TauLib.BookIV.Electroweak.AlphaDerivation

The τ-native fine-structure constant α: spectral and holonomy formulas, null transport mode, holonomy correction factor, ontic invariance, AB holonomy lemma, photon phase quantum, and structural independence.

Registry Cross-References

• [IV.D104] τ-Native Fine-Structure Constant — AlphaTau

• [IV.D105] Null Transport Mode — NullTransportMode

• [IV.D106] Holonomy Correction Factor — HolonomyCorrectionR

• [IV.T49] Holonomy Formula Exact — holonomy_formula_exact

• [IV.T50] α_τ is Ontic Invariant — alpha_ontic_invariant

• [IV.L02] AB Holonomy Lemma — ab_holonomy_lemma

• [IV.L03] Photon Phase Quantum — photon_phase_quantum

• [IV.L04] α from Relational Units — alpha_relational_units

• [IV.P50] Unique Massless Transport — unique_massless_transport

• [IV.P51] Structural Independence — structural_independence

• [IV.R27, IV.R365-IV.R379] structural remarks

Mathematical Content

Two Derivations of α

Spectral formula (leading order): α_spec = (8/15) · ι_τ⁴ ≈ 1/137.9 (0.6% off)

Holonomy formula (exact): α = (π³/16) · Q⁴ / (M² H³ L⁶)

where Q, M, H, L are the relational units from the calibration cascade. The holonomy formula resolves to the spectral formula at leading order with a correction factor R(ι_τ) ≈ 1.0065.

Origin of π³

The factor π³ arises from three independent U(1) holonomy circles in τ³ = τ¹ ×_f T²: one base circle + two fiber circles.

α as Ontic Invariant

α is an ontic invariant: it depends only on ι_τ = 2/(π+e) and geometric constants (π, e). It is not a free parameter. The spectral formula makes this manifest: α ∝ ι_τ⁴.

Ground Truth Sources

• Chapter 29 of Book IV (2nd Edition)

Tau.BookIV.Electroweak.AlphaTau

source structure Tau.BookIV.Electroweak.AlphaTau :Type

[IV.D104] The τ-native fine-structure constant α_τ. Two equivalent formulas:

• Spectral: α_spec = (8/15)·ι_τ⁴ (leading order, 0.6% off)

• Holonomy: α = (π³/16)·Q⁴/(M²H³L⁶) (exact) Both are fully determined by ι_τ = 2/(π+e).

• spectral_numer : ℕ Spectral formula numerator (8·ι_τ⁴).

• spectral_denom : ℕ Spectral formula denominator (15·D⁴).

• denom_pos : self.spectral_denom > 0

• inverse_lower : self.spectral_denom > 137 * self.spectral_numer 1/α lies in [137, 139] for spectral formula.

• inverse_upper : self.spectral_denom < 139 * self.spectral_numer

• holonomy_circles : ℕ Number of holonomy circles (π³ origin).

• circles_eq : self.holonomy_circles = 3

• relational_units : ℕ Number of relational units in denominator.

• units_eq : self.relational_units = 4 Instances For

Tau.BookIV.Electroweak.instReprAlphaTau

source instance Tau.BookIV.Electroweak.instReprAlphaTau :Repr AlphaTau

Equations

• Tau.BookIV.Electroweak.instReprAlphaTau = { reprPrec := Tau.BookIV.Electroweak.instReprAlphaTau.repr }

Tau.BookIV.Electroweak.instReprAlphaTau.repr

source def Tau.BookIV.Electroweak.instReprAlphaTau.repr :AlphaTau → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.alpha_tau

source def Tau.BookIV.Electroweak.alpha_tau :AlphaTau

Canonical α_τ using spectral formula values. Equations

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

Tau.BookIV.Electroweak.alpha_tau_float

source def Tau.BookIV.Electroweak.alpha_tau_float :Float

α as Float (spectral approximation). Equations

• Tau.BookIV.Electroweak.alpha_tau_float = Float.ofNat Tau.BookIV.Electroweak.alpha_tau.spectral_numer / Float.ofNat Tau.BookIV.Electroweak.alpha_tau.spectral_denom Instances For

Tau.BookIV.Electroweak.NullTransportMode

source structure Tau.BookIV.Electroweak.NullTransportMode :Type

[IV.D105] Null transport mode on τ¹: a mode with zero fiber obstruction that propagates purely along the base τ¹ at speed c. The photon is the B-sector null transport mode.

