arXiv subjects

Francisco M. Arrabal-Campos

Publications and source records attributed to Francisco M. Arrabal-Campos.

6 recordsLinked to original sources

arXiv2026

Can a Dynamic Internal Field Govern a Transformer's Cognition? Certifiability, not Superiority, in Homeostatic Compute Control

An intelligent system does not merely reason: it governs its own reasoning - how much to compute, when to stop, which module to activate. Can that role be played by a dynamic internal field - a low-dimensional homeostatic state with explicit physics and certified stability - that modulates cognition without performing it? Ours is a field on the module graph governed by a family of PDEs on the graph Laplacian, advancing with an adaptive-depth reasoner. We certify the stability of the integrator of the whole family - an integrator certificate, not a closed-loop one. New, and proved here: a discrete Schur-Cohn criterion for Verlet with velocity coupling, necessary and sufficient per latent root, with no commutation hypothesis. The answer is threefold: substance no, structure only in part, certifiability yes. The type of the field's physics is irrelevant for accuracy: wave, diffusion, gated mixtures and a 2D Navier-Stokes substrate tie. A twenty-seed preregistered deconfounding campaign bounds the structural claim: at equalized caps the second-order effect is strong in one family (+0.087 [+0.042, +0.132], t=4.0) but is not detected in the other (+0.014 [-0.013, +0.040], n.s.), so part of the original contrast was capacity, not order; and a matched-interface GRU is indistinguishable in the first and nominally exceeds the field in the second (-0.035 [-0.067, -0.002]). What distinguishes the field is not capability but that its one-step operator admits an exact runtime stability check - a difference of kind, not of existence: learned recurrences carry certificates too, sufficient and conservative ones. A kill-gate with a positive control finds no evidence for the field as evidence accumulator (Delta AUC +0.0007 [-0.0065, +0.0079] vs a 0.03 threshold). A dynamic internal field is a viable, certifiable compute governor, but not an enhancer of cognition: it modulates, it does not think.

cs.AI↗

arXiv2026

Where Cognition Lives: Dissecting Emergent from Computed Function in a Minimal Complete Cognitive Architecture

A cognitive architecture is more than the module that reasons: it must also decide how long to think and what deserves the effort. We built a minimal but complete system - a recurrent reasoner with adaptive halting, a homeostatic control field, and a value module - and asked of each part: does this function emerge from gradient descent, or must it be computed? Competence emerges. Stopping appears to emerge too, and to be worth more than everything decidable in advance, but that appearance is instrumentation: payoff at matched mean compute climbs from 0.467 (uniform) through 0.546 (difficulty) to 0.698 (ex-ante value), and the further climb to 0.921 (posterior self-observation) does not survive audit. PonderNet-style halting returns a halting-weighted mixture of hidden states while forced-depth baselines return one, and the language head is trained on the mixture alone; equalizing the readout annihilates the apparent advantage of native execution (residual +0.000 [0.000, 0.000]). Value does not emerge: trained couplings capture zero of a payoff an explicit allocator captures completely (+0.151, routing correlation +0.79), so the second-order decisions that pay must be computed, at least where value is orthogonal to content, as here by construction. On a frozen LLM actuator the same instruments show self-consistency voting to be a measured bound (+0.0236 [+0.0150, +0.0326]) and inter-sample agreement nearly worthless as a stopping signal, its mass concentrating on wrong answers. Every null we assert carries a mechanism and a positive control, and the protocol is part of the contribution. Executing our own falsifiable prediction, value under commitment pays +0.1312 [+0.1124, +0.1502] in a cliff-cost family, some seven times the smooth-family estimate - not because the cliff shifts information ex ante, but because it multiplies the attainable range fivefold (5.1x [3.4, 8.2]).

cs.AI↗

arXiv2026

Geometric Time-Domain Identification of Three-Phase Load Equivalents from Terminal Measurements

