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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

Linear spectral centralization does not replace the full marked Hardy source

In the question: Automated construction of operator maps and sources

Only replacement of this whole marked F/N family by its linear central quotient as a full nonlinear source and the claimed original complex instability. Formal probe variables are not new physical couplings. Preserve positive linear readout, genuine later inverse insertions, endpoint marks and existing source/state/time consumers. No universal source no-go or CP claim.

Read the exact result, assumptions and evidence

Result

Centralizations cM0 and icM0^-1 reproduce first scalar traces, but actual full marked determinant differs from the centralized two-sided replacement already at quadratic order. Exact recorded full polynomial and difference hold for actual periods, with nonzero1+r+r² at real period ratio. The full adjoint relation has a nonzero marked residual; only its centralization agrees. Original delta is real, so the complex analytic saddle is not an admissible original descent. Inverse legs already exist in original Gram/Green/Kstr. Ten exact root identities and independent source/matrix review confirm.

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.

  • All six original induced inputs at the fixed kinetic NS reader

    Evaluate the six existing offdiagonal mu_ab in the original induced NS/Hardy kinetic reader, Phi=0, finite positive ell_NS and half-frequency. Carry actual G_a input and J E^(b-1) output maps, same continuation, metric, spin, both graph faces and normal symbol. Do not identify individual twist lines or assume a physical combination or multiplicative compression of field products.

  • Original closed real delta transport action

    Original EM3 action on its invertible closed epsilon0 branch with real delta, fixed U6 and all three cusps. Use actual common Gbase dictionary U6=diag(M0,-M0) and fixed marked P0. This is not a newly chosen independently projected physical variation.

Original evidence

  • ROOT-FULL-MARKED-READER-AND-ORIGINAL-WEIGHTS-REVIEW.txt lines 1–88

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-FULL-MARKED-READER-AND-ORIGINAL-WEIGHTS-REVIEW.txt

    e262351fa651517b6af17483c079803b0666e407910d9ec2ba5434a6f2733bbc

  • check_actual_marked_spectral_readout.py lines 1–57

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_actual_marked_spectral_readout.py

    07d9954028194f3d3f3a9748783a350324fa9ebeb4c9a87aa0357038c729b15d

  • ROOT-ACTUAL-MARKED-SPECTRAL-READOUT-CHECK.json lines 1–19

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ACTUAL-MARKED-SPECTRAL-READOUT-CHECK.json

    332e42f9d79006973afd3f5ca65a230839402e99a0a666689d1548908ffcbdb9

  • CLAUDE49-CENTRALIZATION-AND-COMPLEX-DELTA-INDEPENDENT-REVIEW.txt lines 1–143

    Source checked at this snapshot

    Original location and fingerprint

    experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE49-CENTRALIZATION-AND-COMPLEX-DELTA-INDEPENDENT-REVIEW.txt

    45b70e359a2e6dd8348b4454ee271a52aa33fd6d94d70b345e2ca21eea935b98

  • 003-subsection-discrete-phase-operator-and-transport-grammar.tex lines 3–125

    Source checked at this snapshot

    Original location and fingerprint

    documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/003-subsection-discrete-phase-operator-and-transport-grammar.tex

    00a2cf1b249b77280dbbf6dfb41c91c77e08aa63e0f30b682d1a8a621f3dd7ec

  • 005-source.tex lines 114–198

    Source checked at this snapshot

    Original location and fingerprint

    documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/005-source.tex

    786d2619e775775d70adf177794138485b261968042a880b2f0f617bb0111814

finding:linear-spectral-centralization-does-not-replace-full-marked-hardy-source