Sheaves and functions
Statement and proof
Trace formalism
Run and audit
Agents
Satake comparison ↗
197 M tokens≈ $106
Tokens used to make these pages
Table 1. Page production by session
tokens US $
This conversation: the search, the audits, the pages and the trace formalism19:56–02:11 UTC 197 M $106
Of this, the search itself (root session and agents, 20:23–23:41 UTC) used 153 M tokens ≈ $84.
Input, cache and output tokens of every call, agents included, priced per model. List prices per million tokens (Opus 5.5: $4 in, $5/$8 cache write 5 min/1 h, $0.20 cache read, $20 out; Fable 5.1: $10 in, $12.50/$20 cache write, $0.25 cache read, $50 out), as reported on 2026-10-17; agent output is estimated from visible text, so the dollar figure is an estimate. Counted 2026-10-17 23:44 UTC.

Agent X3 · Frobenius exchange of maximal-torus cocharacter summands

The false rank equality in A4-1 is replaced by rank invariants <= rk H < 2 rk H. No split maximal torus exists; the unitary setup profile and counterexample input A4-12 survive, with purity restricted to stable labels and with split (R),(C) outside the conclusion's scope.