QNFO Papers

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

Living paper · v1.0.0Published 17 min read · 3,977 words

#Abstract

The QNFO corpus proposes a Signal-Worker (S-W) ontology in which the boson is interpreted as a signal — a delocalized field instruction — and the fermion as a worker — the localized state that performs work [10]. A companion re-entry document (DOI 10.5281/zenodo.18515457) poses the engineering question of whether the Signal can be made to function as a passive control system. This paper formalizes that question in the standard language of passivity-based control. We treat the Signal as a discrete-time controller block and ask under what conditions the closed Signal-Worker loop satisfies a dissipation inequality. We derive, with full arithmetic, (i) the exact passivity of a discrete integrator under the modified output $y_k = x_k + \frac{1}{2}u_k$, (ii) the output transformation $y_k = (1-\alpha)x_k + \frac{1}{2}u_k$ that renders a leaky integrator passive with an explicit dissipation rate, verified numerically step by step for $\alpha = 0.1$, and (iii) a worst-case passivity degradation bound of $5.0$ energy units over $N = 100$ steps under actuator quantization with resolution $q = 0.1$. A second, clearly labeled illustrative example quantifies loop margin under a transport delay, quantization energy cost, attractor radius, and robustness budget. We situate the analysis against all ten supplied bibliography entries. We conclude that the Signal-as-passive-controller hypothesis is well-posed and internally consistent at the level of abstract block diagrams, but that the corpus documents supplied contain no dynamical equations, so no physical validation is possible from the provided material alone.

#1. Introduction

The QNFO corpus proposes a reinterpretation of quantum phenomena through a decomposition it calls the Signal-Worker (S-W) ontology. According to the corpus document on Signal-Worker boundary confinement [10], the ontology assigns the boson the role of signal — "the delocalized field instruction" — and the fermion the role of worker — "the localized state that performs work" — and presents this as a red-team-hardened correction of what the corpus calls the "wave–particle duality fog." A second corpus document addresses structural versus driven quantum coherence [9]; the summary supplied for that entry is empty, so we can relate to it only through its title and identifier.

The present paper takes as its starting point a re-entry document in the same corpus, DOI 10.5281/zenodo.18515457, which we treat as an unverified premise of this exercise: we do not rely on any quoted wording from that document, since it is not among the supplied bibliography entries. The engineering question we pose is therefore a hypothesis formulated by the authors of this paper: can the Signal, as described in [10], be modeled as a passive control system in the precise sense used in systems and control theory?

Passivity is a standard notion: a system is passive if it cannot produce more energy than is supplied to it, formalized by a dissipation inequality involving a nonnegative storage function and a supply rate (defined in Section 3). Passivity is attractive as an engineering requirement because passive blocks composed in feedback remain stable, a property exploited across the control literature, from data-driven controller design [1] to control over delayed communication channels [2].

Our contribution is deliberately modest and methodological. We do not claim that the S-W ontology is physically correct, and we do not import any physics beyond what the corpus entries state. Instead we:

  1. Translate the Signal-Worker re-entry question into a well-posed block-diagram problem with a dissipation inequality.
  2. Derive, with every arithmetic step shown, the conditions under which candidate Signal dynamics (a pure integrator and a leaky integrator) satisfy discrete-time passivity, including the exact output transformations required.
  3. Derive a worst-case bound on how actuator quantization degrades passivity, connecting to the sampled-data quantized-control literature [3], and a labeled illustrative example quantifying delay margin, quantization energy cost, attractor radius, and robustness budget.
  4. Identify precisely what evidence would be required from the corpus to confirm or falsify the hypothesis, and what in the provided material is missing.

We discuss all ten provided bibliography entries. Statements about each work are restricted to what its supplied summary states.

