TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/REFERENCE.txt
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Inclusive original lines: 201-283
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000201 | The unordered smeared-force exponential has the same symmetric real part;
000202 | their difference is the imaginary ordered-commutator integral in(8).
000203 | This is an actual distinction of source callers, not a new physical model.
000204 | 
000205 | The sign and coefficient can be checked analytically. Put
000206 |  a_f(v)=int f(s+v)f(s)ds, a_f(0)=||f||_L2^2.
000207 | For omega>0, integration by parts gives
000208 |  int_0^infinity a_f(v)e^(i omega v)dv
000209 |     =+i ||f||_L2^2/omega+O(omega^-2).                  (9)
000210 | At large |p| the occupied-positive to empty-negative term has frequency
000211 | +2|p|+O(1) and coefficient
000212 |  Tr[P_+(h_p)Ta P_-(h_p)Ta]
000213 |    =Tr[P_(sign(p)gamma)Ta^2]+O(1/|p|).
000214 | The thermal corrections decay exponentially, and the projector errors
000215 | contribute summable remainders after(9). Summing positive and negative
000216 | momenta, each with the factor1/(2|p|), gives
000217 |  B_N=-i [Tr_quark36(Ta^2)/2] ||f||_L2^2 log N+O(1).
000218 | The actual original Yukawa/color trace is
000219 |  Tr_quark36(Ta^2)=6 Tr(Yu^dagger Yu+Yd^dagger Yd),
000220 | so the coefficient is exactly
000221 |  -i sigma^2 ||f||_L2^2 log N,
000222 |  sigma^2=3 Tr(Yu^dagger Yu+Yd^dagger Yd).               (10)
000223 | This sign uses the ACTUAL positive-occupation C and e^(+ith) convention.
000224 | Opposite sea/time conventions must not be inserted halfway through.
000225 | Other retained physical sectors have their own actual multiplicities;
000226 | the quark36 result is not blindly doubled into a96-species determinant.
000227 | 
000228 | The leading UV energy mechanism was already recorded in
000229 | research-source:a00ef03eb014f57051594211:1-128,
000230 | UV-INSERTION.txt, especially94-106, and later recovered. It is reused.
000231 | The new relevance here is the precise quadratic phase comparison between
000232 | the established smeared-force word source and the actual Dyson field call.
000233 | No fresh global nonimplementability or TFPT no-go follows from(10).
000234 | 
000235 | 6. What the existing reference can actually cancel, and the one next test
000236 | 
000237 | Linear centering cancels the epsilon term only. A fixed field-independent
000238 | H0 subtraction has zero quadratic field jet, so it cannot by itself
000239 | produce +i sigma^2||f||^2 logN. The constant odd h_p has paired +/-E
000240 | spectrum, so its total eta vanishes on this test. One must not assign
000241 | the needed continuous quadratic phase to eta alone; the master eta of
000242 | other actual operators is not thereby asserted zero.
000243 | 
000244 | If a relative Dyson determinant uses the SAME coupled insertion in its
000245 | actual reference, its two-jet subtracts the same sigma_ref^2 contribution.
000246 | Then the necessary leading cancellation is sigma_ref^2=sigma^2, with
000247 | finite part fixed by the anchored original connection(2)-(7). If the
000248 | reference source is held at0 as in the fixed-J reading of(1), its two-jet
000249 | is0 instead. The actual caller decides which case applies.
000250 | 
000251 | The already established R032 reference jets illustrate why selecting a
000252 | reference by name is invalid. In its S lift, D_ref=D0+ZL(m), while the
000253 | T lift has D_ref=D0+Z[L(p)+DM], p/m the deck-even/odd Higgs parts. For a
000254 | deck-even H variation, the first has zero H jet; the second follows the
000255 | whole H variation and the entire unscaled geometric pair reader cancels.
000256 | Those conditional results are preserved and do not select the current
000257 | modular matter reference or the intended Dyson phase.
000258 | 
000259 | The next calculation is therefore ONE explicit source jet, not an open
000260 | list: evaluate the original complete reference/contact two-jet on the
000261 | same pulse fTa, with its original domain, cutoff and field-vs-source
000262 | meaning, and compare it to(8)-(10). Use(7) for the supplied finite spectral
000263 | factor, the original eta jet and the real reference denominator. Integrate
000264 | the resulting whole score from its actual identical-reference anchor by(4).
000265 | This simultaneously fixes the finite common phase and the vacuum scalar
000266 | when that original equality is established. A fitted phase subtraction or
000267 | a new H measure would change the question and is not introduced here.
000268 | 
000269 | This report supplies the exact reconstruction rule, its anchor condition,
000270 | the actual reference source/background distinction and the decisive
000271 | native-channel coefficient. It does not claim that the primitive SAME
000272 | S/Z/OS source identity follows merely from the local force theorem.
000273 | No new numerical run, canonical edit, Atlas mutation, absolute-Z promotion,
000274 | physical3+1 derivation or global CAR origin requirement was made.
000275 | 
000276 | Primary formula comparison
000277 | 
000278 | Klich, cond-mat/0209642v1 Section2 and Eq8: actual finite ordered Fock
000279 | traces and one-particle determinants, with the infinite limit separately
000280 | qualified. https://arxiv.org/html/cond-mat/0209642v1
000281 | The score identities, trace jet and signed UV coefficient are the direct
000282 | calculations above on the actual source conventions, not claims borrowed
000283 | from an unrelated model or newly executed benchmark.