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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

P1 parity-Gauss net selection undecidable without original insertion/localization identification

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

Original definition/source comparison, not logical independence or two complete alternative P1 models. Neither universal nonderivability nor incompatibility with every P1 seed proved. A specified full seed already includes its net as input. No new construction or numerical suite and no physical premise removed.

Read the exact result, assumptions and evidence

Result

Literal scalar P1 names seam, reflection positivity, unit winding and c3; stronger boundary data supply A_+, and the operational seed explicitly takes A_loc as input. Admissible local net restricts supplied local insertions. These definitions do not identify primitive physical space and local algebras with the existing Gx=1 gauge net. Overall verdict: UNDECIDABLE DUE TO SPECIFIED DEFINITION GAP. With old local Z fixed, existing gauge isometry is not support-preserving because FZ=-ZF; the neutral pair has restricted compatibility by telescoped Gauss laws. Global Phi retains its old locality failure and cannot be composed with E without a domain/net identification.

Required assumptions

  • 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.

  • Conditional local parity-Gauss completion with common original time

    ADDED comparison contract, NOT P1-derived: old four-state register with total-even matter; redundant Z2 link qubits and local Gx=(-1)^nx tau_(x-1)^x tau_x^x=1; gauge-invariant local observable net. Original QWZ hopping coefficients, common microscopic Hamiltonian and energy reference; no new electric energy. Sector-specific f(Z) subtractions must map to f(W) and can be nonlocal. No identification of Gauss space with original Padm.

  • 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:p1-parity-gauss-net-selection-undecidable-without-original-localization-map