The Central Theorem: From Foam to the Standard Model (Withdrawn as Proof)

Version 3.0 withdraws the composite five-step argument of this paper as a proof. An external referee audit of the public repository found that the gauge group is assumed in the inter-cell link variables rather than derived from the face graph (Steps 1 and 5); that the displayed gamma matrices do not satisfy the Clifford relations (Step 2); that the displayed Yukawa matrix element T·P_A2u·T is identically zero because the inter-type operator T annihilates A2u (Step 3); that the printed Higgs mass-squared is +9 × positive, not negative, so no symmetry breaking follows (Step 4); that the Symanzik matching script builds a non-Hermitian Bloch matrix (Section 7); and that D3 ≅ S3 does not embed in SU(2) (Section 6.4). Each finding is accepted. The original text is retained with the affected sections marked, so that the record of the claim and the record of its failure sit together. What stands: the O_h decomposition of the face space, 2A1g ⊕ Eg ⊕ 2T1u ⊕ T2g ⊕ A2u; the identities T² = −4I on T1u and T21 = 2U; the face-content table; and the face spectrum itself. These are graph theorems and were independently reproduced by the audit. The particle–irrep map, the chirality labelling and the walk-action masses are identifications conditional on stated premises, and are now labelled as such throughout the framework. The statement "all 26 Standard Model parameters determined by seven cell integers" is withdrawn as a theorem. Changes in this version: title changed to state the withdrawal; withdrawal notice added answering audit items R1–R8; status and tier fields changed; affected sections marked; AI disclosure amended to record the audit.