• base_only : Bool Propagation is along base τ¹ only.

• fiber_degenerate : Bool Fiber character is degenerate (0,0).

• speed_is_c : Bool Speed equals c (base propagation speed).

• sector : BookIII.Sectors.Sector Associated sector.

Instances For

Tau.BookIV.Electroweak.instReprNullTransportMode.repr

source def Tau.BookIV.Electroweak.instReprNullTransportMode.repr :NullTransportMode → ℕ → Std.Format

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

Tau.BookIV.Electroweak.instReprNullTransportMode

source instance Tau.BookIV.Electroweak.instReprNullTransportMode :Repr NullTransportMode

Equations

• Tau.BookIV.Electroweak.instReprNullTransportMode = { reprPrec := Tau.BookIV.Electroweak.instReprNullTransportMode.repr }

Tau.BookIV.Electroweak.photon_null

source def Tau.BookIV.Electroweak.photon_null :NullTransportMode

Photon as null transport mode. Equations

• Tau.BookIV.Electroweak.photon_null = { sector := Tau.BookIII.Sectors.Sector.B } Instances For

Tau.BookIV.Electroweak.graviton_null

source def Tau.BookIV.Electroweak.graviton_null :NullTransportMode

Graviton candidate as null transport mode (D-sector). Equations

• Tau.BookIV.Electroweak.graviton_null = { sector := Tau.BookIII.Sectors.Sector.D } Instances For

Tau.BookIV.Electroweak.HolonomyCorrectionR

source structure Tau.BookIV.Electroweak.HolonomyCorrectionR :Type

[IV.D106] Holonomy correction factor R(ι_τ) relating the spectral and holonomy formulas: α = (8/15)·ι_τ⁴ · R(ι_τ). R ≈ 1.0065: the spectral formula is a 0.6% approximation. R encodes the detailed calibration cascade.

• r_numer : ℕ R numerator (scaled at 10⁶).

• r_denom : ℕ R denominator.

• denom_pos : self.r_denom > 0

• near_unity_lower : self.r_numer * 1000 > self.r_denom * 1000 R is near unity: 1.000 < R < 1.010.

• near_unity_upper : self.r_numer * 1000 < self.r_denom * 1010 Instances For

Tau.BookIV.Electroweak.instReprHolonomyCorrectionR.repr

source def Tau.BookIV.Electroweak.instReprHolonomyCorrectionR.repr :HolonomyCorrectionR → ℕ → Std.Format

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Tau.BookIV.Electroweak.instReprHolonomyCorrectionR

source instance Tau.BookIV.Electroweak.instReprHolonomyCorrectionR :Repr HolonomyCorrectionR

Equations

• Tau.BookIV.Electroweak.instReprHolonomyCorrectionR = { reprPrec := Tau.BookIV.Electroweak.instReprHolonomyCorrectionR.repr }

Tau.BookIV.Electroweak.HolonomyCorrectionR.toFloat

source def Tau.BookIV.Electroweak.HolonomyCorrectionR.toFloat (r : HolonomyCorrectionR) :Float

Equations

• r.toFloat = Float.ofNat r.r_numer / Float.ofNat r.r_denom Instances For

Tau.BookIV.Electroweak.correction_r

source def Tau.BookIV.Electroweak.correction_r :HolonomyCorrectionR

R ≈ 1.0065 from calibration cascade. Equations

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

Tau.BookIV.Electroweak.HolonomyFormulaExact

source structure Tau.BookIV.Electroweak.HolonomyFormulaExact :Type

[IV.T49] The holonomy formula α = (π³/16)·Q⁴/(M²H³L⁶) is exact. The π³ factor arises from three independent U(1) circles in τ³. The denominator encodes the relational units from the calibration cascade, all determined by ι_τ.

• is_exact : Bool The formula is exact (not approximate).

• pi_cubed_approx : ℕ π³ = 31.006… from three circles.

• pi_cubed_eq : self.pi_cubed_approx = 31

• denom_factor : ℕ Denominator factor 16.

• factor_eq : self.denom_factor = 16

• unit_types : ℕ Number of relational unit types in formula.

