The Write Window in Embodied Multimodal Memory: An Access Structure Is a Pair, and Capability Is a Product

Memory architectures for embodied multimodal agents differ in how they index, compress and retrieve, and agree silently on what they write: a description of one frame. We make the write window an architectural parameter, formalise an access structure as a pair (a write map over a window of observations and an address algebra over its records, no address richer than the write it runs over), and read capability for conjunctive queries as a product of an identity, an ordinal and a percept factor, so that which component binds is simply which factor is smallest. Two walls follow. The predicates a frame-local write can decide are closed under time reversal, so no reversal-paired verb (put against take, open against close) is writable at any state budget, and any direction a single frame supports is bounded by the majority prior. And an address that indexes by count compounds per-occurrence detector error, so a later occurrence resolves with a probability that falls geometrically in its rank. Both are measured on the ground-truth locator frames of eight EPIC-KITCHENS streams: the standard single-frame write names the verb barely more often than not, and its error mass sits exactly on the reversal pairs. AXIS widens the window to an ordered pair, differences per-object statuses into events, retains every occurrence with its witness, and executes addresses rather than searching by similarity. The registered controls then refuse the obvious reading: the pair's gain is attributable to the prompt's enumerated verb list rather than to the window, since the same frame attached twice gains as much, and direction under every listed rule sits at or below the majority prior. What does escape the prior is a property of the pair's spacing rather than of the pair (one backbone reads direction above the prior when the two frames are a second apart under a free-vocabulary prompt and not when they are one action apart), and an independent public benchmark agrees at the same spacing with the read held fixed. Behind the window the ordinal wall binds: occurrences are detected at a recall and precision no scaffold-side filter improves. Replacing the written ledger by one built from the corpus's own annotations, everything else held fixed, roughly doubles the same loop and lets the address reach its target far more often, which locates the entire end-to-end loss on the write rather than the read. Of the registered predictions, those about the measurement held and those about the write side and the end-to-end result failed; we report all of them and relocate the binding wall to detector reliability at a spacing the detector can actually read.