[#713] Literature retrieval: double-pulse / bilinear kernels vs P398 odd-sector certificate (do not merge)

[LightChainr]

Draft. Do not merge. Retrieval only, for #713 (parent #650). Adds one file: `notes/lit-double-pulse-observability-20260912.md`. No new computation, no enumeration, no transfer matrix, no hardware. No `docs/STATUS.md` edit. Refs #709, #594, #598, #610.

Tripwire answers

1. Bilinear/Hankel prior art claimed as PRIMARY? No. Only Petreczky, ESAIM: COCV 17 (2011) 446–471, Part II is PRIMARY_TEXT_READ for the bilinear Hankel-rank criterion (Def. 2.8; Theorem 2.3(iii) `dim Sigma_min = rank H_Phi`; Theorem 2.7). Fliess 1974, Isidori 1973 are ABSTRACT_ONLY; Ho–Kalman 1966 is [LIT].
2. Does the P398 double-pulse certificate appear in print? No. Nothing retrieved matches the scalar observer, the −16 determinant, or the width-4/5 odd-sector rank attainment. Expected answer confirmed.

Four questions

• Q1 (two-pulse/Volterra kernels recovering a hidden sector after a quotient): the general machinery is published — Lucarini, arXiv:2502.07908v2 §II.2, Eqs. (15)–(19) (two-time second-order Green's function, double convolution, two-mode spectral weights alpha_ij = <m^T Pi_j m^T Pi_i Psi, nu_inv>; §IV.1.3 calls the nonlinear Green functions Volterra kernels). PRIMARY_TEXT_READ. But no retrieved primary paper recovers a parity-odd hidden sector after an even quotient; Lucarini's splitting is by Koopman modes, not by a C2 irrep.
• Q2 (realization theory): word coefficients c(w)=C A_w x0, the Hankel matrix, finite-rank ⇔ realizable, and minimum order = Hankel rank are all prior art (Petreczky 2011 PRIMARY_TEXT_READ; Petreczky–Wisniewski–Leth 2016 PRIMARY_TEXT_READ, which notably states no Hankel criterion). A finite 4×4/16×16 nonzero minor is an instance, not a new theorem.
• Q3 (noncrossing partitions / TL / join-split): closest named relative is the Temperley–Lieb stochastic process (Pearce–Rittenberg–de Gier–Nienhuis 2002), generator sum_j (1-e_j) on link patterns — but it is join-only and acts on matchings, not partitions. Bertoin 2007 EFC has join+detach but is exchangeable/nonlocal. No named process matches P398's G = sum_j (J_j + D_j) (adjacent join + point detach on cyclic noncrossing partitions). Do not call it "the TL process" or "an EFC process".
• Q4 (zero delay misses a delay-mode): for K(tau)=C e^{tau A} B, K(0)=0 with nonzero Hankel rank is the generic strictly-proper/relative-degree case, not a published counterexample. No two-pulse Markov-chain example with K(0)=0 and Hankel rank 4 was found.

All 11 sources are marked PRIMARY_TEXT_READ / ABSTRACT_ONLY / [LIT] in the note. Absence of a retrieved match is recorded as a retrieval gap, not a no-go or an originality certificate. Unique P398 science stays in #709.

[LightChainr]

Independent Grok check (not the agent log).

Petreczky ESAIM: COCV 17 (2011) 446–471 Part II is real; Thm 2.3(iii) is dim Σ_min = rank H_Φ (Numdam). Lucarini arXiv:2502.07908 exists and is a Markov-chain two-time/Volterra response paper. Pearce–Rittenberg–de Gier–Nienhuis math-ph/0209017 is the TL stochastic process (join-only). Bertoin arXiv:0704.3122 is EFC.

Keep: Hankel-rank = min order is prior art; #709 is a finite instance, not a realization theorem. K(0)=0 with nonzero Hankel is generic strictly-proper, not a named counterexample. P398 G=Σ(J_j+D_j) is not the TL process and not EFC.

Do not merge. Do not close #713/#709. Round-1 tripwire for this ticket is met. #711/#712/#714 hit a 429 until 22:55 CST and will be relaunched on the same model.

[LightChainr]

Correction, not a close. The process-identification paragraph is false after a change of representation. Draft #718: endpoint doubling Φ is a bijection NC-partitions(w) ↔ NC-perfect-matchings(2w) with Φ D_i=e_{2i} Φ, Φ J_i=e_{2i+1} Φ. P398 is the periodic IC zero-defect O(1) TL chain on 2w ends (Pearce–Rittenberg–de Gier–Nienhuis; reconnection as Cantini–Sportiello). “Join-only TL on pairings vs join+detach on partitions” was missing the even generators.

Keep #715’s realization/Volterra/Hankel prior-art: those still stand. #709 pulse ranks still stand. P398 is still not microscopic site percolation; IC disk is still not #708 annular rank. Next #713 retrieval should target the exact S,F,H and IC boundary, not another named-process search. Do not merge #715 or #718.