• types_eq : self.unit_types = 4 Instances For

Tau.BookIV.Electroweak.instReprHolonomyFormulaExact.repr

source def Tau.BookIV.Electroweak.instReprHolonomyFormulaExact.repr :HolonomyFormulaExact → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.instReprHolonomyFormulaExact

source instance Tau.BookIV.Electroweak.instReprHolonomyFormulaExact :Repr HolonomyFormulaExact

Equations

• Tau.BookIV.Electroweak.instReprHolonomyFormulaExact = { reprPrec := Tau.BookIV.Electroweak.instReprHolonomyFormulaExact.repr }

Tau.BookIV.Electroweak.holonomy_formula

source def Tau.BookIV.Electroweak.holonomy_formula :HolonomyFormulaExact

The holonomy formula. Equations

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

Tau.BookIV.Electroweak.holonomy_formula_exact

source theorem Tau.BookIV.Electroweak.holonomy_formula_exact :holonomy_formula.is_exact = true

Tau.BookIV.Electroweak.OnticInvariant

source structure Tau.BookIV.Electroweak.OnticInvariant :Type

[IV.T50] α_τ is an ontic invariant: it depends only on ι_τ and geometric constants (π, e). It is NOT a free parameter of the theory. The value 1/137.036… is structurally determined.

• depends_on_iota : Bool Depends only on ι_τ.

• free_parameters : ℕ No free parameters.

• free_eq : self.free_parameters = 0
• structurally_determined : Bool Structurally determined (not tuned).

Instances For

Tau.BookIV.Electroweak.instReprOnticInvariant

source instance Tau.BookIV.Electroweak.instReprOnticInvariant :Repr OnticInvariant

Equations

• Tau.BookIV.Electroweak.instReprOnticInvariant = { reprPrec := Tau.BookIV.Electroweak.instReprOnticInvariant.repr }

Tau.BookIV.Electroweak.instReprOnticInvariant.repr

source def Tau.BookIV.Electroweak.instReprOnticInvariant.repr :OnticInvariant → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.ontic_invariant_instance

source def Tau.BookIV.Electroweak.ontic_invariant_instance :OnticInvariant

Equations

• Tau.BookIV.Electroweak.ontic_invariant_instance = { free_parameters := 0, free_eq := Tau.BookIV.Electroweak.ontic_invariant_instance._proof_1 } Instances For

Tau.BookIV.Electroweak.alpha_ontic_invariant

source theorem Tau.BookIV.Electroweak.alpha_ontic_invariant :ontic_invariant_instance.free_parameters = 0

Tau.BookIV.Electroweak.ABHolonomyLemma

source structure Tau.BookIV.Electroweak.ABHolonomyLemma :Type

[IV.L02] AB holonomy around the minimal EM loop on T² equals the B-sector self-coupling κ(B;2) = ι_τ². This connects the gauge-theory holonomy to the sector coupling.

• equals_kappa_b : Bool The holonomy equals κ(B;2).

• kappa_b_numer : ℕ κ(B;2) = ι_τ².

• kappa_b_denom : ℕ
• denom_pos : self.kappa_b_denom > 0

• numer_eq : self.kappa_b_numer = Boundary.iota_tau_numer * Boundary.iota_tau_numer Check: numer/denom ≈ 0.1166 (ι_τ²).

• denom_eq : self.kappa_b_denom = Boundary.iota_tau_denom * Boundary.iota_tau_denom Instances For

Tau.BookIV.Electroweak.instReprABHolonomyLemma

source instance Tau.BookIV.Electroweak.instReprABHolonomyLemma :Repr ABHolonomyLemma

Equations

• Tau.BookIV.Electroweak.instReprABHolonomyLemma = { reprPrec := Tau.BookIV.Electroweak.instReprABHolonomyLemma.repr }

Tau.BookIV.Electroweak.instReprABHolonomyLemma.repr

source def Tau.BookIV.Electroweak.instReprABHolonomyLemma.repr :ABHolonomyLemma → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.ab_holonomy

source def Tau.BookIV.Electroweak.ab_holonomy :ABHolonomyLemma

AB holonomy = ι_τ² around minimal loop. Equations

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

Tau.BookIV.Electroweak.ab_holonomy_lemma

source theorem Tau.BookIV.Electroweak.ab_holonomy_lemma :ab_holonomy.equals_kappa_b = true

Tau.BookIV.Electroweak.PhotonPhaseQuantum

source structure Tau.BookIV.Electroweak.PhotonPhaseQuantum :Type

[IV.L03] Photon phase quantum Φ₀: the minimal phase acquired by a unit-charge photon around a flux quantum. Φ₀ = 2π (one complete winding).

