Established in scope
The actual W8 response has infinitely many time levels
In the question: Common clock sectors, quartic geometry and operational reconstruction
Exact dynamics in the same source/time contract. Does not exclude finite approximations or finite native observer codes; does not fix absolute physical time.
Read the exact result, assumptions and evidence
Result
For every ell>=1 the connected spectral norm is a_ell=sum_(r=1)^min(ell,8) binom(ell+r-1,2r-1) A_r >=ell A1>0. Smoothing by the existing positive generator exp(-epsilon N) makes the insertion norm finite and only multiplies these spectral contributions by exp(-2epsilon ell). For every epsilon>0 the cyclic time subspace remains infinite dimensional. No finite spectral-support model with this same time reproduces the exact two-point response.
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 174–197
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
- W8-SOURCE-TWOPOINT.txt lines 146–224
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/original-admissible-source-closure-20261025/W8-SOURCE-TWOPOINT.txt
f8f03e184f8813ecaf7439f47903d3835896475e272bd0ea03f4e8d85c12f688
- 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:original-w8-response-has-infinite-same-time-spectral-support