TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/elliptic-moebius-source-bridge-20261026/C3-PAPER-INDEPENDENT-REVIEW.txt
Original file SHA-256: a866494f4a88ab94cdc66bb97d824a6445fcb4e4a301c7807a373ba2fbc2c802
Inclusive original lines: 191-270
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.

000191 |   v117. Then (2) defines a flat unitary four-puncture representation with the
000192 |   required local spectra, and it is the unique tuple attached to that fixed
000193 |   marked pair.
000194 | 
000195 | To claim selection from the original geometric premises, the theorem must
000196 | instead import and state the exact anchor/resonance hypotheses, and it must
000197 | retain the analytic identification status. Full D4 equivariance also needs a
000198 | marked reflection operator; (2) by itself supplies the C4 rotation part.
000199 | 
000200 | 
000201 | 5. Scope relative to the new C3 dictionary report
000202 | --------------------------------------------------
000203 | 
000204 | The main negative conclusion of EXISTING-C3-SOURCE-DICTIONARY.txt survives:
000205 | the native E8 family permutation is only a bare C3-module match to M. The
000206 | corrected tuple (U,M) does not create a Q-equivariant or quarter-equivariant
000207 | intertwiner with the fixed native representatives, and it does not identify
000208 | the Fermat deck carrier with the v117 local system.
000209 | 
000210 | One sentence should be read narrowly: "restating the construction using the
000211 | actual v117 matrices" repairs the explicit monodromy package, but does not by
000212 | itself repair the paper's rigidity/uniqueness proof.
000213 | 
000214 | 
000215 | 6. Independent spin-trace scope correction
000216 | -------------------------------------------
000217 | 
000218 | SPIN-TRACE-LOCAL-KERNEL.txt previously moved too quickly from a holomorphic
000219 | Szego half-form pushforward to transport of a positive CAR covariance. The
000220 | local calculation proves the bilinear holomorphic kernel and its determinant
000221 | Wick expressions. It does not establish a bounded or unitary one-particle
000222 | trace operator on an equal-time Hilbert space.
000223 | 
000224 | That report has now been corrected. A positive base CAR covariance would
000225 | additionally require a real slice, the one-particle measure and inner
000226 | product, a closed branch-domain trace T, and
000227 | 
000228 |   C_base=T C_E T^*,   C_base=C_base^*,   0<=C_base<=I,
000229 | 
000230 | together with the appropriate isometry or coisometry statement for T. The
000231 | square-root Jacobian proves the correct half-form transformation and the
000232 | local quarter principal part; it does not alone prove these Hilbert-space
000233 | properties.
000234 | 
000235 | 
000236 | 7. Sources and checks
000237 | ---------------------
000238 | 
000239 | Original paper source, read through the hash-validated Atlas record
000240 | paper-source:9a3ef8e93be5da1e42c822aa:
000241 | 
000242 | [OMITTED: non-scientific conversation or execution metadata]
000243 | [OMITTED: non-scientific conversation or execution metadata]
000244 | [OMITTED: non-scientific conversation or execution metadata]
000245 | [OMITTED: non-scientific conversation or execution metadata]
000246 | 
000247 | Exact verification source:
000248 | 
000249 | [OMITTED: non-scientific conversation or execution metadata]
000250 | [OMITTED: non-scientific conversation or execution metadata]
000251 | [OMITTED: non-scientific conversation or execution metadata]
000252 | 
000253 | Later scoped selection source:
000254 | 
000255 | [OMITTED: non-scientific conversation or execution metadata]
000256 | [OMITTED: non-scientific conversation or execution metadata]
000257 | 
000258 | Active scoped replacement, hash-validated through Atlas source
000259 | paper-source:7c86eb06f13b0b07e1658c8d for lines 87-114:
000260 | 
000261 | [OMITTED: non-scientific conversation or execution metadata]
000262 | [OMITTED: non-scientific conversation or execution metadata]
000263 | [OMITTED: non-scientific conversation or execution metadata]
000264 | [OMITTED: non-scientific conversation or execution metadata]
000265 | 
000266 | I independently evaluated all four matrices in (2), their ordered product,
000267 | and equation (4) with exact SymPy arithmetic. No floating-point comparison
000268 | enters the defect or the correction.
000269 | 
000270 | No Atlas, original paper, verification or canonical project file was changed.