Telescoping Network Reinstatement in Self-Aware Networks: Dendritic Three-Dimensional Memory, Oscillatory Winner-Take-Most Selection, and NAPOT Reconstruction

This paper develops a Self-Aware Networks (SAN) hypothesis about how a learned state in one dendritic arbor can help regenerate a much larger three-dimensional perceptual or mnemonic configuration. The proposal combines nonlinear dendritic pattern recognition, oscillatory winner-take-most competition, recurrent excitation and inhibition, and Neural Array Projection Oscillation Tomography (NAPOT). During learning, a distributed event changes synapses, dendritic compartments, cellular excitability, and circuit relationships. In the stronger SAN interpretation, a dendritic arrangement can store a three-dimensional relational projection of the network neighborhood that surrounded the neuron during the event. During retrieval, a partial cue activates that learned disposition. Prepared neurons or assemblies reach threshold earlier during an oscillatory opportunity window, recruit local inhibitory circuitry, and bias which sparse population survives the cycle. Their outputs then propagate through recurrent and long-range pathways, regenerating an approximation of the earlier three-dimensional state while incorporating current sensory, bodily, and action context. "Storage of a 3D image" is used here in a physically testable sense. The dendrite may store a structured projection, basis component, or addressable transformation capable of contributing to reconstruction; it need not contain a voxel-for-voxel miniature watched by an inner observer. The experienced image is the distributed network's active observer-action state. The model extends, but is not identical to, Hierarchical Temporal Memory (HTM), sparse distributed representations (SDRs), hippocampal pattern completion, or gamma-cycle competition. For a declared finite-dimensional scene family, a full-column-rank dendritic measurement operator gives exact noiseless reconstruction and a norm bound under additive noise. A deterministic fixture reconstructed a 1,728-voxel structured volume from 24 measurements over a six-dimensional basis with relative error 9.71e-16, satisfied its noise bound, and selected the correct stored perspective. A second deterministic fixture learned the 24-by-6 forward operator from 2,400 noisy examples and reconstructed 384 held-out scenes through a stable excitatory-minus-inhibitory recurrence without a pseudoinverse at inference. Its median relative error was 0.0561, compared with 0.6563 after one iteration and 1.4075 after measurement-scene pairing was shuffled. A third fixture imposed nonnegative excitatory outputs, subtractive inhibitory outputs, bounded states, delayed conductance-style recurrence, projected local updates, and a frozen multi-condition support rule. It reached median error 0.4915 and prototype accuracy 0.8594, but did not improve accuracy over matched feedforward inference and did not meet the required error advantage over the no-inhibition ablation. A signed ridge comparator was also better (median error 0.3745; accuracy 0.9938). The primary constrained-recurrence hypothesis was therefore not supported. A separately frozen 12-seed sensitivity audit produced zero full primary passes: no seed met the required accuracy gain over feedforward or error gain over no inhibition, while every seed beat shuffled pairing and retained sign/state integrity. The constrained fixture uses supervised target-code errors, evaluates new noisy samples from the same eight prototype family, reconstructs six latent coordinates rather than a learned voxel volume, and computes prototype accuracy through an external nearest-prototype decoder. These are constructive sufficiency and pipeline results for the declared models, not evidence that biological dendrites use the mechanism. Alternative models and multiscale perturbation-and-rescue tests are provided.