Gravity Analysis Regge Bloch M2 Symbol4 D Bloch M2 Symbol4 Dstatus Flags

A status card for a gravity computation

The declaration blochM2Symbol4DStatus is a status card, not a theorem. It records, in one place, which pieces of a specific 4D gravity calculation have been formally verified and which have not. The calculation concerns the small-momentum behavior of a quantity called blochFold11, a discrete fold of a 4D Regge gravity action. The status card lists eight boolean flags, each marking a separate claim as closed (true) or open (false).

Five of the eight flags are set to true. They establish that: the fold is an even function of momentum, so its first derivative at zero vanishes; the leading small-momentum coefficient is nonzero for a particular background configuration called axisTTPlus; that same coefficient vanishes for a gauge configuration called decoyGauge; and the limit of the fold divided by momentum squared tends to the computed coefficient for both of those configurations. These are concrete, machine-checked facts about the (1,1) orbit contribution only, not about the full Hessian of the action.

The remaining three flags are false, and they are the honest part of the card. The full Hessian symbol is not closed. The convergence of the entire framework to the Einstein-Hilbert action in 4D, tagged as convergesEH4d, is not proved. And the recovery of a gap in the action, tagged as gapActionRecovery, is not proved. These are open targets, not failures; the card exists precisely to say so.

What the card does not claim is as important as what it does. It does not claim that the (1,1) orbit contribution is the whole story; other orbit contributions are not covered. It does not claim that the limit statement for a general background matrix H is closed; that remains open. And it does not claim that the small-momentum behavior of this fold implies anything about the convergence of the full 4D theory to general relativity. The card is a precise inventory, and its precision is its value.

def blochM2Symbol4DStatus : BlochM2Symbol4DStatus where
  evennessClosed := true
  m2CoeffAxisClosed := true
  m2CoeffGaugeClosed := true
  axisNonvacuity := true
  m2TendstoAxisGaugeClosed := true
  fullHessianSymbol := false
  convergesEH4d := false
  gapActionRecovery := false

def blochM2Symbol4DStatus : BlochM2Symbol4DStatus where
  evennessClosed := true
  m2CoeffAxisClosed := true
  m2CoeffGaugeClosed := true
  axisNonvacuity := true
  m2TendstoAxisGaugeClosed := true
  fullHessianSymbol := false
  convergesEH4d := false
  gapActionRecovery := false

def blochM2Symbol4DStatus : BlochM2Symbol4DStatus where
  evennessClosed := true
  m2CoeffAxisClosed := true
  m2CoeffGaugeClosed := true
  axisNonvacuity := true
  m2TendstoAxisGaugeClosed := true
  fullHessianSymbol := false
  convergesEH4d := false
  gapActionRecovery := false

What this page does not claim

The card does not claim that the (1,1) orbit contribution is the whole story for the small-momentum symbol. The card does not claim that the limit statement for a general background matrix H is closed. The card does not claim that the small-momentum behavior of this fold implies convergence of the full 4D theory to general relativity.

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/ReggeBlochM2Symbol4D.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: