AI Memory at the Boundary: A Directional-Balance Framework for Weave-Primary Continuance

Artificial memory is usually framed as storage and retrieval: prior information must be preserved in context, cached, summarised, retrieved, or explicitly reintroduced into active computation. This paper develops a complementary geometric hypothesis: some forms of continuity may depend not on stored contents alone, but on the relational pathways through which prior state is reconstructed.

The framework is motivated by a sequence of results in aperiodic projection tilings. Native aperiodic connectivity can act as a passive retention medium; address and weave provide separable channels of persistence; silent relational corruption reveals whether identity-relevant structure survives graph damage; and depth-dependent directional balance explains why boundary regimes produce drift. In Ammann-Beenker and Penrose substrates, paths can nearly close in physical space while failing to close in hidden address space. This residue is not governed by loop area, dwell time, or local step magnitude. It is governed by directional balance: deep positions provide balanced direction sets whose contributions cancel, while boundary positions provide truncated, biased direction sets whose contributions accumulate.

The same results refine the address/weave distinction. Both substrates are weave-primary under native conditions: the live relational topology is the main carrier of identity-relevant structure. The address channel is not the leader but a backup, becoming important when the weave is weakened, corrupted, or pushed into a boundary regime.

We propose that this distinction offers a useful framework for AI memory. Artificial continuance should not be evaluated only by asking what facts are stored, but by asking whether continuity-bearing relational structure can be reconstructed after interruption, compression, perturbation, or context loss. The paper outlines falsifiable diagnostics, including anchor-balance drift assays, selective stabilisation tests, weave-corruption tests, boundary-backup tests, and fossil-versus-ecology evaluations.

Directional balance, relational weave integrity, and independent backup channels may provide measurable conditions under which continuity-bearing representations resist drift without requiring constant active upkeep.

Contact: niedzkatie@gmail.com

GitHub: https://github.com/kekekatie/geometric-impedance/tree/claude/bold-ritchie-l1Mc4