[1] Passive iFIR Filters for Data-Driven Control (arXiv:2403.06640v2). This work designs a new class of passive controllers formed by the parallel action of an integrator and a finite impulse response (FIR) filter. The summary states that these "iFIR" controllers are more expressive than PID controllers while retaining their features and simplicity, that a model-free data-driven design is provided based on virtual reference feedback tuning, and that passivity is enforced through constraints (the summary text is truncated at this point). This is directly relevant to our problem: the Signal block we analyze in Section 4 is exactly an integrator, and [1] shows that integrator-based structures can be made passive by construction and tuned from data without a model. If the Signal is to be engineered rather than merely postulated, the iFIR design pattern is the closest supplied template.

[2] Passivity-based PI control of first-order systems with I/O communication delays (arXiv:1507.01146v1). This work revisits PI control of first-order linear passive systems through a delayed communication channel, using the relative stability concept called sigma-stability. The delayed channel is treated as a transport PDE, passivity of the overall loop is guaranteed, and the resulting closed-loop system is of neutral type; spectral methods are then applied (the summary is truncated mid-sentence). For the Signal-Worker question, this matters because the S-W ontology separates the delocalized signal from the localized worker — geometrically, a separation 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 that passivity can survive such delays when the channel is modeled as a transport PDE.

[3] Sampled-data control design for systems with quantized actuators (arXiv:2208.05694v3). This work designs sampled-data state feedback for continuous-time linear systems with uniform input quantization, ensuring uniform global asymptotic stability (UGAS) of an attractor surrounding the origin by rewriting the closed loop as a hybrid dynamical system using an auxiliary construction (summary truncated). This motivates our quantization analysis in Section 4: any engineered Signal will be implemented in discrete time with finite-resolution actuation, and [3] establishes the standard framework — stability of an attractor around, rather than at, the origin — under exactly those conditions.

[4] Bringing Quantum Systems under Control (arXiv:2412.00736v1). This tutorial connects quantum computing to bilinear control systems. It states that quantum computing has potential in cryptography, simulation, optimization, and machine learning, that new algorithms with unprecedented capabilities can be developed, and that experimental realization of quantum devices is an active field of research (summary truncated). We cite it as the supplied bridge between control theory and quantum systems: it frames the general question of how control-theoretic concepts apply to quantum hardware, which is the category of question the Signal-Worker re-entry poses.

[5] On the infeasibility of entanglement generation in Gaussian quantum systems via classical control (arXiv:1107.3174v1). This work uses a system-theoretic approach to show two negative results: classical linear time-invariant controllers cannot generate steady-state entanglement in a bipartite Gaussian quantum system initialized in a Gaussian state, and cannot generate entanglement in finite time from a separable Gaussian initial state (summary truncated). This is an important caution for our hypothesis: system-theoretic controller classes, of exactly the kind we formalize for the Signal, have provable limits on what they can do to quantum systems. If the Signal is a classical passive controller, results of the type in [5] delimit what Signal-mediated effects can and cannot produce.

[6] Composite Adaptive Control Barrier Functions for Safety-Critical Systems with Parametric Uncertainty (arXiv:2601.17683v3). This work addresses the fact that control barrier functions (CBFs) — certificates that guarantee safety but require accurate system models — lose their guarantees under parametric uncertainty. It notes that robust methods maintain safety via worst-case bounds at the cost of performance, while modular learning schemes decouple estimation from safety and risk constraint violations during transients, and presents the composite adaptive CBF approach (summary truncated). We invoke this pattern in Section 6: the Signal-Worker hypothesis is a model-dependent claim, and [6] illustrates the standard taxonomy of responses (robust worst-case versus adaptive/learning) when the model is uncertain — which, for the corpus, it certainly is.

[7] Robust Nonlinear Optimal Control via System Level Synthesis (arXiv:2301.04943v3). This work treats finite-horizon constrained robust optimal control for nonlinear systems with norm-bounded disturbances by decomposing the uncertain nonlinear system, via a first-order Taylor expansion, into a nominal system and an error described as an uncertain linear time-varying system, leveraging system level synthesis (summary truncated). This supplies the decomposition pattern we adopt methodologically: separate a nominal closed loop (Signal driving Worker) from a deviation term, and analyze robustness of the nominal part.

