Passive Signal as Passive Controller: A Systems-Theoretic Feasibility Analysis of the Signal-Worker Ontology

In the paper's words

The Signal-Worker (S-W) ontology interprets the boson as a signal — a delocalized field instruction — and the fermion as a worker — the localized state that performs work, and proposes that passive, structure-encoded control is thermodynamically superior to active, energy-intensive control. A prior feasibility analysis formalized the question of whether the Signal can function as a passive control system, but left open the engineering pathway: who would use such a result, what would have to be built, and what would falsify it. This paper closes that gap.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. A labeled illustrative example quantifies delay margin (safety ratio $\rho \approx 4.71$), quantization energy cost ($2.5\%$ per packet), attractor radius ($r_q = 0.05$), and robustness budget ($16.7\%$ margin erosion tolerance).

   from Abstract

2. The Signal-Worker ontology addresses exactly this trade-off: it analyzes actively driven quantum systems (light-induced superconductivity, high-pressure hydrides, dynamical instabilities) as relying on an external, energy-intensive Signal, and passive structural control (proximity effects, Moiré engineering, biological scaffolds) as relying on an intrinsic, architectural Signal, and hypothesizes a Complexity-Efficiency relationship linking the structural complexity of the scaffold to stabilization performance [10].

   from 1. Introduction

3. A worst-case quantization degradation bound ($5.0$ energy units over $100$ steps at resolution $q = 0.1$) and a labeled illustrative example quantifying delay margin, quantization energy cost, attractor radius, and robustness budget (Sections 4.3–4.4, reported in Section 5).

   from 1. Introduction

4. For the S-W question this matters because the ontology separates the delocalized signal from the localized worker across a boundary; if the Signal acts on the Worker across any spatial extent, a transport delay is the minimal model of that separation, and [2] shows passivity can survive it — but only with an explicit transformation and at a quantifiable cost, which motivates the delay-margin analysis of Section 4.4. [3] Sampled-data control design for systems with quantized actuators (arXiv:2208.05694v3).

   from 2. Background and Related Work

5. This supplies the decomposition pattern adopted in Section 4.4's robustness budget: separate a nominal closed loop (Signal driving Worker) from a norm-bounded deviation term, and analyze how much margin erosion the nominal passivity tolerates. [6] Safe Control Synthesis via Input Constrained Control Barrier Functions (arXiv:2104.01704v1).

   from 2. Background and Related Work

6. This work proves that the vector field of a CBF-controlled system is a Krasovskii-like perturbation of the set-valued map of a projected dynamical system (PDS), with a quantitative bound on the perturbation (Theorem 3.1), and its conclusion states that CBF-controlled systems uniformly converge to trajectories of the PDS and may serve as continuous implementations of discontinuous PDSs, preserving asymptotic stability of the origin without introducing undesired equilibria in the convex, fully-actuated case.

   from 2. Background and Related Work

How it is done

1. A worst-case quantization degradation bound ($5.0$ energy units over $100$ steps at resolution $q = 0.1$) and a labeled illustrative example quantifying delay margin, quantization energy cost, attractor radius, and robustness budget (Sections 4.3–4.4, reported in Section 5).

   from 1. Introduction

2. Its conclusion states that sufficient conditions take the form of bilinear matrix inequalities and that an iterative convex-concave algorithm minimizes the size of the closed-loop attractor.

   from 2. Background and Related Work

3. Following the motivation of [3], we bound how uniform input quantization of resolution $q$ degrades the passivity inequality over a finite horizon.

   from 3.3 Perturbation analysis under quantization and delay

4. Every input number below is either a structural constant of the candidate dynamics or an explicitly stated assumption or illustrative chosen parameter.

   from 4. Analysis

What would falsify it

1. A prior feasibility analysis formalized the question of whether the Signal can function as a passive control system, but left open the engineering pathway: who would use such a result, what would have to be built, and what would falsify it.

   from Abstract

2. Without that bridge, the ontology's central engineering question — can the Signal function as a passive control system? — cannot be checked, designed against, or falsified.

   from 1. Introduction

3. That analysis established that the framing is not vacuous — it produces concrete, arithmetic-checkable quantities — but it stopped at the block-diagram level and did not connect the result to the corpus's own thermodynamic and complexity arguments, nor state what evidence would confirm or refute the hypothesis, nor assess whether the result is anywhere near engineering practice.

   from 1. Introduction

Where the claim stops

1. Second, the loop-passivity argument for $T_d \gt 0$ leans on the guarantee pattern of [2] rather than a new proof; a neutral-type closed loop can lose stability in ways a finite-dimensional passive loop does not, and the margin proxy $M_n$ is a heuristic, not a $\sigma$-stability certificate.

   from 6. Discussion

2. Third, the attractor-radius result R6 assumes a linear contraction constant $\lambda_W$; for nonlinear Workers the radius bound does not transfer.

   from 6. Discussion

3. Fourth, the safety-wrapper pattern inherits exactly the fragility [4] identifies: parametric uncertainty invalidates model-based guarantees, and the robust fallback trades performance for safety; [6] likewise flags robustness to noise and model mismatch as open for input-constrained barrier controllers.

   from 6. Discussion

Where to read

1. Abstract235 words · 1 min
2. 1. Introduction503 words · 2 min
3. 2. Background and Related Work1,522 words · 7 min
4. 3. Methods382 words · 2 min
5. 4. Analysis1,341 words · 6 min
6. 5. Results349 words · 2 min
7. 6. Discussion1,036 words · 5 min
8. 7. Practical Implications and Engineering Pathways854 words · 4 min
9. 8. Conclusion205 words · 1 min
10. Provenance and AI Involvement225 words · 1 min