TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/BLOCKING-PATH.txt
Original file SHA-256: bb2b6ac13400c4267819de29189f00d006545fdff8c0acb80e4036757bbe05e3
Inclusive original lines: 201-256
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000201 | state's modular generator. It is not generally P h P or Schur(h), and
000202 | the original unnormalized scalar must still be retained. The original
000203 | M1 logodds reader and full determinant source already supply these
000204 | operations; no new Gibbs state or ell is selected.
000205 | 
000206 | For fixed H backgrounds even a purely bilinear source produces an
000207 | H-dependent exterior det K_ii(H,g,A). It becomes part of the coarse
000208 | bosonic weight. Integrating the same common H with its ORIGINAL measure
000209 | also induces the higher matter interactions. The existing
000210 | DYNAMICAL-HIGGS-SOURCE-PROOF.txt:34-139 already carries those conditional
000211 | fiber integrals, determinant weights and all higher cumulants. Therefore
000212 | one effective Dirac matrix alone need not parameterize the full coarse
000213 | source. The whole effective weight(4) remains the correct original object.
000214 | This is a positive closure under full integration, not a claim that
000215 | the original source is Gaussian or must keep its bare spectral form.
000216 | 
000217 | 5. WHAT THE ORIGINAL GEOMETRIC D_Vn THEOREM ACTUALLY SAYS
000218 | 
000219 | Freshly read exact original:
000220 |  paper-source:4321c3004ffbc46103ca5760:136-178,
000221 |  documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/
000222 |  005-section-absolute-dimensionless-metrology-from-the-bounda.tex,
000223 |  SHA256 b19c58deb3ee905c16e659dd26b15ca8d1998bab6f703cd350e04e54129a9a4c.
000224 | It displays
000225 |  dmu_n proportional exp[-Tr f_star(D_Vn^2/Lambda^2)]dnu_Vn
000226 | on the BRST-reduced geometric configuration space. Its proof166-168
000227 | uses compatibility of the blocked D_Vn and fixed profile to claim
000228 | projective consistency. It does not define D_Vn there as PDP. It also
000229 | does not print D_Vn as the effective Schur/logodds operator or identify
000230 | the full effective weight(4) with this same spectral ansatz.
000231 | 
000232 | This is the already reviewed R080 weighted-marginal scope, not a new
000233 | claim that no valid blocking producer exists. In particular it does
000234 | not invalidate the exact transfer family(1), the full-source fiber
000235 | operation(3)-(4), the existing geometric realization from G, or the
000236 | separate later state-limit construction. No entire TFPT measure or
000237 | physical field map is excluded by interpreting this paragraph literally.
000238 | 
000239 | For the actual full caller use the already supplied effective-weight
000240 | operation and retain all induced terms. If a specific blocked D_Vn is
000241 | intended to encode that ENTIRE weight, the identity to verify is (2)/(4),
000242 | not equality of unweighted operator compressions. A separately preserved
000243 | bare spectral form would be an additional closed-family statement;
000244 | it is not a prerequisite for the existing exact source integration.
000245 | 
000246 | OUTCOME
000247 | 
000248 | The requested normalized weighted equality is explicitly obtained for
000249 | the actual stationary transfer producer and for the full original
000250 | source under its actual fiber integration. Effective actions/weights
000251 | run; sources, exterior determinants, higher H interactions and reference
000252 | remain. No new harness, UV-mass countercase, bare-form assumption or
000253 | global measure choice was introduced. The three-state transfer source,
000254 | the full geometric/Higgs/matter caller and the later finite-Hamiltonian
000255 | limit retain their actual separate field scopes. Their established
000256 | projective full moments and G's whole U transport are preserved.