Afterform: Persistent Interference Geometry for History-Dependent Spectral Audio Processing

Afterform is a real-time spectral audio processing architecture that separates a decaying complex signal state from a persistent, input-written coupling geometry. Input-derived feature increments update unitary SU(2) links in a rhombic interference network; the signal state may subsequently be cleared while the written geometry remains, allowing a fresh signal to encounter propagation conditions determined by earlier input. The architecture is evaluated as a write-persist-read memory channel. Across 5,000 randomly sampled pairs of closed histories, SU(2) commutator magnitude predicts fresh-probe distinguishability (Pearson r = 0.770; Spearman ρ = 0.775), establishing a population-level relationship between non-commutativity and readable temporal-order dependence. Codebook experiments demonstrate 8.807 ± 0.008 bits of recoverable information at M = 512, with no observed saturation. The v3.3 analysis identifies an important finite-sample boundary: with approximately four probe trials per message at M = 512, the empirical message entropy limits the observable plug-in mutual information to approximately 8.79 bits. The measured result is therefore effectively at the sampling ceiling; the small gap from the nominal 9-bit codebook entropy should not be interpreted as channel loss. A persistent writable matrix-FDN baseline achieves near-parity in recoverable information, demonstrating that raw matrix-memory capacity is not unique to Afterform. The architectural distinction instead lies in organizing memory as local, input-written, confinement-preserving coupling geometry with explicit write, clear, hold and erase semantics. Continued writing produces strongly recency-dominated memory. Whole-message recovery falls from 100% with no subsequent write to 17.25% after one distractor history and 2.25% after two. Version 3.3 additionally audits the finite-sample bias of the confusion-matrix mutual-information estimator: with n = 400 trials over a 64 × 64 confusion table, a zero-information decoder produces approximately 3.22 ± 0.03 bits of plug-in MI. Consequently, the apparent nonzero MI at depths ≥ 2 does not support partial retention of older histories; essentially all recoverable information about the earlier history is overwritten after the first subsequent write. Across seven controlled source classes, the relational renderer remains substantially different from a conventional uncoupled resonator bank while remaining much closer to a marginal-matched surrogate. Residual cross-band coherence differences are objectively measurable but small, and perceptual discrimination of that residual remains explicitly open for future blinded listener testing. Real-time engineering tests demonstrate block-partition-independent operation over 32–1024-sample blocks at 44.1, 48 and 96 kHz. Version 1.1 / Research preprint v3.3. This revision resolves the finite-sample mutual-information bias issue identified in v1.0 and strengthens the interpretation of both the forgetting and codebook-scaling experiments without modifying the underlying Afterform DSP architecture. DOI: 10.5281/zenodo.22712783