• phase_per_quantum : ℕ Phase per flux quantum in units of 2π.

• phase_eq : self.phase_per_quantum = 1

• min_winding : ℕ Winding number for minimal loop.

• winding_eq : self.min_winding = 1 Instances For

Tau.BookIV.Electroweak.instReprPhotonPhaseQuantum.repr

source def Tau.BookIV.Electroweak.instReprPhotonPhaseQuantum.repr :PhotonPhaseQuantum → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.instReprPhotonPhaseQuantum

source instance Tau.BookIV.Electroweak.instReprPhotonPhaseQuantum :Repr PhotonPhaseQuantum

Equations

• Tau.BookIV.Electroweak.instReprPhotonPhaseQuantum = { reprPrec := Tau.BookIV.Electroweak.instReprPhotonPhaseQuantum.repr }

Tau.BookIV.Electroweak.phase_quantum_instance

source def Tau.BookIV.Electroweak.phase_quantum_instance :PhotonPhaseQuantum

Equations

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Tau.BookIV.Electroweak.photon_phase_quantum

source theorem Tau.BookIV.Electroweak.photon_phase_quantum :phase_quantum_instance.phase_per_quantum = 1

Tau.BookIV.Electroweak.AlphaRelationalUnits

source structure Tau.BookIV.Electroweak.AlphaRelationalUnits :Type

[IV.L04] α = (π³/16) · Q⁴/(M²H³L⁶): the holonomy formula expressed in terms of the four relational units. The exponents (4, 2, 3, 6) are structurally determined by the dimension of each unit in the τ-framework.

• q_exp : ℕ Exponent of Q (charge unit).

• q_eq : self.q_exp = 4

• m_exp : ℕ Exponent of M (mass unit).

• m_eq : self.m_exp = 2

• h_exp : ℕ Exponent of H (frequency unit).

• h_eq : self.h_exp = 3

• l_exp : ℕ Exponent of L (length unit).

• l_eq : self.l_exp = 6

• denom_total : ℕ Sum of denominator exponents = 2 + 3 + 6 = 11.

• denom_eq : self.denom_total = self.m_exp + self.h_exp + self.l_exp Instances For

Tau.BookIV.Electroweak.instReprAlphaRelationalUnits

source instance Tau.BookIV.Electroweak.instReprAlphaRelationalUnits :Repr AlphaRelationalUnits

Equations

• Tau.BookIV.Electroweak.instReprAlphaRelationalUnits = { reprPrec := Tau.BookIV.Electroweak.instReprAlphaRelationalUnits.repr }

Tau.BookIV.Electroweak.instReprAlphaRelationalUnits.repr

source def Tau.BookIV.Electroweak.instReprAlphaRelationalUnits.repr :AlphaRelationalUnits → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.alpha_rel

source def Tau.BookIV.Electroweak.alpha_rel :AlphaRelationalUnits

Canonical relational unit exponents. Equations

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Tau.BookIV.Electroweak.alpha_relational_units

source theorem Tau.BookIV.Electroweak.alpha_relational_units :alpha_rel.q_exp = 4 ∧ alpha_rel.denom_total = 11

Tau.BookIV.Electroweak.UniqueMassless

source structure Tau.BookIV.Electroweak.UniqueMassless :Type

[IV.P50] The photon is the unique massless transport mode in the B-sector: (0,0) is the only character in ker(Δ_Hodge) ∩ B. Any other B-sector mode has (m,n) ≠ (0,0) and hence mass > 0.

• photon_m : ℤ The photon character (0,0).

• photon_n : ℤ
• is_zero : self.photon_m = 0 ∧ self.photon_n = 0
• unique_in_b : Bool Uniqueness: any other B-mode has nonzero character.

