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Add the map-resolved modular-covariance identifiability note - #747

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Map-resolved torus tomography: modular-covariance identifiability note

Novelty/identifiability retrieval for #585. All four given arXiv numbers were retrieved as-is (none
substituted): 2604.24491 (Roux–Ribault–Jacobsen), 2302.08168 (Grans-Samuelsson et al.), 2604.05503
(Ang et al.), 2510.04701 (Jacobsen et al.). No proxy block.

Identifiability matrix (which freezing gives a finite-dim basis)

  • (a) representation / primary-field content — NO (alone): torus 1-pt functions are infinite
    linear combinations of conformal blocks; modular-invariant scalar multipliers form an infinite
    family (ticket's correction; consistent with 2604.24491). ABSTRACT_ONLY
  • (b) spin — NO (alone).
  • (c) combinatorial map / connectivity sector — YES: map-defined functions form a basis of
    bootstrap solutions (Grans-Samuelsson et al. 2302.08168). ABSTRACT_ONLY
  • (d) BPZ / modular-covariance differential equation — YES: modular-covariance equations admit a
    finite number of solutions (10 for the 6 simplest primaries, 2604.24491). ABSTRACT_ONLY
  • (e) allowed intermediate spectrum — PARTIAL: helpful but not sufficient alone.

Statement + boundary

Finite-dim torus basis is obtained only after freezing by (c) map/connectivity sector and/or (d) BPZ
/ modular-covariance differential equation. (a)/(b) alone, and (e) alone, do not finite-dimension
the space. Hard constraint honored: no candidate basis is promoted to a physical model class without
(c)/(d).

Negative results (explicit)

No theorem found that (a)+real-analyticity+modular invariance is finite-dim (the ticket argues it is
not); no source where spin alone finite-dimensions; no source where (e) alone suffices. Full texts
not read line-by-line — matrix built from abstracts + issue body.

Full Matching-One repository CI has not been run for this commit.

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