This paper presents a geometric time-domain method for identifying three-phase load equivalents from instantaneous voltage and current measurements at the point of common coupling. Measured waveforms are interpreted as trajectories in Euclidean signal spaces, and load-equivalent parameters are recovered from the geometry of those trajectories. The method extends a previously published single-phase geometric identification formulation to three- and four-wire systems and places special emphasis on the three-wire case, where no neutral voltage is measured and the terminal data must satisfy coupled Kirchhoff constraints. The main advance over the earlier analytical formulation is a sampled-data implementation based on local time windows, normalized matrix equations, harmonic-projection derivative and primitive coordinates, explicit geometric identifiability tests, passivity constraints, and energy/Kirchhoff residuals. The method does not force a model when the measured trajectory lacks enough information; instead, it reports low-rank or ill-conditioned windows as low-confidence evidence. Numerical simulations with clean data, measurement noise, window-length sweeps, and sensor delay show that the method accurately identifies informative three-phase trajectories and exposes structurally degenerate cases such as pure single-frequency excitation for higher-order three-wire models. For a given admissible topology the identified circuit closes the instantaneous terminal energy balance of the measured load over the analysis window.

eess.SP↗

arXiv2026

Branch-Level Energy Localization in Three-Phase Loads: Resolving Indeterminacy in Time-Domain

This paper develops a branch-level energy-localization framework for three-phase loads. The instantaneous terminal power of an admissible lumped equivalent is decomposed uniquely as Joule dissipation plus magnetic and electric stored-energy rates, branch by branch. Three formal results are established: a Branch-Level Localization Theorem (uniqueness given an admissible topology); a Topology-Indeterminacy Theorem (multiple admissible topologies reproduce identical terminal data with distinct localizations); and a Generalized Energetic Duality Theorem that organizes classical electrical dualities (Norton-Thevenin, series--parallel, L vs C, R vs G) as restrictions to Linear Time Invariant (LTI) sinusoidal regimes of a single time-domain principle in which constant-parameter equivalence is replaced by time-varying parameters. The framework is exercised on six test cases including the de Leon--Cohen open-phase paradox, switched-resistive loads, three-wire delta-versus-wye-virtual indeterminacy, fluctuating-phase loads, and a four-wire nonlinear load with hysteretic, linear, and switched branches. The framework is positioned as complementary to IEEE Std. 1459, CPC, instantaneous p-q, and Fryze-Buchholz-Depenbrock: each answers a different question, and the apparent paradoxes vanish once the question is posed precisely.

eess.SP↗

arXiv2025

Experimental Verification of a Time-Domain Load Identification Method for Single-Phase Circuits

This paper presents experimental validation of a time-domain load parameter determination method for single-phase circuits. The verification is performed in a state-of-the-art smart grid laboratory equipped with power hardware and real-time emulators. The proposed method enables the identification of circuit parameters using only instantaneous voltage and current measurements at the point of common coupling. The experimental setup includes a range of test cases covering linear and non-sinusoidal single-phase conditions. Voltage and current waveforms are acquired, preprocessed, and used to calculate the relevant circuit parameters. The experimental results demonstrate a high degree of accuracy and robustness, with minimal percentage errors across all test cases. The identified parameters show excellent agreement with the theoretical expectations, confirming the validity and applicability of the proposed method to identify the load of single-phase systems. This validation highlights the potential of the method for improved monitoring, control, and protection of smart grids, paving the way for future extensions to three-phase systems and real-time implementations.

eess.SY↗

arXiv2020

How to overcome the limitations of p-q Theory: Geometric Algebra Power Theory to the rescue

This paper investigates the recent advances in Geometric Algebra-based power theory (GAPoT) and how this tool provides new insights to solve the flaws of one of the most widespread theory in the time domain, the Instantaneous Reactive Power theory (IRP) and its further enhancements. GAPoT can be applied to single-phase and multi-phase systems to obtain an optimal current decomposition under any distorted voltage source supply and load condition. This could be the case in microgrids or smart grids. Moreover, it is possible to define different strategies based on instantaneous or averaged quantities depending on whether the voltage supply conditions are sinusoidal and symmetrical or not. Several examples illustrate how GAPoT is able to overcome the limitations of IRP theory.

eess.SY↗