remark)

  • [IV.D275] Gravitational self-coupling — grav_self_coupling

  • [IV.P160] Numerical value κ(D) — grav_coupling_value

  • [IV.D276] Weak self-coupling — weak_self_coupling

  • [IV.P161] Numerical value κ(A) — weak_coupling_value

  • [IV.D277] EM self-coupling — em_self_coupling

  • [IV.P162] Numerical value κ(B) — em_coupling_value

  • [IV.D278] Strong self-coupling — strong_self_coupling

  • [IV.P163] Numerical value κ(C) — strong_coupling_value

  • [IV.R248] Lean verification — (structural remark)

  • [IV.D279] Omega self-coupling — omega_self_coupling

  • [IV.P164] Numerical value κ(ω) — omega_coupling_value

  • [IV.D280] Weak-gravity cross-coupling — weak_grav_cross

Ground Truth Sources

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

Tau.BookIV.Calibration.grav_self_coupling

source@[reducible, inline]

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

[IV.D275] Gravitational self-coupling κ(D;1) = 1 − ι_τ ≈ 0.658541. Depth 1, χ₊-dominant. The largest primitive coupling. Equations

  • Tau.BookIV.Calibration.grav_self_coupling = Tau.BookIV.Sectors.kappa_DD Instances For

Tau.BookIV.Calibration.grav_coupling_value

source theorem Tau.BookIV.Calibration.grav_coupling_value :grav_self_coupling.numer * 1000 > 658 * grav_self_coupling.denom ∧ grav_self_coupling.numer * 1000 < 659 * grav_self_coupling.denom

[IV.P160] Numerical value: κ(D;1) is in (658, 659)/1000.

Tau.BookIV.Calibration.weak_self_coupling

source@[reducible, inline]

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

[IV.D276] Weak self-coupling κ(A;1) = ι_τ ≈ 0.341304. Depth 1, balanced polarity. Equals the master constant. Equations

  • Tau.BookIV.Calibration.weak_self_coupling = Tau.BookIV.Sectors.kappa_AA Instances For

Tau.BookIV.Calibration.weak_coupling_value

source theorem Tau.BookIV.Calibration.weak_coupling_value :weak_self_coupling.numer * 1000 > 341 * weak_self_coupling.denom ∧ weak_self_coupling.numer * 1000 < 342 * weak_self_coupling.denom

[IV.P161] Numerical value: κ(A;1) is in (341, 342)/1000.

Tau.BookIV.Calibration.em_self_coupling

source@[reducible, inline]

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

[IV.D277] Electromagnetic self-coupling κ(B;2) = ι_τ² ≈ 0.116594. Depth 2, χ₊-dominant. Equations

  • Tau.BookIV.Calibration.em_self_coupling = Tau.BookIV.Sectors.kappa_BB Instances For

Tau.BookIV.Calibration.em_coupling_value

source theorem Tau.BookIV.Calibration.em_coupling_value :em_self_coupling.numer * 1000 > 116 * em_self_coupling.denom ∧ em_self_coupling.numer * 1000 < 117 * em_self_coupling.denom

[IV.P162] Numerical value: κ(B;2) is in (116, 117)/1000.

Tau.BookIV.Calibration.strong_self_coupling

source@[reducible, inline]

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

[IV.D278] Strong self-coupling κ(C;3) = ι_τ³/(1−ι_τ) ≈ 0.06046. Depth 3, χ₋-dominant. Confinement coupling. Equations

  • Tau.BookIV.Calibration.strong_self_coupling = Tau.BookIV.Sectors.kappa_CC Instances For

Tau.BookIV.Calibration.strong_coupling_value

source theorem Tau.BookIV.Calibration.strong_coupling_value :strong_self_coupling.numer * 1000 > 60 * strong_self_coupling.denom ∧ strong_self_coupling.numer * 1000 < 61 * strong_self_coupling.denom

[IV.P163] Numerical value: κ(C;3) is in (60, 61)/1000.

Tau.BookIV.Calibration.omega_self_coupling

source@[reducible, inline]

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

[IV.D279] Omega self-coupling κ(ω) = ι_τ³/(1+ι_τ) ≈ 0.02968. Crossing-point readout. The smallest primitive coupling. Equations

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

Tau.BookIV.Calibration.omega_coupling_value

source theorem Tau.BookIV.Calibration.omega_coupling_value :omega_self_coupling.numer * 1000 > 29 * omega_self_coupling.denom ∧ omega_self_coupling.numer * 1000 < 30 * omega_self_coupling.denom

[IV.P164] Numerical value: κ(ω) is in (29, 30)/1000.

Tau.BookIV.Calibration.weak_grav_cross

source@[reducible, inline]

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

[IV.D280] Weak-gravity cross-coupling κ(A,D) = ι_τ(1−ι_τ) ≈ 0.2249. Both sectors on base τ¹. Near sin²θ_W = 0.2312. Equations

  • Tau.BookIV.Calibration.weak_grav_cross = Tau.BookIV.Sectors.kappa_AD Instances For