Batch 359-A (ROUTE A, STEP A-2 LANDED: the definitions read the book's OWN section; the (P1)/(beta) gauge route is RETIRED and the field bridge is re-spelled as FLM (8.5.1) UNIQUENESS -- the FLM861Book cone goes from TWO sorries to ONE).

Owner's decision of record (batch 358-B, NOTES section 275): FLM never compare two sections; they fix ONE extension -- the one of (7.2.22)/(7.2.23) -- and write Y(a,z) of (8.4.17) at ITS section (7.1.24).

A-1b: hypothesis861_evenSect PROVED in Definitions/FLM861BookDefs.lean -- (8.6.1) holds at evenSect for EVERY pair (the book's commutator is the quotient of the section, (7.2.26) is eps_div_eps_swap_eq_signPow, and the parity bridge is the landed MM.FLM86.signPow_zmod_two_eq_zpow).

A-2: the whole (6.1.27)--(6.1.29) eps1 block (phi, eps1Map, eps1Map_basis, phi_pair, flipB, castForm, eps1Map_symm, add_self_zmod2, eq_of_add_eq_zero, q_polar, Q_add, Q_basis, eps1Map_self, exists_eps1) MOVED verbatim from the battlefield into FLM861BookDefs.lean, joined by bookEvenCocycle / bookEvenCocycle_eps1 / bookEvenCocycle_eps (eps(a,b) = (-1)^(eps1(a,b)), (7.1.24) at the (7.2.22)/(7.2.23) extension); and azPowD is RE-POINTED -- its lattice coefficient is signPow F (eps1Map bL form a b), the book's own section -- so IsBaseField/IsVertexOperator no longer read E.eps; the extension parameter stays only because the three book-facing statements are FROZEN with FLM's own (7.1.6)/(8.6.1) parameterization, and hE is no longer consumed by their proofs.

Definitions/FLM861BookTransport.lean (584 -> 196 lines): the (P1) entry epsExists_of_hE, the (beta) sorry symmCocycle_normalised_isCoboundary (with symmCocycle_isCoboundary, cocycle_zero_eq, ratio_zero_eq_one, ratio_symm, ratio_cocycle, isCoboundary_of_ratio, lamCob, lamCob_succ, rankK, rankK_zero, rankK_shift, rankK_one, lamCob_coboundary, lam_add_right, lam, ratio_symmetric_cocycle) are DELETED -- they existed only to compare two sections; exists_evenCocycle (now one line from bookEvenCocycle) and commutator_matches ((7.2.26)) are KEPT; rigidity_of_hY is re-spelled as FLM (8.5.1) uniqueness (Y = ZAligned (bookEvenCocycle ...)) and is this cone's ONE registered sorry.

Definitions/FLM861Book.lean: exists_evenCocycle_conjFam_eq_zAligned -> exists_evenCocycle_eq_zAligned (exists C, Y = ZAligned (C.toCentralExtension h2)), PROVED from the canonical bookEvenCocycle + even_of_hypothesis861 + rigidity_of_hY; FLM_8_6_1 and FLM889Book's FLM_8_8_9 keep their byte-frozen statements and drop the gauge transport; the batch-346-A gauge modules and the batch-346-B conjGauge block are OFF the chain (their headers record it).

The equality form's REFUTATION MM.B345A.bridge_conclusion_false STANDS: the honest field of the trivial section does not satisfy the book's own prescription -- the statement's HYPOTHESIS changed meaning, so this is not a re-registration of a refuted spelling.

Four-question test: (1) the FLM861Book entry is RE-SPELLED (route A) and TWO route-internal entries ((P1), (beta)) are DELETED, so the file's registry goes 2 sorries -> 1; (2) the registered statement is PROVED in Lean from the new declarations (compiled one-liner), and the frozen FLM_8_6_1/FLM_8_8_9 follow from it plus the landed theorems; (3) no new declaration is deletable (azPowD reads bookEvenCocycle; hypothesis861_evenSect is the (8.6.1) content at that section; the eps1 block builds that section); (4) the touched modules are imported by FinalCheck.lean and reached from MM.FLM810T861S.theorem861_source and the 8.10.2 assembly.

Evidence: lake build Definitions.FLM861Book EXIT=0 (3508 jobs); lake build Definitions.FLM861BookProducer Definitions.FLM889Book Definitions.FLM8102Book EXIT=0 (3522 jobs); lake build FinalCheck EXIT=0 (9172 jobs) with EIGHT 'declaration uses sorry' warnings, ONE of them in this cone; lake env lean Refuted/MMFLM861BookBridgeRefute.lean EXIT=0 and Refuted/MMFLM861BookFieldRefute.lean EXIT=0, both SILENT (every #guard_msgs matched); Probe/forbidden_tokens.py on the nine touched Lean files: admit=0 axiom=0 native_decide=0, sorry only where registered (Transport 1, FLM889Book 1, FLM8102Book 2); the three book-facing statements byte-identical (3 blocks, 0 mismatches).  Records: NOTES.md section 276; HANDOVER.md sections 0, 3 and 6; Refuted/README.md.
