{"path":"research/catching-a-proposal-made-unnecessary/cases-negatives/AF1.md","content":"*About: That a general rule a machine writes for an inference starts no wider than its links, and widens or narrows by evidence.* **For a step from a general statement and a case, the general sentence a machine writes is a guess that a group of links prompts: it starts no wider than those links, widens as far as a stated mechanism reaches, and narrows at each case that breaks it; a sentence drafted under one link is a draft that nothing hangs on.** *Revised the same day after the founder's questions* (*\"There are many intermediate reasoning steps in that link chain, no?\"* · *\"I feel like there's a clear place here for mechanistic evidence about WHY decomposition occurs\"*). The first wording read the rule off its cases (*the narrowest that covers them*), where the corpus holds that cases prompt a guess and test it; and it spoke of all links, where 206 of the 443 links under the four shapes have this shape. A step from a sign, like his squirrel, has no width to set: what is written is the law from the thing to its sign and what else would produce the sign, and a mechanism answers both. The contrast with Mathlib stands: a prover makes width safe there; here a mechanism is the nearest licence for width, and a case that breaks the rule, found in a text or brought by a person, is the nearest check. The order of work is Proof-Refactor's (arXiv:2606.03743, read in part): cut each fragment in its own terms, group, then word one helper per group with the stored statements on the table. Grouping is a judgement of likeness, which a machine gives as everyone's average, so a group says in what respect its links are alike. Each wording stays on the page when a wider or a narrower one is added. Sharpens AD10, AD18, AD25 and AD27, and meets Q8's stream for mechanistic evidence. (§ 4.6, § 6b) **Meets:** extends J5; depends on T1, principle:contributions-are-added-never-overwritten, principle:never-ask-a-mind-to **Outside reader:** extends principle:machine-work-is-judged-by (\"narrows at each case that breaks it\" against \"does the output give a reader MORE places to disagree, or fewer\"); repeats principle:propose-never-assert (\"the general sentence a machine writes is a guess\" against \"Propose, never assert\").\n"}