theorem
scaffolding
sorry stub
is
show as:
view Lean formalization →
formal statement (Lean)
36theorem is either an algebraic tautology or named as a hypothesis-discharge.
37Zero `sorry`, zero new `axiom`.
38
39## References
40
41- Piran, T. & Williams, R. M. (1986). Three-plus-one formulation of Regge
42 calculus. *Phys. Rev. D* **33**, 1622–1633.
43- Brewin, L. C. (2000). The Riemann and extrinsic curvature tensors in the
44 Regge calculus. *Class. Quantum Grav.* **17**, 545.
45- Cheeger, J., Müller, W. & Schrader, R. (1984). On the curvature of
46 piecewise flat spaces. *Commun. Math. Phys.* **92**, 405–454.
47- Washburn, J. (2026 draft). *Gravity from Recognition*, §5 (field-curvature
48 identity, discharged in this module modulo the stated linearization
49 hypothesis).
50-/
51
52namespace IndisputableMonolith
53namespace Foundation
54namespace SimplicialLedger
55namespace EdgeLengthFromPsi
56
57open Constants Cost ContinuumBridge
58
59noncomputable section
60
61/-! ## §1. Vertex / edge indexing for a conformal patch
62
63We work with a finite ledger of `n` simplices (indexed by `Fin n`) connected
64by a symmetric, non-negative adjacency matrix. An *edge* is an unordered
65pair `(i, j)` with `i ≠ j` and `weight i j > 0`. The edge set is captured
66by the weighted graph structure already in `ContinuumBridge`. -/
67
68/-- A log-potential assignment `ε : Fin n → ℝ` with `ε i = ln ψ(σ_i)`.
69 This is the same object used by `ContinuumBridge.laplacian_action`. -/
used by (40)
-
optimalT60 -
hearingLossPenalty -
hearingLossPenalty_zero -
applied -
energyConservationCert -
christoffel -
const_one_is_geodesic -
costRateEL_const_one -
costRateEL_iff_const_one -
costRateEL_implies_const_one -
geodesicEquationHolds -
geodesic_iff_hessianEnergy_EL -
actionJ_convex_on_interp -
actionJ_local_min_is_global -
actionJ_minimum_unique_value -
geodesic_minimizes_unconditional -
Jcost_convex_combination -
energy_conservation -
hamiltonPDotEquation -
totalEnergy -
newtonSecondLawCert -
NewtonSecondLawCert -
spaceShift -
spaceTranslationFlow -
space_translation_invariance_implies_momentum_conservation -
timeShift -
timeTranslationFlow -
actionJ_def -
const_apply -
fixedEndpoints_trans