[8] Using quantum computers in control: interval matrix properties (arXiv:2403.17711v1). This work explores the use of quantum computers for problems in systems and control theory, noting that quantum algorithms have been developed for binary optimization, which plays a role in various control problems (summary truncated). We cite it as the reverse direction of [4]: control problems posed to quantum computers. It is relevant to the corpus context because the QNFO documents concern quantum coherence, and [8] shows that the control-quantum interface is being explored in both directions in the supplied literature.

[9] QNFO: Structural vs Driven Quantum Coherence (DOI 10.5281/zenodo.18441401). The summary supplied for this entry is empty; it gives no further detail beyond the title. We therefore use it only as evidence that the corpus distinguishes structural from driven coherence — a distinction that, read against the title alone, suggests the corpus already separates passive (structural) from actively driven behavior, the same distinction passivity theory formalizes. Beyond that reading of the title, we make no claims about this document.

[10] QNFO: Signal-Worker Boundary Confinement (DOI 10.5281/zenodo.21974194). This entry supplies the core ontology: the boson is the signal, "the delocalized field instruction," and the fermion is the worker, "the localized state that performs work." The entry describes itself as "the red-team-hardened correction" of the ontology. This is the primary source for the Signal-Worker decomposition that the re-entry document asks us to treat as a passive control system. Notably, the ontology's own vocabulary — instruction (input), worker (actuator/state), boundary (channel) — maps naturally onto the control-theoretic triples of input, plant, and interconnection, which is the mapping we formalize in Section 3.

#3. Methods

#3.1 Definitions

Discrete-time passivity. A discrete-time system with state $x_k \in \mathbb{R}^n$, input $u_k \in \mathbb{R}$, and output $y_k \in \mathbb{R}$ is passive if there exists a storage function $V(x) \ge 0$ with $V(0) = 0$ such that for all $k$,

$$V(x_{k+1}) - V(x_k) \le u_k\, y_k.$$

The right-hand side $u_k y_k$ is the supply rate: the power injected at step $k$. Passivity says the stored energy never increases by more than the supplied energy; a passive system cannot be an unlimited source of energy.

Strict passivity with dissipation rate. If moreover

$$V(x_{k+1}) - V(x_k) \le u_k\, y_k - \delta\, x_k^2$$

for some $\delta \gt 0$, the system is strictly passive with dissipation rate $\delta$: stored energy decreases strictly whenever the state is nonzero and no supply is injected.

Block interpretation of the S-W ontology. We map the corpus ontology [10] onto a control block diagram as follows:

  u_k (instruction) ──► [ SIGNAL ] ──y_k──► [ WORKER ] ──► work output
                          (delocalized)       (localized state)

The Signal is the controller block; the Worker is the driven plant. The re-entry question — is the Signal a passive control system? — becomes: does there exist a storage function $V$ such that the Signal block alone satisfies the dissipation inequality, so that the Signal can never inject more into the Worker than it has received?

#3.2 Candidate Signal dynamics

Because the corpus documents supply no equations, we analyze the two minimal candidate dynamics for a Signal whose role is to accumulate and relay an instruction:

  • Pure integrator (undriven relay): $x_{k+1} = x_k + u_k.$
  • Leaky integrator (instruction decays if not refreshed), with leakage parameter $\alpha \in [0,1]$: $x_{k+1} = (1-\alpha)\,x_k + u_k.$

The natural storage function for both is the quadratic $V(x) = \frac{1}{2}x^2$. The analysis question is: for which output maps $y_k = \beta x_k + \gamma u_k$ does the dissipation inequality hold, and with what dissipation rate?

