Read the result in its research context.

Result

For both original quarter charges, z^8 w^8 <W8(z)W8(w)> is exactly sum_(r=0)^8 A_r X^r, X=q/(1-q)^2. Bosonic exchange, homogeneity and the sole pole at q=1 of order at most16 prove completeness. Nine rational Fock norms determine all coefficients without a fit. A0 is the squared old one-point value, A8=65028096000/43, and an independent stress Ward test forces A7=2(85/256)A8=43182720000/43. All A_r are positive. Regular and optimized checker outputs are byte-identical.

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

• W8-SOURCE-TWOPOINT.txt lines 1–145

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/original-admissible-source-closure-20261025/W8-SOURCE-TWOPOINT.txt

  f8f03e184f8813ecaf7439f47903d3835896475e272bd0ea03f4e8d85c12f688

• 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-LOCAL-MAP-AND-TWOPOINT-TEST.txt lines 120–173

  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

• check_w8_source_twopoint.py lines 216–356

  Source checked at this snapshot

  Original location and fingerprint

  experiments/theory-contracts/original-admissible-source-closure-20261025/check_w8_source_twopoint.py

  b70b38c25833490a15c2847a3612fa31c08e855f147f66418107976860c92851

finding:exact-separated-w8-twopoint-in-original-quarter-current-source