Encyclopedia Masses Masses Mass Genesis Anchor Sector Transport Tail Local Topology Charge Numerator
Masses Mass Genesis Anchor Sector Transport Tail Local Topology Charge Numerator
A charge numerator is an integer that counts something about a light pattern; this declaration connects one way of computing it to another.
The charge numerator
A charge numerator is an integer that counts a topological feature of a light pattern, a discrete record of eight phase values around a cycle. In the Recognition Science framework, the mass of a particle is built from such patterns, and the charge numerator is one of the quantities that distinguishes one particle from another. The declaration tailLocalTopologyChargeNumeratorNormalizedBranchScalarGaugeData_of_tailLocalTopologyDyadicExponentChargeNumeratorBranchScalarGaugeData establishes that two different ways of computing this integer agree: one route uses a normalized branch scalar gauge, the other uses a dyadic exponent. The theorem is a bridge between two formal definitions, showing they describe the same underlying quantity.
The context matters. The framework's mass genesis module splits a particle's amplitude into a sector base and a phi transport step. The charge numerator is part of the local topology that describes the sector base. The declaration is a formal statement in the framework's machine-checked library of formal theorems, meaning the equality is verified by the library's logic rather than asserted by hand. It does not, however, say what the charge numerator equals for any specific particle, nor does it connect the numerator to a measured mass value. Those are separate claims that would require additional theorems and empirical checks.
What the declaration does not claim is as important as what it does. It does not claim that the charge numerator is the only invariant distinguishing particles, nor that the dyadic exponent route is the physically preferred one. It does not claim that the charge numerator is conserved under all transformations, nor that it matches any particular experimental quantity. The declaration is a local consistency result: two formal definitions agree. It is a step in a larger derivation, not the derivation itself.
THEOREM AnchorSectorTransportCert · IndisputableMonolith/Masses/MassGenesis/AnchorSectorTransport.lean
structure AnchorSectorTransportCert where
canonical_sector_base :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseSectorBaseCP6 ψ (canonicalSectorBaseVector ψ)
canonical_sector_base_norm :
∀ ψ : LightPattern (Fin 8),
normSq8 (canonicalSectorBaseVector ψ) =
primitiveAnchorSectorLoad ψ
rung_transport_amplitude_pos :
∀ ψ : LightPattern (Fin 8),
0 < primitiveRungTransportAmplitude ψ
charge_skew_transport_amplitude_pos :
∀ ψ : LightPattern (Fin 8),
0 < primitiveChargeSkewTransportAmplitude ψ
charge_skew_ratio_amplitude_pos :
∀ ψ : LightPattern (Fin 8),
0 < primitiveChargeSkewRatioAmplitude ψ
charge_skew_transport_amplitude_eq_ratio_amplitude :
∀ ψ : LightPattern (Fin 8),
primitiveChargeSkewTransportAmplitude ψ =
primitiveChargeSkewRatioAmplitude ψ
phi_transport_amplitude_splits :
∀ ψ : LightPattern (Fin 8),
primitivePhiTransportAmplitude ψ =
primitiveRungTransportAmplitude ψ *
primitiveChargeSkewTransportAmplitude ψ
sector_base_norm :
∀ (ψ : LightPattern (Fin 8)) {base : Fin 8 → ℂ},
AnchorPhaseSectorBaseCP6 ψ base →
normSq8 base = primitiveAnchorSectorLoad ψ
phi_transport_norm :
∀ (ψ : LightPattern (Fin 8)) {base : Fin 8 → ℂ},
AnchorPhasePhiTransport ψ base →
normSq8 base = primitiveAnchorSectorLoad ψ →
normSq8 (neutralize (ψ.window 0)) =
primitiveAnchorSectorLoad ψ * primitivePhiTransport ψ
sector_transport_iff_primitive_amplitude_cp6 :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseSectorTransportCP6 ψ ↔
AnchorPhasePrimitiveAmplitudeCP6 ψ
sector_transport_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3SectorTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
canonical_phi_transport_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalPhiTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
closed_amplitude_window_from_canonical_phi_transport :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseCanonicalPhiTransport ψ →
AnchorPhaseCanonicalClosedAmplitudeWindowData ψ
canonical_phi_transport_closes_via_closed_amplitude_window :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalPhiTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
canonical_phi_transport_from_rung_charge :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseCanonicalRungChargeTransport ψ →
AnchorPhaseCanonicalPhiTransport ψ
rung_charge_transport_from_ratio_transport :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseCanonicalRungChargeRatioTransport ψ →
AnchorPhaseCanonicalRungChargeTransport ψ
rung_charge_transport_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalRungChargeTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
rung_charge_transport_closes_via_closed_amplitude_window :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalRungChargeTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
rung_charge_ratio_transport_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalRungChargeRatioTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
rung_charge_ratio_transport_closes_via_closed_amplitude_window :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalRungChargeRatioTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
canonical_transport_iff_coordinates :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseCanonicalPhiTransport ψ ↔
AnchorPhaseCanonicalTransportCoordinates ψ
coordinate_transport_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalCoordinateTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
coordinate_transport_iff_components :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseCanonicalTransportCoordinates ψ ↔
AnchorPhaseCanonicalTransportComponents ψ
closed_amplitude_window_from_coordinates :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseCanonicalTransportCoordinates ψ →
AnchorPhaseCanonicalClosedAmplitudeWindowData ψ
component_transport_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalComponentTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
coordinate_transport_closes_via_closed_amplitude_window :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalCoordinateTransportMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
component_transport_iff_pair_data :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseCanonicalTransportComponents ψ ↔
AnchorPhaseCanonicalPairData ψ
pair_data_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalPairDataMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
antisymmetry_from_two_phase_support :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseTwoPhaseSupport ψ →
AnchorPhaseAnchorAntisymmetry ψ
support_amplitude_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalSupportAmplitudeMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
positive_magnitude_from_support_and_norm :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseTwoPhaseSupport ψ →
AnchorPhasePrimitiveAmplitudeNorm ψ →
AnchorPhasePositiveMagnitude ψ
positive_amplitude_from_magnitude_orientation :
∀ ψ : LightPattern (Fin 8),
AnchorPhasePositiveMagnitude ψ →
AnchorPhasePositivePhaseOrientation ψ →
AnchorPhasePositiveTransportAmplitude ψ
support_norm_orientation_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalSupportNormOrientationMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
support_factor_orientation_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalSupportFactorOrientationMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
positive_orientation_from_real_nonnegative :
∀ ψ : LightPattern (Fin 8),
AnchorPhase0Real ψ →
AnchorPhase0Nonnegative ψ →
AnchorPhasePositivePhaseOrientation ψ
support_factor_sign_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalSupportFactorSignMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
support_factor_gauge_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalSupportFactorGaugeMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
tail_vanishes_iff_two_phase_support :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseTailVanishes ψ ↔ AnchorPhaseTwoPhaseSupport ψ
tail_factor_gauge_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalTailFactorGaugeMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMass ψ = predictedMass ψ ∧
T.readout.inertialMass ψ = restMass ψ ∧
T.readout.gravitationalMass ψ = restMass ψ
factor_norm_iff_local_factor_magnitude_from_tail :
∀ ψ : LightPattern (Fin 8),
AnchorPhaseTailVanishes ψ →
(AnchorPhasePrimitiveFactorNorm ψ ↔
AnchorPhase0LocalFactorMagnitude ψ)
tail_local_gauge_closes_full_chain :
∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)},
Q3CanonicalTailLocalGaugeMassPatternEvidence ψ →
(∀ k : ℕ,
integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧
0 < restMass ψ ∧
PhiRungQuantized ψ ∧
restMas
-- … truncated for the page; open the module for the rest.