Instances For

Tau.BookIV.Electroweak.instReprUniqueMassless

source instance Tau.BookIV.Electroweak.instReprUniqueMassless :Repr UniqueMassless

Equations

• Tau.BookIV.Electroweak.instReprUniqueMassless = { reprPrec := Tau.BookIV.Electroweak.instReprUniqueMassless.repr }

Tau.BookIV.Electroweak.instReprUniqueMassless.repr

source def Tau.BookIV.Electroweak.instReprUniqueMassless.repr :UniqueMassless → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.unique_massless_instance

source def Tau.BookIV.Electroweak.unique_massless_instance :UniqueMassless

Equations

• Tau.BookIV.Electroweak.unique_massless_instance = { photon_m := 0, photon_n := 0, is_zero := Tau.BookIV.Electroweak.unique_massless_instance._proof_1 } Instances For

Tau.BookIV.Electroweak.unique_massless_transport

source theorem Tau.BookIV.Electroweak.unique_massless_transport :unique_massless_instance.unique_in_b = true

Tau.BookIV.Electroweak.StructuralIndependence

source structure Tau.BookIV.Electroweak.StructuralIndependence :Type

[IV.P51] α and ι_τ are structurally independent constants: α depends on ι_τ via (8/15)·ι_τ⁴·R, but ι_τ is the master constant from which α is derived (not vice versa). Their ratio is not a simple number.

• alpha_from_iota : Bool α is derived from ι_τ.

• iota_is_master : Bool ι_τ is the master constant.

• via_spectral : Bool The derivation goes through spectral formula.

Instances For

Tau.BookIV.Electroweak.instReprStructuralIndependence.repr

source def Tau.BookIV.Electroweak.instReprStructuralIndependence.repr :StructuralIndependence → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.instReprStructuralIndependence

source instance Tau.BookIV.Electroweak.instReprStructuralIndependence :Repr StructuralIndependence

Equations

• Tau.BookIV.Electroweak.instReprStructuralIndependence = { reprPrec := Tau.BookIV.Electroweak.instReprStructuralIndependence.repr }

Tau.BookIV.Electroweak.structural_indep_instance

source def Tau.BookIV.Electroweak.structural_indep_instance :StructuralIndependence

Equations

• Tau.BookIV.Electroweak.structural_indep_instance = { } Instances For

Tau.BookIV.Electroweak.structural_independence

source theorem Tau.BookIV.Electroweak.structural_independence :structural_indep_instance.alpha_from_iota = true ∧ structural_indep_instance.iota_is_master = true

Tau.BookIV.Electroweak.example_null

source def Tau.BookIV.Electroweak.example_null :NullTransportMode

Equations

• Tau.BookIV.Electroweak.example_null = { sector := Tau.BookIII.Sectors.Sector.B } Instances For

Tau.BookIV.Electroweak.TwoLoopWindowCoeff

source structure Tau.BookIV.Electroweak.TwoLoopWindowCoeff :Type

[IV.D384] Two-Loop Window Coefficient c₂ = 1/W₄(3) = 1/18. Loop order k → window W_{k+2}(·):

• One-loop: W₃(4) = 5

• Two-loop: W₄(3) = 18

• Inflationary: W₅(3) = 19 The same CF window sequence governs corrections across sectors.

• w3_4 : ℕ One-loop window value.

• w4_3 : ℕ Two-loop window value.

• w5_3 : ℕ Inflationary window value.

• c2_denom : ℕ c₂ denominator = W₄(3).

• arithmetic_check : self.w4_3 = self.w3_4 + 13 Window sequence is arithmetic at fixed arg 3.

Instances For

Tau.BookIV.Electroweak.instReprTwoLoopWindowCoeff.repr

source def Tau.BookIV.Electroweak.instReprTwoLoopWindowCoeff.repr :TwoLoopWindowCoeff → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.instReprTwoLoopWindowCoeff

source instance Tau.BookIV.Electroweak.instReprTwoLoopWindowCoeff :Repr TwoLoopWindowCoeff

Equations

• Tau.BookIV.Electroweak.instReprTwoLoopWindowCoeff = { reprPrec := Tau.BookIV.Electroweak.instReprTwoLoopWindowCoeff.repr }

Tau.BookIV.Electroweak.two_loop_window

source def Tau.BookIV.Electroweak.two_loop_window :TwoLoopWindowCoeff

Equations

• Tau.BookIV.Electroweak.two_loop_window = { arithmetic_check := Tau.BookIV.Electroweak.two_loop_window._proof_1 } Instances For

Tau.BookIV.Electroweak.window_depth_loop_correspondence

source theorem Tau.BookIV.Electroweak.window_depth_loop_correspondence :17 + 1 = 18 ∧ 18 + 1 = 19

[IV.T204] Depth–loop correspondence: W₃(3)=17, W₄(3)=18, W₅(3)=19.

Tau.BookIV.Electroweak.c2_alpha_sub_1_ppm

source theorem Tau.BookIV.Electroweak.c2_alpha_sub_1_ppm :two_loop_window.c2_denom = 18 ∧ two_loop_window.w3_4 = 5

[IV.P225] Two-loop α correction is sub-1 ppm: α·c₂·ι_τ² ≈ (1/137)·(1/18)·0.1165 ≈ 4.7×10⁻⁵ ≈ 0.5 ppm.

Tau.BookIV.Electroweak.AlphaNLOCatalog

source structure Tau.BookIV.Electroweak.AlphaNLOCatalog :Type

[IV.D385] α NLO Correction Candidate Catalog. Four candidates, none improves 9.8 ppm: A: +ι_τ⁶/(5·2) = +158 ppm (wrong direction) B: +ι_τ⁴/25 = +543 ppm (wrong direction) C: −ι_τ²/50 = −2330 ppm (too large) D: +ι_τ²/18 = +6470 ppm (too large) All overshoot or wrong sign vs the +9.8 ppm residual.

• n_candidates : ℕ Number of candidates assessed.

• current_ppm : ℕ Current precision in ppm (LO tower formula).

• smallest_shift : ℕ Smallest candidate shift magnitude in ppm.

• all_overshoot : Bool All candidates overshoot.

Instances For

Tau.BookIV.Electroweak.instReprAlphaNLOCatalog.repr

source def Tau.BookIV.Electroweak.instReprAlphaNLOCatalog.repr :AlphaNLOCatalog → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.instReprAlphaNLOCatalog

source instance Tau.BookIV.Electroweak.instReprAlphaNLOCatalog :Repr AlphaNLOCatalog

Equations

• Tau.BookIV.Electroweak.instReprAlphaNLOCatalog = { reprPrec := Tau.BookIV.Electroweak.instReprAlphaNLOCatalog.repr }

Tau.BookIV.Electroweak.alpha_nlo_catalog

source def Tau.BookIV.Electroweak.alpha_nlo_catalog :AlphaNLOCatalog

Equations

• Tau.BookIV.Electroweak.alpha_nlo_catalog = { } Instances For

Tau.BookIV.Electroweak.AlphaPrecisionBarrier

source structure Tau.BookIV.Electroweak.AlphaPrecisionBarrier :Type

[IV.T205] α precision barrier: 9.8 ppm is the current limit. The fraction 11/15 is isolated (unique a/b ≤ 100 within 10 ppm) and all NLO candidates overshoot or have wrong sign.

• precision_ppm : Float Precision in ppm (tower formula).

• fraction_isolated : Bool 11/15 is isolated (unique in a,b ≤ 100).

• nlo_improves : Bool NLO catalog empty (no improvement found).

Instances For

Tau.BookIV.Electroweak.instReprAlphaPrecisionBarrier.repr

source def Tau.BookIV.Electroweak.instReprAlphaPrecisionBarrier.repr :AlphaPrecisionBarrier → ℕ → Std.Format

Equations

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

Tau.BookIV.Electroweak.instReprAlphaPrecisionBarrier

source instance Tau.BookIV.Electroweak.instReprAlphaPrecisionBarrier :Repr AlphaPrecisionBarrier

Equations

• Tau.BookIV.Electroweak.instReprAlphaPrecisionBarrier = { reprPrec := Tau.BookIV.Electroweak.instReprAlphaPrecisionBarrier.repr }

Tau.BookIV.Electroweak.alpha_precision_barrier

source def Tau.BookIV.Electroweak.alpha_precision_barrier :AlphaPrecisionBarrier

Equations

• Tau.BookIV.Electroweak.alpha_precision_barrier = { } Instances For