The Arrow of Records: Structured Boundary Conditions, Receptive Capacity, and Why History Accumulates Toward the Future

This paper is the ninth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of objects independently existing within spacetime. It completes a triptych on time. The second paper (Uchida, 2026b) gave order: a relativistically invariant causal partial order that needs no clock. The eighth paper (Uchida, 2026h) gave temporal address: a clock indexes correlations but does not orient them. The present paper takes the third question, deferred by design, the arrow - why physical records are systematically formed, retained, and proliferated along one direction of the causal order only. The paper's reframing, and its main correction to a tempting reading, is that the arrow of records is not, in the first instance, the heat released when a record is written. An individual imprinting interaction can be unitary and thermodynamically reversible, and Landauer's principle constrains logically irreversible information loss, not every act of writing or copying (Uchida, 2026f). The asymmetry is instead a fact about an asymmetric resource: at a one-sided boundary of the relevant history there is an abundance of dynamically accessible degrees of freedom whose target-relative correlation capacity is unsaturated; for typical microstates compatible with the adopted boundary measure, evolution into the interior converts this receptive capacity, on net, into retained and dispersed correlations. Within the invertible microscopic setting considered here, the distinctive thesis is a Refined Record-Arrow Principle: such an asymmetric resource is necessary for the systematic formation, stabilization, and proliferation of physical record carriers; individual imprinting may be reversible; practical irreversibility enters at the preparation and reuse of receptive states, uncontrolled correlation dispersal, metastable stabilization, error correction with syndrome disposal and ancillary-state refresh, logically irreversible reset, and finite-resource maintenance; and clocks label the resulting correlations but do not orient their proliferation. Crucially the resource condition is necessary but not sufficient: a causally produced, retained, stabilized trace is a record, but it may be erroneous, and being a veridical record is a separate, event-level matter. The paper is emphatic about its limits. It does not derive the Past Hypothesis; it adopts a structured package of boundary conditions - low entropy, low initial correlation, and an unsaturated-capacity (Receptive-Capacity) boundary condition - as input, each member a boundary-condition hypothesis rather than an established physical result. The status of the paper is L2; it makes no independent empirical prediction.