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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

Boundary minimality proves neither seed inverse nor unique source

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

Precise proof/definition audit of the cited arguments. No independence theorem, two complete P1 models or unconditional rescaling of undefined finite-block/action classes. No new physical model; historical problem status is preserved.

Read the exact result, assumptions and evidence

Result

From d_seed=d o C_seed one obtains minimization only over im(C_seed). The original proof supplies neither attainment of the global minimum in that image nor classification of the equal-minimum fibre; well-foundedness alone gives no object uniqueness or unit spectral flow. Under explicit scale-covariant reference, action and cutoff conditions, B_lambda with lambda D and lambda B retain defects but have different spectra for a compact self-adjoint realization. This rescaling theorem remains conditional. An honest OS inverse needs complete supported Schwinger data with OS II assumptions, or a full Euclidean net/action, regular RP state and time-zero condition; arbitrary positive-time insertions do not automatically act on the OS quotient.

Required assumptions

  • Literal boundary-minimality and analytic-perturbation statements

    Audit objects are the original boundary-source definitions and proofs: C_seed maps an operational seed forward to a spectral boundary tuple; defect order is lexicographic on N4; the self-adjointness statement asserts relative bound0 for every symmetric bounded-coefficient differential perturbation of order at most1. These source assertions are audited rather than assumed true. No special symbol cancellation, domain invariance or absolute scale is silently added.

  • Original P1, boundary, seed and local restriction definitions

    Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.

  • 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:original-minimality-does-not-reconstruct-operational-source