What this page does not claim
This declaration does not specify the charge numerator's value for any particular particle. This declaration does not connect the charge numerator to any measured experimental quantity. This declaration does not establish that the charge numerator is conserved or unique.
Verify this page
Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:
$ lake env lean IndisputableMonolith/Masses/MassGenesis/AnchorSectorTransport.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)
A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.
Derived articles
This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red:
- What physical quantity does the charge numerator correspond to in the framework's mass ladder?
- How does the charge numerator relate to the measured charges of known particles?
- What is the role of the dyadic exponent in the framework's topology?
- Does the charge numerator remain invariant under the framework's allowed transformations?
MACHINE LAYER · GROUNDED CLAIM TABLE · CLICK TO EXPAND
THEOREM AnchorSectorTransportCert · IndisputableMonolith/Masses/MassGenesis/AnchorSectorTransport.lean
structure AnchorSectorTransportCert where canonical_sector_base : ∀ ψ : LightPattern (Fin 8), AnchorPhaseSectorBaseCP6 ψ (canonicalSectorBaseVector ψ) canonical_sector_base_norm : ∀ ψ : LightPattern (Fin 8), normSq8 (canonicalSectorBaseVector ψ) = primitiveAnchorSectorLoad ψ rung_transport_amplitude_pos : ∀ ψ : LightPattern (Fin 8), 0 < primitiveRungTransportAmplitude ψ charge_skew_transport_amplitude_pos : ∀ ψ : LightPattern (Fin 8), 0 < primitiveChargeSkewTransportAmplitude ψ charge_skew_ratio_amplitude_pos : ∀ ψ : LightPattern (Fin 8), 0 < primitiveChargeSkewRatioAmplitude ψ charge_skew_transport_amplitude_eq_ratio_amplitude : ∀ ψ : LightPattern (Fin 8), primitiveChargeSkewTransportAmplitude ψ = primitiveChargeSkewRatioAmplitude ψ phi_transport_amplitude_splits : ∀ ψ : LightPattern (Fin 8), primitivePhiTransportAmplitude ψ = primitiveRungTransportAmplitude ψ * primitiveChargeSkewTransportAmplitude ψ sector_base_norm : ∀ (ψ : LightPattern (Fin 8)) {base : Fin 8 → ℂ}, AnchorPhaseSectorBaseCP6 ψ base → normSq8 base = primitiveAnchorSectorLoad ψ phi_transport_norm : ∀ (ψ : LightPattern (Fin 8)) {base : Fin 8 → ℂ}, AnchorPhasePhiTransport ψ base → normSq8 base = primitiveAnchorSectorLoad ψ → normSq8 (neutralize (ψ.window 0)) = primitiveAnchorSectorLoad ψ * primitivePhiTransport ψ sector_transport_iff_primitive_amplitude_cp6 : ∀ ψ : LightPattern (Fin 8), AnchorPhaseSectorTransportCP6 ψ ↔ AnchorPhasePrimitiveAmplitudeCP6 ψ sector_transport_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3SectorTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ canonical_phi_transport_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalPhiTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ closed_amplitude_window_from_canonical_phi_transport : ∀ ψ : LightPattern (Fin 8), AnchorPhaseCanonicalPhiTransport ψ → AnchorPhaseCanonicalClosedAmplitudeWindowData ψ canonical_phi_transport_closes_via_closed_amplitude_window : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalPhiTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ canonical_phi_transport_from_rung_charge : ∀ ψ : LightPattern (Fin 8), AnchorPhaseCanonicalRungChargeTransport ψ → AnchorPhaseCanonicalPhiTransport ψ rung_charge_transport_from_ratio_transport : ∀ ψ : LightPattern (Fin 8), AnchorPhaseCanonicalRungChargeRatioTransport ψ → AnchorPhaseCanonicalRungChargeTransport ψ rung_charge_transport_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalRungChargeTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ rung_charge_transport_closes_via_closed_amplitude_window : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalRungChargeTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ rung_charge_ratio_transport_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalRungChargeRatioTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ rung_charge_ratio_transport_closes_via_closed_amplitude_window : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalRungChargeRatioTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ canonical_transport_iff_coordinates : ∀ ψ : LightPattern (Fin 8), AnchorPhaseCanonicalPhiTransport ψ ↔ AnchorPhaseCanonicalTransportCoordinates ψ coordinate_transport_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalCoordinateTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ coordinate_transport_iff_components : ∀ ψ : LightPattern (Fin 8), AnchorPhaseCanonicalTransportCoordinates ψ ↔ AnchorPhaseCanonicalTransportComponents ψ closed_amplitude_window_from_coordinates : ∀ ψ : LightPattern (Fin 8), AnchorPhaseCanonicalTransportCoordinates ψ → AnchorPhaseCanonicalClosedAmplitudeWindowData ψ component_transport_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalComponentTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ coordinate_transport_closes_via_closed_amplitude_window : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalCoordinateTransportMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ component_transport_iff_pair_data : ∀ ψ : LightPattern (Fin 8), AnchorPhaseCanonicalTransportComponents ψ ↔ AnchorPhaseCanonicalPairData ψ pair_data_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalPairDataMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ antisymmetry_from_two_phase_support : ∀ ψ : LightPattern (Fin 8), AnchorPhaseTwoPhaseSupport ψ → AnchorPhaseAnchorAntisymmetry ψ support_amplitude_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalSupportAmplitudeMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ positive_magnitude_from_support_and_norm : ∀ ψ : LightPattern (Fin 8), AnchorPhaseTwoPhaseSupport ψ → AnchorPhasePrimitiveAmplitudeNorm ψ → AnchorPhasePositiveMagnitude ψ positive_amplitude_from_magnitude_orientation : ∀ ψ : LightPattern (Fin 8), AnchorPhasePositiveMagnitude ψ → AnchorPhasePositivePhaseOrientation ψ → AnchorPhasePositiveTransportAmplitude ψ support_norm_orientation_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalSupportNormOrientationMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ support_factor_orientation_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalSupportFactorOrientationMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ positive_orientation_from_real_nonnegative : ∀ ψ : LightPattern (Fin 8), AnchorPhase0Real ψ → AnchorPhase0Nonnegative ψ → AnchorPhasePositivePhaseOrientation ψ support_factor_sign_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalSupportFactorSignMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ support_factor_gauge_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalSupportFactorGaugeMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ tail_vanishes_iff_two_phase_support : ∀ ψ : LightPattern (Fin 8), AnchorPhaseTailVanishes ψ ↔ AnchorPhaseTwoPhaseSupport ψ tail_factor_gauge_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalTailFactorGaugeMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMass ψ = predictedMass ψ ∧ T.readout.inertialMass ψ = restMass ψ ∧ T.readout.gravitationalMass ψ = restMass ψ factor_norm_iff_local_factor_magnitude_from_tail : ∀ ψ : LightPattern (Fin 8), AnchorPhaseTailVanishes ψ → (AnchorPhasePrimitiveFactorNorm ψ ↔ AnchorPhase0LocalFactorMagnitude ψ) tail_local_gauge_closes_full_chain : ∀ (T : StableLoadReadoutTheory (Fin 8)) {ψ : LightPattern (Fin 8)}, Q3CanonicalTailLocalGaugeMassPatternEvidence ψ → (∀ k : ℕ, integratedMeaningLoad (evolvePattern k ψ) = integratedMeaningLoad ψ) ∧ 0 < restMass ψ ∧ PhiRungQuantized ψ ∧ restMas -- … truncated for the page; open the module for the rest.The declaration establishes that two different ways of computing the charge numerator agree. AnchorSectorTransportCert · IndisputableMonolith/Masses/MassGenesis/AnchorSectorTransport.lean