Established in scope
EM origin: solved finite steps and precise remaining functional identification
In the question: Alpha: derived terms, unique root and physical EM identification
Source-reviewed status/type correction, not a new general nonderivability theorem or gate. P1/P2 remain accepted starting principles; being axioms is not an objection. The line is derived on the old circle, not an arbitrary vector to select again. v382 replay26October:6/6; literalTrue status checks do not prove open functional origin. Ledger Numerical and full physical status remain unchanged.
Read the exact result, assumptions and evidence
Result
Coefficient identities and the unique alpha root are retained. The old circle canonically supplies Pi and det_F(1-qPi)=1-q; for trace-class C-P the same relative factor survives exactly in every faithful KMS polarization class on that same circle. Actual full positive projection covariance fixes the whole CAR state without an extra Gaussian premise. The finite Quillen chain is beyond its older open summary: v985 resolves the finite mu4 channel swap; v995 closes finite KMS rigidity and state extension; v1014 checks the finite determinant-line restriction isomorphism and records reference A0. Do not reopen those steps. What remains is the original local EM source/operator map and relative real renormalized determinant norm producing the seam factor with response exponent5/4, coupling q(alpha), local variation terms and normalization in the same channel. Abstract continuum/Bismut-Freed identification and matching to the physical Thomson coupling do not follow from finite calculations. Chiral phase cancellation does not refute real EM susceptibility. EM.WARD.01 and ALPHA.QUILLEN.EXACT.01 retain their existing physical residual.
Required assumptions
- Specified EM function with positive seam response
F(x)=x³−2c³x²+(4/5)c⁶M log(p+q(1−q)^(−5/4)), c=1/(8π), p=1/(6π), q=48c⁴exp(−2x), M>0; original budget M=41. The function and inputs are premises here.
- Model results remain conditional
Calculations in a fixed E8 net, quotient, family packet, or readout apply only under their stated inputs and do not select those inputs.
- P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
- Same original circle with trace-class changed polarization
For the mathematical continuation retain H,B_a psi_n=(n+a)psi_n,0<a<1,u psi_n=psi_(n+1),P=1_(B_a<0),uPu*=P+Pi. C is a positive contraction with trace-class C-P; actual functional-calculus C_beta=(I+exp(beta B_a))^-1,beta>0 belongs to this class. Physical KMS/OS/EM source identification is not presumed.
- Test a positive joint CAR source against the full geometric projection
Consider an arbitrary normalized positive state on the specified joint charged two-face CAR algebra,without assuming quasifreeness or U1 invariance. The geometric target is the existing closed chiral annulus graph P_A with both marked faces,W=1/2 and original NS B_Sigma. Actual identity C_source=P_A is an explicit condition of the uniqueness theorem and an unresolved P1 source equation,not a fact inferred from geometry or RP. A finite error test applies only on a genuinely P_A reducing CAR block. Complete Dirac vector source,OS Padm and physical time are not identified with this chiral scalar target. No freely chosen purification supplies missing physical cross correlations.
- 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.
Original evidence
- 007-source.tex lines 50–101
Source checked at this snapshot
Original location and fingerprint
documents/tfpt_1_architecture_e8/sections/007-source.tex
7e1cb59fef4de49deefe8f63b5d777e83528d0119e51191595784ee8c30dcd86
- DIRECT-DEFECT-CLOSURE.txt lines 20–109
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/DIRECT-DEFECT-CLOSURE.txt
84a79c74da8b18387a3d2d8a9928e4a437a608120b52a46c7ede6392cf1128ff
- EM-MEASURE-AND-QUILLEN.txt lines 18–127
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/EM-MEASURE-AND-QUILLEN.txt
a08abf23cab682b6c4733fb2403293b1de0245973864f77447544cde53422c65
- status_ledger.csv lines 445–445
Source checked at this snapshot
Original location and fingerprint
verification/status_ledger.csv
8723b921bdc50a6157acc6bee4342b40586eb89bec6d7dcc0abc3309562c78b4
- status_ledger.csv lines 752–754
Source checked at this snapshot
Original location and fingerprint
verification/status_ledger.csv
8723b921bdc50a6157acc6bee4342b40586eb89bec6d7dcc0abc3309562c78b4
- KMS-AND-CARRIER-TRANSPORT.txt lines 38–159
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/KMS-AND-CARRIER-TRANSPORT.txt
9efcfb0d68e16db842aab97b7171b2d667e7b065cb4c6ab8138102acc4c8fb68
- PROJECTOR-STATE-RIGIDITY.txt lines 30–100
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-arc-charge-source-interface-20261026/PROJECTOR-STATE-RIGIDITY.txt
2e14e8875c263d71bd6bda61d005461cb718bdf30fdf34a6312db53167cd80c6
finding:alpha-exact-coefficients-and-root-retain-specific-physical-ward-obligation