Memory Capacity as a Retrieval Limit: Direct Synaptic Measurement Across a Capacity Range in a Sparse Binary Assembly Network

Storage capacity in associative memory is normally treated as a property of the synaptic substrate: patterns superpose until interference makes them unrecoverable. This paper reports a sparse binary assembly network in which that account does not hold over the range where recall fails, established by measuring the synapses directly rather than inferring their state from behaviour. The network has 131,072 neurons and 1.07 × 10⁹ binary synapses with bounded 4-bit counters, contrastive learning and an exact k-winners-take-all readout, and runs on a single consumer GPU. Over the range 24 to 60 stored patterns, at five random seeds per load, the sustained-recall ratio falls by a factor of 3.7 while the functional density of recurrent synapses within stored assemblies remains constant at 80.7–82.2%. The constancy holds separately for neurons exclusive to one assembly (82.7% → 81.2%) and for neurons shared across several (69.3% → 82.1%, rising) while the shared fraction of each assembly grows from 4.8% to 64.4%, so it is not an artifact of averaging over a degrading sub-population. Retrieval initiation is likewise load-invariant in two independent measurements, and at intermediate load recurrent drive is maintained at unity gain while the retrieved population nonetheless drifts away from the stored assembly. The failure mode is identity drift into a structured neighbourhood: neurons visited during free running but outside the target assembly receive within-assembly recurrent input at 6.9× the population baseline at low load, falling to 1.8× at high load as the composition of that neighbourhood shifts from unallocated neurons to neurons belonging to competing assemblies. Because recall depends on how long retrieval is allowed to run, capacity is reported as a pair: sustained capacity ≈ 36 patterns and transient capacity ≈ 200.