Fixed original CAR time and admissible eight-arc word; the P1 seed does not specify the clustering direction. No exclusion of other P1 times or states, finite KMS interval, CAR vacuum, or excited insertions; no derivation of P1 localization, reflection or physics. The input basis is not orthonormal.
Read the exact result, assumptions and evidence
Result
All five original charge-zero inputs have K_alpha energy 4. The original J8 Gram is positive definite for both quarters with the stated exact determinant. A smooth quotient profile with nonzero first coefficient gives a bounded eight-arc Weyl word that reaches energy 3 from every nonzero vector in the input span. The connected Euclidean response based on K_alpha-4 grows on the infinite half-line; the same applies to positive states supported entirely in this span. The P0 vacuum channel J32 has the two exact R32 weights in the source. The R093 response remains an original vacuum word with the finite raising-current polynomials B_i.
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.
Given CAR source time, smooth profiles and direct cover pullback; the one-mode Fock case tests an identity and is not a TFPT source state. Other local P1 embeddings or compressions are not excluded. No identification with OS time, all E8 Cartan currents, Higgs measure or F1.
Read the exact result, assumptions and evidence
Result
In the given folded CAR source contract the derivative of the same ordered Weyl source computes the left-inserted smeared total current response J(h)T(t)T*, including its noncommutative phase and alpha-dependent state kernels. An independent one-mode Fock test confirms the operator order and sign. For a nonconstant smooth phase profile the direct pullback T=W(-b∘F), F(theta)=8theta, acts nontrivially on a bounded even CAR bilinear in each of the eight disjoint cover arcs; hence T is not in the even local von Neumann algebra of any single such arc.
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 original folded CAR source contract, fixed input states, source time K_alpha and smooth comparison profiles; no primitive P1 OS time identification, original profile selection, full Ward or dynamical Higgs source, or F1 completion. Historical replay does not validate active source pins or ledger projection.
Read the exact result, assumptions and evidence
Result
In the given folded CAR source contract the full ordered T(t)T* response on the five actual states is determined by the original Schur kernel and an explicit Weyl Gaussian including all modes. The state polynomial has modes 8,16,24,32 due to cover degree 32; the Gaussian retains all modes. Normalized original P0 states in quarters 1/4 and 3/4 differ already in R8=||J8P0||²/||P0||²: 766710528/328635469 versus 770249472/331641421. A smooth admissible comparison profile with b3=0 distinguishes their responses at t=pi in the quadratic term. An additional smeared CAR total current is a derivative of the same Weyl source. The historical mixed-current-origin checker was replayed in a targeted temporary overlay with original pins and returns 29 PASS, PARTIAL and no local origin; the full ledger-checked overlay was not passed.
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.