Add the #588 projected-memory literature check

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#588 projected-memory literature check (P398 retrieval)

This is a novelty-only retrieval note. It is not evidence about any percolation threshold.
A negative search here is not proof of originality (see the note's §6).

Object (from P398, frozen)

Exact finite CTMC (widths 4–8, 14→1430 states). P = orthogonal projection onto a rank-6
observable-Krylov span, Q=I−P, K(τ)=B exp(τD)C. Four findings judged for prior art:
F1 order saturation 2,3,4,4,4; F2 ~96% seed-readout residual is memory; F3 held-out split
~40% memory / ~43% unrepresented; F4 strong lumping collapses under pencil-outside perturbations
while memory/signed-low-rank stay robust.

Retrieval matrix (Q1–Q4) — cite-or-gap

• Q1 (highest value): theorem bounding McMillan degree / Hankel rank of a Krylov-seed MZ
  memory kernel independently of env dimension → GAP. Closest: MZ with finite-rank Krylov
  projection (Mori 1965; Gouasmi 2017; Ma–Li–Liu 2018, arXiv:1802.10133); Ho–Kalman McMillan
  degree = rank of infinite Hankel matrix (Hokanson 2018, arXiv:1803.00043). General LTI bound is
  only ≤ dim(D).
• Q2 (positive realization): no positive/Metzler realization theorem for the projected MZ
  kernel found → GAP.
• Q3 (highest value, per update): order saturation = theorem or accident? → GAP on theorem;
  the flat low order is explained structurally by rank K(τ) ≤ rank C = 3 (a span identity), not a
  general bound. Numerical order actually grows 12,13,14 (accuracy-target-dependent).
• Q4 (finite-horizon balancing of Markov chains): finite/time-limited balanced truncation is
  known for LTI; no MZ-CTMC finite-horizon balancing theorem found → GAP (relevant: Agarwal et
  al. 2023, arXiv:2305.20083).
• F2/F3/F4: the exact 4-way attribution, the 96% and 40/43% figures, and the
  lumping-collapse-vs-memory-robustness comparison are not found in the searched literature →
  GAP (the qualitative "error is mostly memory" claim is classical = [LIT]).

Searched

Google Scholar, arXiv, Royal Society A, AIP PoF, ScienceDirect, handwiki, ResearchGate. No proxy
block encountered.

Negative results (explicit)

No theorem bounds McMillan degree/Hankel rank of the Krylov-seed MZ kernel independent of env
dimension; no positive-realization theorem; no MZ-CTMC finite-horizon balancing theorem; no
published exact 4-way closure attribution nor the 96% / 40%–43% split; no published
lumping-collapse-vs-memory-robustness comparison.

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