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]).
F. Arrabal-Campos, Francisco G. Montoya, A. Alcayde et al.· 1 citation
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.
F. Arrabal-Campos, Ignacio Fernández, Francisco G. Montoya et al.· 1 citation
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