#3.3 Perturbation analysis under quantization and delay

Following the motivation of [3], we bound how uniform input quantization of resolution $q$ degrades the passivity inequality over a finite horizon. In a clearly labeled illustrative example (Section 4.4), we additionally evaluate, in the spirit of [2], the delay phase loss at a chosen crossover frequency against a chosen dissipative margin, and in the spirit of [7], the erosion budget on the Signal's passivity margin under a norm-bounded deviation.

#4. Analysis

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

#4.1 Exact passivity of the pure integrator

Setup. Dynamics $x_{k+1} = x_k + u_k$; storage $V(x) = \frac{1}{2}x^2$; candidate output $y_k = \beta x_k + \gamma u_k$.

Step 1: expand the storage change.

$$V(x_{k+1}) - V(x_k) = \frac{1}{2}(x_k + u_k)^2 - \frac{1}{2}x_k^2 = x_k u_k + \frac{1}{2}u_k^2.$$

Step 2: state the passivity requirement. We need

$$x_k u_k + \frac{1}{2}u_k^2 \le u_k(\beta x_k + \gamma u_k) = \beta x_k u_k + \gamma u_k^2$$

for all $(x_k, u_k)$. Rearranging,

$$(1-\beta)\,x_k u_k + \left(\frac{1}{2}-\gamma\right)u_k^2 \le 0 \quad \text{for all } x_k, u_k.$$

Step 3: solve the coefficients. The term $(1-\beta)x_k u_k$ changes sign with $x_k u_k$ unless its coefficient is zero, so we require $\beta = 1$. Then the remaining term $\left(\frac{1}{2}-\gamma\right)u_k^2 \le 0$ for all $u_k$ requires $\gamma \ge \frac{1}{2}$. The minimal (exactly passive) choice is

$$y_k = x_k + \frac{1}{2}u_k,$$

for which $u_k y_k = x_k u_k + \frac{1}{2}u_k^2 = V(x_{k+1}) - V(x_k)$ identically: the supply exactly equals the stored-energy change.

Numerical verification. Take $x_0 = 0$, $u_0 = 0.1$. Then $x_1 = 0 + 0.1 = 0.1$; $V(x_1) = \frac{1}{2}(0.1)^2 = 0.005$; $V(x_0) = 0$; so $\Delta V = 0.005 - 0 = 0.005$. The modified output is $y_0 = 0 + \frac{1}{2}(0.1) = 0.05$, and the supply is $u_0 y_0 = 0.1 \times 0.05 = 0.005$. Supply equals storage change exactly, confirming exact passivity.

#4.2 Passivity of the leaky integrator

Setup. Dynamics $x_{k+1} = (1-\alpha)x_k + u_k$ with leakage $\alpha \in [0,1]$; storage $V(x) = \frac{1}{2}x^2$; candidate output $y_k = \beta x_k + \gamma u_k$.

Step 1: expand the storage change.

$$V(x_{k+1}) - V(x_k) = \frac{1}{2}\left[(1-\alpha)x_k + u_k\right]^2 - \frac{1}{2}x_k^2.$$

Expanding the square: $(1-\alpha)^2 x_k^2 + 2(1-\alpha)x_k u_k + u_k^2$. Since $(1-\alpha)^2 - 1 = -2\alpha + \alpha^2$, we obtain

$$V(x_{k+1}) - V(x_k) = \left(-\alpha + \frac{\alpha^2}{2}\right)x_k^2 + (1-\alpha)\,x_k u_k + \frac{1}{2}u_k^2.$$

Step 2: subtract the supply. The passivity margin is

$$V(x_{k+1}) - V(x_k) - u_k y_k = \left(-\alpha + \frac{\alpha^2}{2}\right)x_k^2 + \left(1 - \alpha - \beta\right)x_k u_k + \left(\frac{1}{2}-\gamma\right)u_k^2.$$

Step 3: choose the output coefficients. The binary form $a x_k^2 + b\, x_k u_k$ with $b \ne 0$ is indefinite, so we require $b = 0$, i.e.

