Established in scope
Exact mixed retarded time response of original historical action
In the question: Recursion, hypergraphs and mirroring at the original joint source
Exact classical linear response of same historical action in supplied background.Two branches are not full interacting TFPT spectrum or vacuum mass.H2 is positive classical energy,not identified H_tr,pos.Retardation does not choose full symmetric quantum correlator/state.Actual S/a embedding in whole original field caller,reference and physical time remains unresolved.Canonical phase-space scaling has unit Jacobian;quantum elimination prefactors are distinct and retained.No universal beta=0 selection or new helper branch.Preserve full96,E8,clocks,flavor,alpha and previous findings.
Read the exact result, assumptions and evidence
Result
Actual second variation L2=(dotphi²-k²phi²+dotA²-k²A²)/2-G*phi*dotA,G=gB0. Both full equations give detD=(z²-k²)²-G²z² and Omega_plus/minus=sqrt(k²+G²/4)+/-|G|/2. Exact retarded matrix theta(t)[[d,o],[-o,d]] has complete residues in source;o=G[cos(Omega_plus*t)-cos(Omega_minus*t)]/(Omega_plus²-Omega_minus²),o(t)=-Gt²/2+O(t⁴). Laplace product,residues,source jumps directly checked. sin²(gB0 L/2) is a high-frequency approximation. Original anomaly matching differs by factor two with unchanged definitions.
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.
- Actual historical axial action with its own conventions
P25-L explicitly uses torsionless hats,signature(+---),dimensionless a and kappa=mu*kappa_phys,K=epsilon S/2,and its complete algebraic S terms. Evaluate that supplied historical action only,no whole current primitive Sadm identity. Classical a/Maxwell positivity only on supplied fixed background with constant real nonzero coefficients and actual Gauss reduction. Quantum elimination retains full reference,boundary,contour and prefactors.
- Original action in supplied magnetic background
Same P25-L action,phi=f_eff*a,g=g0/f_eff,fixed Minkowski,constant a,E0=0,uniform B0,k perpendicular B0,transverse photon potential parallel B0. Actual Gauss reduction;other angles retain longitudinal response.No inserted cavity,damping or quantum state.
Original evidence
- HISTORICAL-MIXED-TIME-RESPONSE.txt lines 1–104
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/historical-dynamics-source-recovery-20261103/HISTORICAL-MIXED-TIME-RESPONSE.txt
fa6d1a3f0ab68725ef1f4529dbddf99b2121039c90a1b4cc9badcfadd891bd98
finding:hist20261103r-exact-mixed-retarded-time-response