TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FULL-SOURCE-REGULATOR-PROOF.txt
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Inclusive original lines: 177-232
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000177 | 5. Graded finite exact implementation
000178 | 
000179 | Existing joint_source.py supplies the original exact finite exterior algebra.
000180 | Use four ordered Grassmann field variables chi and four source variables eta,
000181 | with exponent sum eta_i chi_i and integral of ordered chi0 chi1 chi2 chi3=1.
000182 | For an even bilinear V=sum_(i<j) a_ij chi_i chi_j, the insertion operator is
000183 |  D_V=sum_(i<j) a_ij partial_eta_i partial_eta_j, with LEFT derivatives and
000184 | the written composition order. It satisfies D_V exp(eta.chi)=V exp(eta.chi).
000185 | The exponential of D_V terminates. Z_R=exp(-D_V)Z_0 and inverse exp(D_V)
000186 | hold for ANY even density, including quartic terms, with no bosonic Taylor
000187 | convergence assumption. No untyped STr shorthand sets the Grassmann signs.
000188 | 
000189 | check_full_source_regulator.py checks all8 symbolic even-density coefficients
000190 | and all6 bilinear regulator coefficients simultaneously; direct Berezin
000191 | integration equals the differential map, its inverse and two-step composition.
000192 | It also checks the full/normalized pair flow, null-source score, denominator,
000193 | generic exterior-source loss and the Gaussian matrix/class controls.
000194 | These are algebraic controls on the existing implementation, not8 new physical
000195 | parameters. They do not evaluate the missing original full S_adm or identify
000196 | this test field space with the native68 states.
000197 | 
000198 | 6. Verdict and next actual source step
000199 | 
000200 | The original full functional has a source-preserving regulator/readout
000201 | composition when all induced source legs, higher vertices, scalar and reference
000202 | data are retained. Exact source differential flow, full reweighting and the
000203 | quadratic universal RP cone make this explicit and automatically checkable.
000204 | The known full moment/relative-normalization results are reused. A Gaussian
000205 | Schur truncation and treating a regulator scale as physical time are excluded
000206 | as shortcuts, not the existing TFPT outputs or the whole source route.
000207 | 
000208 | The first actual physical map remains the originally supported field insertion
000209 | into the same primitive action/source (or a local OS image with the same full
000210 | functional), together with its original state, support, reflection and time.
000211 | Do not require a new complete ambient measure for every local neutral image.
000212 | Do not optimize a regulator as a physical selector, infer S_adm from the68
000213 | state space, or reopen solved Yukawa/alpha/clock searches.
000214 | 
000215 | The current operational Atlas task already retains a common Clifford
000216 | field/state/reflection/same-time diagram and the actual v252/P2 SM wedge map.
000217 | The free or exactly decoupled g+ channel already carries the older local
000218 | quarter source; no new null-mode/reflection selection is demanded there.
000219 | Continue the joint original source WITH dynamical bosons and relevant actual
000220 | field/sector operations. Do not force that interacting source to equal the
000221 | old free one, alter current levels, or replace the original mixed source
000222 | coupling by a regulator choice. This is the next physical step; the finite
000223 | preservation rules above are now reusable and need no parameter scan.
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