Batch 225-A ACCEPTED -- residual #1 IS FLM's display: the (8.5.13) window synchronization is ABSORBED (no groundedness quantifier, no window raising, no hypothesis)

Definitions/MMFLM86WindowSyncAbsorbed.lean (354), added to FinalCheck.lean (acceptance green).

* THE BRIDGE BETWEEN THE CURRENCIES: groundedPairWindow_iff_aboveThreshold -- for any N above which the
  (8.5.24) iterate family of a pair vanishes, a grounded window of that pair IS (8.5.13) at every window
  at or above N (raising: Corollary851.of_cutoff; lowering: MM.FLM86M8625P.corollary851_of_grounded_of_le);
  pairWindowAboveThreshold_mono.  This is the precise reading of FLM's parenthetical in (8.5.13).
* THE NEW MATHEMATICS: groundedPairWindow_modeVL_left_of_commutatorInsertion and ..._right_... -- the
  (8.10.5) threshold of the DESCENDANT pair is itself a grounded window there, and the identity at that
  window is the display (8.6.23)/(8.6.24) read at the honest insertion
  (MM.FLM86M8625P.honestIns8625, whose (8.6.27) half is rfl).  No window is RAISED -- the batch-223-A
  WindowSyncAtStates obstruction is bypassed, not solved -- and no input window is consumed.
* HEADLINE 1: groundedModeStep_of_commutatorInsertion : CommutatorInsertion8625 E (honestIns8625 E) ->
  GroundedModeStepAtStates (ZAligned E), with NO hypothesis at all: no symmetry hs of (7.1.1), no even
  cocycle, no (2:F) != 0, no boundary input.  So residual #1's own hypothesis (the grounded window of the
  input pair) is REDUNDANT, and the whole window-synchronization layer of residual #1 lies inside the
  display.
* DescendantsGroundedWindows (the hypothesis-free spelling of residual #1's conclusion) and
  descendantsGrounded_of_commutatorInsertion (the displays give it outright).
* HEADLINE 2 (the accounting, both ways, at an even cocycle): groundedModeStep_iff_commutatorInsertion_of_evenCocycle :
  CommutatorInsertion8625 E (honestIns8625 E) <-> GroundedModeStepAtStates (ZAligned E) -- batch 223-B's
  commutatorInsertion8625_iff_spanningEventual composed with batch 224's
  spanningEventual_zAligned_iff_groundedStep -- with the spanning corollary
  spanningEventual_of_commutatorInsertion_of_evenCocycle.  So residual #1 is EXACTLY FLM's displayed
  (8.6.23)/(8.6.24) cross contraction, with no window bookkeeping left outside it.
* the delivery re-hung on the display: groundedZeroFace_of_commutatorHalf (the assembly's grounded
  Res_{z_0} face), stepCorrected_of_commutatorHalf (the reduced Jacobi step from the display +
  NegativeResidual), theorem8102_of_matching_and_commutatorHalf (FLM Theorem 8.10.2 on the display list:
  ResidueMatching8625 + the honest commutator half + the reduced Jacobi step + the six boundary inputs).
* non-vacuity on record (batch 223-B's falsifications): the zero insertion FAILS the commutator half at
  the rank-one datum (MM.FLM86M8625P.not_commutatorInsertion8625_zeroIns_rankOne) while the honest
  insertion is nonzero at the (8.5.11) boundary index (honestIns8625_ne_zero) -- the honestness of the
  insertion is genuinely consumed.

EXACT RESIDUAL after batch 225: (1) CommutatorInsertion8625 E (honestIns8625 E) -- the displayed
(8.6.23)/(8.6.24) cross contraction; (2) NegativeResidual; (3) the Fock named residuals
(HonestNegPairingCoeffAtStates, ResidueMatching8625NegSecondSlot); (4) the six boundary inputs.

Verification: tools/build.ps1 Definitions/MMFLM86WindowSyncAbsorbed.lean OK; python Probe/forbidden_tokens.py
all zeros; tools/build.ps1 FinalCheck.lean --- OK with exit 0; every public declaration carries a
#guard_msgs #print axioms guard with footprint exactly [propext, Classical.choice, Quot.sound].  ROADMAP
batch 225 entry and NOTES section 122 appended; HANDOVER.md updated (residual #1's row, section 0, the
proved-formulas table, the next steps).
