Foundations of STC (v1.1) — request for comments on core spec and empirical bridge

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Context. We share a Foundations paper that proposes a compact spectral–operator core and a QM-inspired (but strictly methodological) bridge from formal states to observables. This thread is about the theory only (no protocols).
PDF: http://dx.doi.org/10.2139/ssrn.5390743

Minimal core (for reference). States \lvert\psi\rangle in a Hilbert space \mathcal H; intentional subspace S\subset\mathcal H with projector \Pi_S; a coherence functional \kappa; and meta-operators M. One simple instantiation is

\kappa(\psi) \;=\; \frac{\lVert \Pi_S\,\psi\rVert^2}{\lVert \psi\rVert^2}\,.

The empirical bridge uses self-adjoint observables \hat A, pointer-level POVMs (e.g., \sum_i E_i=\mathbf{1}_{\mathcal H_{\mathrm{ptr}}}), reference overlaps p_k(\psi)=\lvert\langle\phi_k\mid\psi\rangle\rvert^2, and trajectories under M.

Focused RFC (section-level comments appreciated):

  1. Core specification sufficiency. Is the tuple (\mathcal H,S,\Pi_S,\kappa,M) stated precisely enough to be self-contained? Would you strengthen or relax the coherence/invariance requirements? Pointers to counterexamples are welcome.
  2. Empirical bridge assumptions. Are the premises (self-adjoint \hat A, pointer POVM, reference overlaps p_k, effective dynamics) minimal yet adequate for mapping to data without circularity? Any missing identifiability assumption you’d make explicit?
  3. Reference construction & validation. The paper sketches practical estimators for \{\lvert\phi_k\rangle\} (e.g., templates/PCA/ICA/NMF) with held-out calibration and stability reporting. Would you prefer a concise formal identifiability condition (e.g., frame/orthogonality/tolerance band) right in Foundations?
  4. Falsifiability set. Do the failure criteria form an independent, practically checkable set that excludes strong non-spectral countermodels? Which wording would you tighten to avoid loopholes?
  5. Stability/Emergence (local uniqueness). Is a margin \delta\kappa>0 within an \varepsilon-neighborhood the right minimal notion here, or would you suggest a topological/measure-theoretic variant?

Why here. NeuroStars has a strong methods/theory audience; concise edits (tight wording, missing lemma, counterexample) are most helpful. We plan a v1.2 with a short changelog acknowledging concrete suggestions.