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

Scoped exclusion

Smooth unitary endpoint removal diverges at fixed compact source time

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

Only normalized smooth UNITARY vector-state sequence on fixed compact source circle. Nonunitary sums/field intertwiners,microscopically derived charged covariance cocycles and decompactified time outside scope. Local normality away from removed point is not finite global original energy. Individuallambda_i±1/2 distinct from totalQ=sumlambda_i; two-point exponent/energy alone no128/FE-GEN/ALG-EXH proof.

Read the exact result, assumptions and evidence

Result

Original Weyl/CCR time formula andphi(theta)=f(8theta) give exactDeltaK=8sum_n>0 n²|f_n|²=(2/pi)int|f'|². Any pi->0 return squeezed intoeps costsDeltaK>=2pi/eps. Normalized W(phi)Omega states therefore have no bounded-energy separation limit under same global K reference; scalar normalization leaves Rayleigh quotient unchanged. Class lower bound,not profile scan. Known conditional K_lambda=K_0+lambda.p+lambda²/2+delta.lambda retained; its positive charged sectors are NOT excluded.

Required assumptions

  • Smooth unitary pair return at fixed compact source time

    Given original chiral current/Weyl source, sea and K=Hcover/8 with delta_k=(k+alpha)/8-1/2. Periodic real phi(theta)=f(8theta), normalized UNITARY vector state W(phi)Omega; pi->0 return squeezed into base width eps on fixed source circle, same original energy reference. No assertion about general nonunitary sums, charged covariant representations, sector energy connections or decompactified time. Conditional Sugawara sector energy already fixed once lambda is given.

  • 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.

  • 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

finding:smooth-unitary-endpoint-removal-diverges-at-fixed-source-time