Established in scope
Local current phase test and conditional cyclic P1 image of W8
In the question: Common clock sectors, quartic geometry and operational reconstruction
Sufficient conditional current route and necessary test within that route. Actual P1 image and full target comparison remain open. A single Weyl pair is insufficient; charged seam fields and closed collar/reference domains require additional original transport. No universal P1 no-go claim.
Read the exact result, assumptions and evidence
Result
On a proper interval choose real compactly supported chi, kappa=(1/(2pi))integral(chi_prime)^2, f=chi and g=-2chi_prime/kappa. The original level1 current cocycle is c(f,g)=-2i; the Weyl commutator is exp(2ist)I. A normal unital local current embedding must preserve this identity. If it also preserves state, time, reflection and original eight-arc support, GNS gives an isometry onto its cyclic image. On that image the same point-split products and counterterms fix W8. A global unitary onto the entire P1 space is unnecessary for this subfield. Reviewed original passages give C_seed from an already supplied local seed to boundary data and assume the positive CAR kernel; they do not supply the concrete reverse current embedding.
Required assumptions
- Fixed octic completion in the existing current space
In the supplied positive c8 current space,seek W8 only in the declared17 dimensional space:H8=sum_roots(alpha.h_-1)^8-30Q11^4 and the16 weight8 Q_ab monomials. H8 leading coefficient is1;root zero mode and L1=L2 must vanish. This specifies a mathematical existence ansatz,not an extra physical source or preparation rule. Uniqueness beyond this space is not assumed.
- Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
- Full existing local E8 field algebra with observer five-code
Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule.
- 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
- P1-W8-LOCAL-MAP-AND-TWOPOINT-TEST.txt lines 27–119
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/P1-W8-LOCAL-MAP-AND-TWOPOINT-TEST.txt
072b6588666504ec4f04024e279030bbdf83b724102bac181ee3696133c1be28
- P1-W8-LOCAL-MAP-AND-TWOPOINT-TEST.txt lines 199–212
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/P1-W8-LOCAL-MAP-AND-TWOPOINT-TEST.txt
072b6588666504ec4f04024e279030bbdf83b724102bac181ee3696133c1be28
- 002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex lines 103–143
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/002-section-intrinsic-closed-branch-and-canonical-rigid-obje.tex
1de90a4a7379bef804cc7815d72c0f86bb398a5771e9b00997c4bb15e8815f9e
- 007-subsection-bosonic-relative-index-and-higgs-selection.tex lines 365–394
Source checked at this snapshot
Original location and fingerprint
documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/007-subsection-bosonic-relative-index-and-higgs-selection.tex
cf801a467465db8d72e4eb3f8e32eea2e23393bf42232a225116c34ed093f761
- P1-W8-INDEPENDENT-REVIEW.txt lines 365–455
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/P1-W8-INDEPENDENT-REVIEW.txt
62ecf1ed58792ae7bb88193194dbd392ad2895c1d48d954b475d136b5288a2d3
finding:local-current-phase-and-conditional-cyclic-p1-w8-image