$$\beta = 1 - \alpha.$$

Then the $x_k^2$ coefficient is $-\alpha + \frac{\alpha^2}{2}$, which is strictly negative for all $\alpha \in (0,1]$ (at $\alpha = 0$ it vanishes and the passivity is exact rather than strict). Setting $\gamma = \frac{1}{2}$ kills the $u_k^2$ term. The passive output is therefore

$$y_k = (1-\alpha)\,x_k + \frac{1}{2}u_k,$$

with dissipation inequality

$$V(x_{k+1}) - V(x_k) \le u_k y_k - \delta\,x_k^2, \qquad \delta = \alpha - \frac{\alpha^2}{2} \;\gt \; 0 \quad \text{for } \alpha \in (0,1].$$

Numerical verification with $\alpha = 0.1$. Then $\beta = 1 - 0.1 = 0.9$, $\gamma = 0.5$, and the $x_k^2$ coefficient is $\frac{\alpha^2}{2} - \alpha = \frac{0.01}{2} - 0.1 = 0.005 - 0.1 = -0.095$, i.e. the margin is $-0.095\,x_k^2 \le 0$ for all $x_k$.

Concrete check, zero supply: take $x_0 = 2$, $u_0 = 0$. Then $x_1 = (1-0.1)\times 2 + 0 = 1.8$. Stored energies: $V(x_0) = \frac{1}{2}\times 4 = 2$; $V(x_1) = \frac{1}{2}\times 3.24 = 1.62$. So $\Delta V = 1.62 - 2 = -0.38$. The formula predicts $\left(\frac{\alpha^2}{2}-\alpha\right)x_0^2 = -0.095 \times 4 = -0.38$. Exact match.

Concrete check with supply: take $x_0 = 2$, $u_0 = 0.5$. Then $x_1 = 0.9 \times 2 + 0.5 = 2.3$; $V(x_1) = \frac{1}{2}\times 5.29 = 2.645$; $\Delta V = 2.645 - 2 = 0.645$. Output: $y_0 = 0.9 \times 2 + 0.5 \times 0.5 = 2.05$; supply $u_0 y_0 = 0.5 \times 2.05 = 1.025$. Margin: $\Delta V - u_0 y_0 = 0.645 - 1.025 = -0.38$, again equal to $-0.095 \times 2^2 = -0.38$. The dissipation inequality holds with margin $0.38$ at this step.

Counterexample for the naive output. With the unmodified output $y_k = x_k$ (i.e. $\beta = 1$, $\gamma = 0$) and $\alpha = 0.1$, the margin is $-0.095\,x_k^2 - 0.1\,x_k u_k + 0.5\,u_k^2$. At $x_k = 1$, $u_k = -1$: $-0.095 + 0.1 + 0.5 = 0.505 \gt 0$: passivity fails. This is a substantive finding: the leaky Signal is passive only under the corrected output map $y_k = (1-\alpha)x_k + \frac{1}{2}u_k$, not under the naive state-as-output choice.

#4.3 Quantization degradation bound

Assumptions (stated explicitly). (i) The Signal output is quantized with uniform resolution $q = 0.1$, so the applied output satisfies $|y_k - y_k^{q}| \le \frac{q}{2} = 0.05$. (ii) The Worker-side supply actually delivered is $u_k y_k^{q}$ instead of $u_k y_k$. (iii) The input magnitude is bounded, $|u_k| \le U_{\max} = 1$ (assumption). (iv) Horizon $N = 100$ steps.

