Gravity Analysis Regge Bloch Transported All Orbit4 D Transported Orbit Slot Ter

The zero-momentum slot term

The declaration transportedOrbitSlotTerm_zeroMoment is a definition inside the Recognition Science library, a machine-checked collection of formal statements. It names a specific condition: a term in a four-dimensional gravity analysis, built from transported orbit slots, should vanish when the momentum is zero. The definition states this as a property to be established, not as a fact that has been proven.

In the framework's language, the term is part of a ledger, a discrete record of events, that tracks how geometric quantities like area and deficit kernels move under orbit coverings. The zero-momentum condition is a target: if the term behaves correctly, it should drop out at zero momentum, leaving a cleaner expression. The library records this as an open goal, meaning it remains to be shown, rather than a completed result.

The definition sits alongside other results in the same module. Some statements are proven, such as the recovery of the base slot area and deficit kernel for a specific orbit type, and the quadratic homogeneity of the full fold. These give the surrounding machinery a solid footing. But the zero-momentum condition itself is not among the proven results. It is a checkpoint on the way to a larger goal, not a destination already reached.

What the declaration does not claim is just as important. It does not assert that the zero-momentum condition holds for all configurations. It does not say that the term is physically meaningful or that it matches any measured quantity. It does not imply that the full continuum limit of the framework's gravity model has been reached. Those remain open questions, and the definition is a marker of where the work stands, not a claim of completion.

/-- OPEN: transported zero-momentum all-orbit fold equals the committed
true-weight assembly quadratic for general `H`.  Reindex gives
`classDot (push v p) H = ∑ v d0 * classCoeff H (permClass p d0)`, which
equals `classDot v H` only under class-coeff invariance along `p`, not in
general.  Banked separately from the m² continuum symbol. -/
def ZeroMomTrueWeightMatchOpen : Prop :=
  ∀ H : Mat4, blochFoldAll H (fun _ => (0 : ℝ)) = trueWeightZeroMomQuadratic H

/-- Compatibility wrapper (audit / older callers): same as `slotOrbitAreaCov_t11`. -/
theorem slotOrbitAreaCov_t11_eq (s : Fin 24) (t : Fin 10) (h : isT11 s t) :
    slotOrbitAreaCov .t11 s t = slotAreaCov s t :=
  slotOrbitAreaCov_t11 s t h

What this page does not claim

The zero-momentum condition holds for all configurations. The term has a direct physical interpretation or matches any measured quantity. The continuum limit of the framework's gravity model has been reached.

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/Gravity/Analysis/ReggeBlochTransportedAllOrbit4D.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: