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Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Established in scope

All original global time-winding histories reduced exactly

In the question: Historical: common source, state and event selection

Only given global free source time/W_n/Q phases, not all local fields. No closed-C5 axiom or performed projection. Total time acts on grade superpositions. E8 half-sector needs its lift; global W2 is not local root vertex.

Read the exact result, assumptions and evidence

Result

Given Ward increments are c_n(q)=Falpha(q+n)-Falpha(q), Falpha(q)=q(q-1)/16+alpha q/8. Thus K-Falpha(Q) is winding invariant and alpha independent. Actual CAR space factors via W_n as ell2(Z) tensor H_Q0, not an assumed rotor. Every finite ordered time/winding word has the stated exact normal form; all n=8z+r checked symbolically. On a fixed neutral R_b,k field mode the input multiplicity is unchanged. Charge-return acts scalarly in actual B_k metric, retaining all intermediate charges/modes. W1 lies in original odd vector sector; W2 is smallest even winding and ends at an actual E8 root.

Required assumptions

  • Charged CAR algebra and original negative sea

    Assume the actual field algebra is charged CAR(H) and its reference state is the pure quasifree sea with occupation 1−C. Relative charge and positive excitation time are normal ordered against this sea. This physical identification is an additional premise.

  • Fixed scalar Hardy model with quarter time

    H=L²(S¹), C projects onto n≥0, B_alpha=−i∂theta+alpha with alpha=1/4 or 3/4. C and B remain fixed for every candidate. Consider scalar unimodular multiplication operators: continuous symbols for isometry classification and H1 symbols for finite excitation energy. This source class is not derived from P1/P2.

Original evidence

finding:original-source-global-time-winding-history-factorization