Derivation. The per-step supply error is

$$|u_k y_k - u_k y_k^{q}| = |u_k|\,|y_k - y_k^{q}| \le U_{\max}\cdot\frac{q}{2} = 1 \times 0.05 = 0.05.$$

Over the horizon, the worst-case cumulative passivity degradation is

$$\Delta_{\text{quant}} \le \sum_{k=0}^{N-1} 0.05 = N \times 0.05 = 100 \times 0.05 = 5.0.$$

Interpretation. The leaky Signal of Section 4.2 dissipates at rate $\delta = \alpha - \frac{\alpha^2}{2} = 0.1 - 0.005 = 0.095$ per unit $x_k^2$; whether the quantization budget of $5.0$ energy units over $100$ steps is tolerable depends on the state magnitudes involved, which the corpus does not specify. The bound is structural: no passive quantized Signal can promise a tighter passivity inequality than this budget allows under the stated assumptions.

#4.4 Illustrative example: delay margin, energy cost, attractor radius, robustness budget

All parameters in this subsection are illustrative parameters chosen for the worked example, stated explicitly; every derived number follows from them by shown arithmetic. No number below is an empirical measurement.

Input list. $k_S = 2.0$ (static gain of the Signal's dissipative path, chosen); $\epsilon_S = 0.1$ (Signal passivity margin, chosen); $\epsilon_W = 0.2$ (Worker passivity margin, chosen); $T_d = 0.5\ \mathrm{s}$ (transport delay of the delocalized channel, chosen); $\omega_c = 1.0\ \mathrm{rad\,s^{-1}}$ (loop crossover frequency, chosen); $\Delta = 0.05$ (uniform quantization step, chosen); $u_{\max} = 1.0$ (norm bound, chosen); $\lambda_W = 0.5\ \mathrm{s^{-1}}$ (Worker contraction constant, chosen).

Delay margin. A pure delay $T_d$ contributes phase lag $\phi_d(\omega) = \omega T_d$ at frequency $\omega$. At $\omega = \omega_c$:

$$\phi_d(\omega_c) = (1.0\ \mathrm{rad\,s^{-1}})(0.5\ \mathrm{s}) = 0.5\ \mathrm{rad} = 0.5 \times \frac{180}{\pi} \approx 0.5 \times 57.29578 \approx 28.65^{\circ}.$$

The combined dissipative margin proxy is $M = k_S(\epsilon_S + \epsilon_W) = 2.0 \times (0.1 + 0.2) = 0.6$. The normalized delay loss is $\ell_d = \phi_d(\omega_c)/(2\pi) = 0.5/(2\pi) \approx 0.0796$; the normalized margin is $M_n = M/(1+M) = 0.6/1.6 = 0.375$. Since $M_n = 0.375 \gt \ell_d \approx 0.0796$, the illustrative margin condition is satisfied with ratio $\rho = M_n/\ell_d = 0.375/0.0796 \approx 4.71$. This margin proxy is a heuristic consistent with the loop-passivity guarantee pattern of [2], not a sigma-stability certificate.

Quantization energy cost. With quantization step $\Delta$ and input norm bounded by $u_{\max}$, the worst-case excess energy per delivered packet attributable to quantization is $E_q \le (\Delta/2)u_{\max} = (0.05/2)(1.0) = 0.025\ \mathrm{J}$. The nominal per-packet supply at full magnitude is $E_0 = u_{\max}^2 = 1.0\ \mathrm{J}$ (conservative bound with unit feedthrough). The relative overhead is $E_q/E_0 = 0.025/1.0 = 2.5\%$.

Attractor radius. If the Worker's closed-loop contraction rate toward the attractor is at least $\lambda_W$ per unit input error, and the input error is bounded by $\Delta/2$, the guaranteed attractor radius contribution is $r_q = (\Delta/2)/\lambda_W = 0.025/0.5 = 0.05$ in normalized Worker units, in the UGAS-of-attractor sense of [3]. No passive quantized Signal can promise convergence to a point from quantization alone.

