Established in scope
Inverse variation fixes action,boundary term and bosonic backreaction
In the question: Complete physical Hamiltonian source with Gauss sector and thermal word limit
Explicit classical variational derivation on the existing field chart; no new CAR or quantization assumption for the homotopy. Exact Euler/zero-field identifications are conditional; the same Cauchy graph alone is insufficient. Existing whole Clifford source remains,but is not automatically primitive physical S_adm. No identification of C0 with finite J_F or equality of branches. Zero modes retained as source polynomial; logarithmic bosonic cumulants require actual Z_B!=0. Full primitive action and joint physical spectrum remain underived.
Read the exact result, assumptions and evidence
Result
The exact original skew Euler operator E=M_b Psi integrates by scaling homotopy to S_F=1/2 Psi^T M_b Psi. In the existing charged chart the original input/output polarization gives S_F,open=int barpsi(partial_r+h_b)psi-barpsi_out psi_out and on solutions -barpsi_out R_b psi_in. The actual unintegrated zero-fermion value fixes B[b]. Joint bosonic variation is delta S_B+1/2 Psi^T delta M_b Psi. Exactly one compatible fermionic integration gives delta(S_B-logPfM)=delta S_B-1/2Tr(M^-1deltaM),with actual reference/eta phase. A genuine linear quantum-source identity yields the same conditional quadratic action; integrating the same bosons produces effective higher fermion terms as their cumulants.
Required assumptions
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
- Exact Euler operator and unintegrated zero-fermion restriction
Conditional variational statement on the same original Clifford field chart: M_b=C L_b with the actual skew pairing and compatible domain/boundary polarization is the exact off-shell fermionic Euler operator, not merely an equation with the same classical solution set. The bosonic remainder is the identified original unintegrated zero-fermion value. Fulfillment of these physical identifications by the whole primitive S_adm source is neither assumed nor established. Pfaffian logarithms only on the actual invertible domain with original orientation.
Original evidence
- ADMISSIBLE-ACTION-DERIVATION-20261103.txt lines 131–271
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/ADMISSIBLE-ACTION-DERIVATION-20261103.txt
d3b7ea73d59c1c671af0fec4a4f9b1048dfc297eb26a932fe18fda2af03b972d
- ADMISSIBLE-ACTION-DERIVATION-20261103.txt lines 272–320
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-local-source-variable-background-20261102/ADMISSIBLE-ACTION-DERIVATION-20261103.txt
d3b7ea73d59c1c671af0fec4a4f9b1048dfc297eb26a932fe18fda2af03b972d
- NORMAL-KINETIC-PAIRING.txt lines 37–94
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/tfpt-unified-source-derivation-20261029/pfaff_source_review/NORMAL-KINETIC-PAIRING.txt
28061f015df5c5bb2a07a12ffd1d45f84cab49fb84939606201a1efe77b49f62
finding:r112-inverse-variation-fixes-action-boundary-and-bosonic-backreaction