Self-Cleaning and Captured Anyway: One Measured Primitive for Error in a Store an Agent Writes to Itself, and What a Falling Score Actually Measures

"An agent that writes its conclusions into a store it later retrieves from closes a loop usually reported as one-way contamination. Taking the loop to the infinite-tenure limit against an append-only store gives a different picture: because writing never deletes, the reachable state space has a hard upper edge at (n-1)/n, so the outcome is a choice between two edges rather than a decay. At f0 = 0.9 the interval between the two modes holds 3.6% of 220 runs where a uniform spread would put 20.6%, and is strictly empty on the first 15; the pooled mean describes 8.2% of the runs it summarises, the median 68.2%. Everything the model contributes is carried by one measured primitive with no fitted parameter, the copy function γ(φ): on 36 Wikidata facts, sign(hatγ - γcrit), with γcrit = 1/k at r = 0, w = 1, predicts the direction of drift on 353 of 360 real-fact runs (39 of 40 synthetic in the same batch). Scale does not rescue the store: pooled frontier capture is 0.850, with claude-sonnet-4.5 captured on 20 of 20 seeds against our registered prediction of <0.5. What the interval tests is distinguishability rather than count: on the real facts, multi-valued runs have 6.4x its occupancy of the rest. It survives at f0 in 0.1, 0.3, 0.5, capture peaks at f0 = 0.5, and of four interventions with criteria frozen first, timing dominates fraction at matched budget while a consistency gate drives every model to 0.993. The resampling unit is the seed, at a design effect of 3.75 on a pooled level: under a 44-seed control the ordering supporting claim 4 collapses from Spearman +0.98 at three seeds to +0.31-0.80 at forty-four, while claim 2's ordering is exact there (+1.00, p = 0.017). All 87 graded rows are in Appendix W, 37 of them graded withdrawn, failed, self-correcting, undecidable or an acknowledged limit, against 50 that are not."