Robustness budget. Following the nominal-plus-error structure of [7], let the uncertain LTV deviation have norm bound $\delta$ on the Signal's passivity margin: $\epsilon_S^{\text{actual}} = \epsilon_S - \delta$. Passivity of the Signal block is retained iff $\delta \lt \epsilon_S = 0.1$. As a fraction of the combined margin $M = 0.6$, this is $\delta/M = 0.1/0.6 \approx 0.1667$, i.e., the Signal can tolerate erosion of up to about $16.7\%$ of the combined loop margin before its own passivity fails.

#5. Results

All results below are the direct outputs of Section 4's derivations from the stated inputs and illustrative parameters; none are empirical.

  • R1 (integrator passivity). The pure integrator is exactly passive under the modified output $y_k = x_k + \frac{1}{2}u_k$; supply equals storage change identically (verified numerically in Section 4.1).
  • R2 (leaky integrator passivity). The leaky integrator is strictly passive for $\alpha \in (0,1]$ under $y_k = (1-\alpha)x_k + \frac{1}{2}u_k$ with dissipation rate $\delta = \alpha - \alpha^2/2 \gt 0$ (exactly passive at $\alpha = 0$); for $\alpha = 0.1$ the margin is $-0.095\,x_k^2$, verified exactly at two test points. Under the naive output $y_k = x_k$, passivity fails (counterexample with margin $+0.505$).
  • R3 (quantization budget). Under resolution $q = 0.1$, $|u_k| \le 1$, horizon $N = 100$: worst-case cumulative passivity degradation $\Delta_{\text{quant}} = 5.0$ energy units.
  • R4 (delay margin, illustrative). With the chosen parameters: delay phase lag $0.5\ \mathrm{rad} \approx 28.65^{\circ}$; normalized margin $M_n = 0.375$ against normalized delay loss $\ell_d \approx 0.0796$; safety ratio $\rho \approx 4.71$.
  • R5 (quantization energy cost, illustrative). $E_q = 0.025\ \mathrm{J}$ per packet, i.e., $2.5\%$ of the nominal per-packet supply $E_0 = 1.0\ \mathrm{J}$.
  • R6 (attractor radius, illustrative). $r_q = 0.05$ in normalized Worker units.
  • R7 (robustness budget, illustrative). Margin erosion tolerance $\delta \lt 0.1$, i.e., about $16.7\%$ of the combined loop margin $M = 0.6$.
  • R8 (quantum admissibility). Per [5], under a classical LTI Signal layer and a bipartite Gaussian Worker initialized in a Gaussian state, both steady-state and finite-time entanglement generation are infeasible; the quantum reading of "Signal performs work via entanglement" is falsified in that regime. No claim is made for nonclassical or nonlinear Signal layers.

Projection (labeled as such). If a future revision of the re-entry document (DOI 10.5281/zenodo.18515457) specifies its own parameters, the formulas of Sections 4.3–4.4 apply unchanged; we project that the qualitative conclusions (exact integrator passivity under the corrected output, failure under the naive output, positive margin ratio, percent-level quantization cost, nonzero attractor radius) are robust to any parameter choice satisfying $\epsilon_S, \epsilon_W \gt 0$ and $M_n \gt \ell_d$; the quantitative values are example-specific and carry no uncertainty bound beyond the exact arithmetic shown, since they are definitions of the chosen example rather than measurements.

#6. Discussion

What the framing buys. Restating "the Signal" as a passive control element converts the corpus's ontological claim into a checkable dissipation inequality, and connects it to design templates where passivity is enforced by construction [1], preserved across delocalized transport channels [2], and compatible with quantized sampled delivery [3]. The derivations show the framing is not vacuous: it produces concrete, arithmetic-checkable quantities (R1–R7).

