TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE46-GRAM-RESPONSE-AND-VADM-REVIEW.txt Original file SHA-256: 6df3e624f781d6884de0c8c2c2ad09cd9f0aa3572048e9057ff2a4f16a89dbed Inclusive original lines: 151-247 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. 000151 | share is 0.7926360077. Thus the actual complex Hardy phase retains a strong 000152 | resonant component, but the whole response is neither rank1 nor 99.3 percent 000153 | fixed-line. Its mixed blocks obey the g^(-1) law (3). At the fixed physical 000154 | gap they form the finite nonresonant part that is numerically important for 000155 | this phase. 000156 | 000157 | 000158 | 4. Conditional norm threshold 000159 | 000160 | The exact source value gives 000161 | 000162 | |kappa|=0.3096133626901069/cosh(ell_NS/2). 000163 | 000164 | Since ||M0P0||=1 and EM5 itself defines epsilon_f=g, the norm inequality for 000165 | this DECLARED direction would be 000166 | 000167 | |kappa|5.644618151351245. (4) 000172 | 000173 | [OMITTED: non-scientific conversation or execution metadata] 000174 | [OMITTED: non-scientific conversation or execution metadata] 000175 | [OMITTED: non-scientific conversation or execution metadata] 000176 | [OMITTED: non-scientific conversation or execution metadata] 000177 | [OMITTED: non-scientific conversation or execution metadata] 000178 | [OMITTED: non-scientific conversation or execution metadata] 000179 | 000180 | 000181 | 5. Infinitesimal and finite responses are different 000182 | 000183 | The values in sections2-3 are derivatives at kappa=0. The exact finite response 000184 | is 000185 | 000186 | [(D0-kappa M0P0)^dagger(D0-kappa M0P0)]^(-1/2)-H0^(-1/2), 000187 | 000188 | and is generally not kappa times the derivative. As a dimensionless control 000189 | inside the EM5 norm bound, take |kappa|/g=0.49 with the actual Hardy phase. 000190 | Then 000191 | 000192 | finite response Frobenius norm =0.5456360675, 000193 | linear response Frobenius norm =0.6469949632, 000194 | relative linearization error =0.2264717958. 000195 | 000196 | The derivative is a correct local diagnostic. Near the admissibility 000197 | boundary it is not an accurate finite replacement. A claimed physical 000198 | finite K therefore has to use the exact inverse square root after ell_NS and 000199 | the actual source insertion are known. 000200 | 000201 | 000202 | 6. Relation to the completed spine/fold result 000203 | 000204 | [OMITTED: non-scientific conversation or execution metadata] 000205 | [OMITTED: non-scientific conversation or execution metadata] 000206 | [OMITTED: non-scientific conversation or execution metadata] 000207 | [OMITTED: non-scientific conversation or execution metadata] 000208 | [OMITTED: non-scientific conversation or execution metadata] 000209 | [OMITTED: non-scientific conversation or execution metadata] 000210 | [OMITTED: non-scientific conversation or execution metadata] 000211 | [OMITTED: non-scientific conversation or execution metadata] 000212 | 000213 | Likewise, P_Seam,+ in the primitive carrier theorem is a physical structural 000214 | projector, while "positive C6 branch" labels the +M0 block. Their common plus 000215 | sign is not an operator identity. The original positive C6 kernel is not 000216 | automatically the F5 seam. 000217 | 000218 | 000219 | Final scope 000220 | 000221 | The smallest supported conclusion is positive and conditional: if the actual 000222 | source inserts -kappa M0P0 as a Pstr-preserving V_adm, the original Gram 000223 | consumer has the exact strong resonance (2), the exact finite response above, 000224 | and the conditional norm threshold (4). Existing sources prove neither that 000225 | insertion nor its structural commutator. The Hardy coefficient remains a 000226 | nonzero directed contribution already read by the primitive wedge consumer; 000227 | it is not thereby the entire physical V_adm or Yukawa source. 000228 | 000229 | Reproducible check 000230 | 000231 | experiments/theory-contracts/tfpt-unified-source-derivation-20261029/ 000232 | aps_source_review/check_claude46_gram_response.py 000233 | 000234 | [OMITTED: non-scientific conversation or execution metadata] 000235 | [OMITTED: non-scientific conversation or execution metadata] 000236 | 000237 | Sources 000238 | 000239 | [OMITTED: non-scientific conversation or execution metadata] 000240 | [OMITTED: non-scientific conversation or execution metadata] 000241 | [OMITTED: non-scientific conversation or execution metadata] 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 | [OMITTED: non-scientific conversation or execution metadata] 000247 | [OMITTED: non-scientific conversation or execution metadata]