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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

Whole response reconstruction needs the actual entire source family

In the question: Recursion, hypergraphs and mirroring at the original joint source

Exact reconstruction criterion and scoped sufficiency test, not a new complete P1 countercandidate or global TFPT nonuniqueness theorem. Retain actual admissibility, source patch, phases and zeros. No evaluated primitive bosonic density, action or spectrum.

Read the exact result, assumptions and evidence

Result

On an actual star-shaped source chart W[J]=W[0]+Wprime[0].J+int0¹(1-s)Wdoubleprime[sJ](J,J)ds. Evaluated a4/current vertices are not the entire evaluated Hessian family. Cross blocks alone leave single-source functions on genuine local product charts. This introduces no new freedom in supplied original omega. Rk is auxiliary; given Sadm fixes higher1PI terms.

Required assumptions

  • 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.

  • Actual whole source response and paired product domains

    Original QFT007 caller with entire supplied Sadm, allowed sources, bound reference and existing time. Reconstruction on actual star-shaped local source chart, log Z only on a nonzero patch; even and ordered odd sources distinguished. Product normalization additionally needs actual J-real selfadjoint Gamma-odd D on compatible paired domains, actual Eeps and full96 constructor retaining all Y/MR; Eeps is not Padm. Proper-time/local coefficients remain scoped diagnostics, selecting no physical measure.

  • Original whole master chain and common physical space

    Read original Source42 PrimitiveCompletion027 with Source45 Boundary002/QFT002/QFT007/QFT008. Operational seed contains state and time. Padm is a product of commuting original filters, not an independent product-state/Hamiltonian decomposition. Explicit mixed bulk response additionally uses existing ordinary Spin4 product, constant radial H, fixed MR, deck-even tangential S, unscaled bound reference and original heat conventions.

Original evidence

finding:torsion20261104f-whole-response-reconstruction-does-not-follow-from-local-vertices