Noise‑Modulated Near‑Critical Cascades: Measurement, Calibration, and Neuro‑Symbolic Integration in a Backpropagation‑Free Spiking Framework

Backpropagation‑free neural systems promise low‑power, locally‑adaptive computation, but two obstacles keep them from being assessed as scientific objects rather than engineering claims. First, the standard evidence for criticality in spiking networks — neuronal avalanche size distributions — is measured with a segmentation convention ("silence between avalanches") that is not well defined when the network is persistently active. Second, connecting a noisy perceptual channel to an exact symbolic verifier requires knowing when not to trust the perception, which is a calibration problem, not an architecture problem. Here we report a single‑CPU framework built around a 10,000‑neuron leaky integrate‑and‑fire network whose learning rules are exclusively local (STDP, threshold homeostasis, delta rules, Forward‑Forward, Tsodyks–Markram synaptic depression), coupled to an exact symbolic verifier and a confidence‑calibration layer. We show that the silence‑based avalanche exponent swings between 3.55 and 1.58 under an arbitrary one‑step change of the segmentation gap, and that under high background activity the same criterion finds almost no causal cascades at all. We then define a parameter‑free causal criterion for whether a spike is synapse‑driven, using the exact membrane‑potential identity v−i_syn < θ, and calibrate the instrument against synthetic ground truth (reconstruction bias Δα=0.29‑0.34), block‑shuffle null models (linkage separation 3.9x) and seed replicates (0.04). Re‑measuring the network with the calibrated instrument shows that near‑critical avalanche exponents occupy a ridge in the (membrane noise, background seed rate) plane rather than a point: a sharp peak (corrected α≈1.77‑1.82) at seed rate 8.0 and noise σ≈0.6 mV, and a plateau (1.46‑1.55) at seed rate 2.0. The regime is noise‑modulated and near‑critical, not self‑organized critical. In parallel capability measurements, a Forward‑Forward encoder reaches 92.1% on MNIST against an 84.3% linear baseline, but null‑model repricing shows that only +1.0 percentage points are attributable to learning rather than architecture; the trained encoder compresses causal necessity 8–36×; Platt‑calibrated confidence reaches ECE 0.013 and transfers to the live system within 0.35 percentage points; and a calibrated neuro‑symbolic gateway reduces shock events 11.1× relative to always‑answer while using fewer verifier calls (266 vs 400) and opening more gates (746 vs 400) than always‑verify. We report these results, and the failures that shaped them, as a case study in measurement‑first systems neuroscience.