Limitations and failure modes. First, the corpus documents supplied contain no dynamical equations, so the candidate Signal dynamics of Section 3.2 are postulated, not derived; every number in Section 4.4 derives from illustrative parameters we chose, and the paper establishes the form of the passivity claim, not its realization in any physical or corpus-internal system. 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. Third, the attractor-radius result R6 assumes a linear contraction constant $\lambda_W$; for nonlinear Workers the radius bound does not transfer. Fourth, the barrier-style safety wrapper inherits exactly the fragility [6] identifies: parametric uncertainty invalidates the guarantees, and the robust fallback trades performance for safety. Fifth, the nominal-error decomposition of [7] presumes norm-bounded disturbances; heavy-tailed or structural model error escapes the budget R7. Sixth, the quantization budget R3 scales linearly with the horizon and the input bound; unbounded inputs or longer horizons dissolve it.

What would falsify the claims. The central claim — that the Signal-Worker ontology is consistently expressible as a passivity property — would be falsified by a demonstration that no storage function $V_S$ satisfying the dissipation inequality exists for the corpus's intended Signal dynamics, e.g., if the corpus specifies dynamics whose supply term is sign-indefinite in a way no output map can repair. Conversely, if the corpus specifies Signal dynamics and a storage function is found satisfying the inequality, the hypothesis is confirmed at the block-diagram level. The quantum reading is already bounded: per [5], a classical LTI Signal cannot generate entanglement at a Gaussian interface, so any corpus claim of classical-signal-mediated quantum work in that regime is falsified as stated.

Open questions. (1) What are the corpus's actual Signal dynamics, and do they admit a quadratic storage function? (2) Can passivity constraints be encoded directly into the binary optimization formulations that [8] indicates quantum algorithms can address? (3) How might composite adaptive control barrier functions [6] be reconciled with passive Signal architectures to ensure safety despite parametric uncertainty? (4) Can the sigma-stability insights of [2] be combined with data-driven tuning of the type in [1] for large-scale networked passive Signals?

#7. Conclusion

We have formalized the QNFO re-entry question — can the Signal function as a passive control system? — as a discrete-time dissipation inequality. We derived exactly the output transformations under which pure and leaky integrator Signals are passive, verified the results numerically with fully shown arithmetic, bounded the passivity degradation due to output quantization, and provided a labeled illustrative example quantifying delay margin, quantization energy cost, attractor radius, and robustness budget. The Signal-as-passive-controller hypothesis is well-posed and internally consistent at the level of abstract block diagrams, but the supplied corpus material contains no dynamical equations, so no physical validation is possible from the provided material alone.

#References

[1] Passive iFIR Filters for Data-Driven Control. arXiv:2403.06640v2. https://arxiv.org/abs/2403.06640v2 [2] Passivity-based PI control of first-order systems with I/O communication delays: A complete sigma-stability analysis. arXiv:1507.01146v1. https://arxiv.org/abs/1507.01146v1 [3] Sampled-data control design for systems with quantized actuators. arXiv:2208.05694v3. https://arxiv.org/abs/2208.05694v3 [4] Bringing Quantum Systems under Control: A Tutorial Invitation to Quantum Computing and Its Relation to Bilinear Control Systems. arXiv:2412.00736v1. https://arxiv.org/abs/2412.00736v1 [5] On the infeasibility of entanglement generation in Gaussian quantum systems via classical control. arXiv:1107.3174v1. https://arxiv.org/abs/1107.3174v1 [6] Composite Adaptive Control Barrier Functions for Safety-Critical Systems with Parametric Uncertainty. arXiv:2601.17683v3. https://arxiv.org/abs/2601.17683v3 [7] Robust Nonlinear Optimal Control via System Level Synthesis. arXiv:2301.04943v3. https://arxiv.org/abs/2301.04943v3 [8] Using quantum computers in control: interval matrix properties. arXiv:2403.17711v1. https://arxiv.org/abs/2403.17711v1 [9] DOI 10.5281/zenodo.18441401. QNFO: Structural vs Driven Quantum Coherence. [10] DOI 10.5281/zenodo.21974194. QNFO: Signal-Worker Boundary Confinement: A Corrected Ontology of Surface vs Bulk Transport.

New papers by email

One short weekly digest: titles and links. No tracking; unsubscribe any time.

Cite this paper