Research 140, 027's stage 3 measured: a board of columns of cards of tags (aup's stored_nested) alike in memory and on a store restarting eight times, every step's fault, states and a view (2,400 snapshots, 54 restarts); killed at the tree's four stages and the log's two, all or nothing; replacement moving nested lists by name at depth; appending into a stored item's list costs about 170 ns an item it already holds (append_cost.c: 42 µs an add on average over the first 500, 738 µs over 8,000), building one by appends quadratic; instruction counts: the first commit's BFS +1.45% with batches and +1.68% without, from branches in the hot steps, gone with the load's internal ops (b29 against b27: BFS 0.000%/+0.034%, the others within 0.008%; the bank's queries -0.25% to +0.22%); what remains (a message's rows holding lists, a list field's .count in a fold, for over xs[i].f); 027's stage 3 as made (the representation chosen against the plan, its cost); 008's wording (kind 5 in images' headers alone); CHECKPOINT's direction row through stage 3

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diff --git a/research/experiments/044-specs/2026-10-18-stage3-append.jsonl b/research/experiments/044-specs/2026-10-18-stage3-append.jsonl
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+{"cards":500,"ns_per_add_so_far":42451}
+{"cards":1000,"ns_per_add_so_far":84048}
+{"cards":2000,"ns_per_add_so_far":170537}
+{"cards":4000,"ns_per_add_so_far":348505}
+{"cards":8000,"ns_per_add_so_far":738448}