Collects means never larger, and Common declares sixteen more growths

[Rafael-SOWNet]

#746 tier 2's next item is a declared growth for the rules still at Unknown — #1194 showed the
growth ceiling protects only an inverse pair whose directions are declared, so every Unknown is
a pair it cannot see. This is the first set, Common, and the contract change it needed.

What the census found

A probe over the corpus split the 152 Unknown rules into 55 never fired, 28 mixed, 27/21/21
looking like Rearranges/Collects/Expands — and a corpus can only refute, so Common's 22
were then read in hole sizes. Thirteen are one shape: a hole matched twice and written once
beside one new node — a + a = 2a, a·a = a², a + a·b = a(1 + b), (v − a)(v + a) = v² − a²
and their relatives. Every one is 1 − |a|: exactly as large at a leaf, smaller everywhere else.

That is the commonest collecting shape there is, and the contract could not say it: Collects was
"always fewer", Rearranges "always the same", so the family sat at Unknown as a finding and
WritingARule.md listed it among the shapes that look declarable and are not.

The decision

Collects now promises never larger, and smaller for some input. Rearranges is the same size
for every input; Expands larger for every input. Nothing consumed the strict reading: RulesUpTo(Rearranges) wants "never grows", the selector-cost test asks for a majority, and the only
check that read Collects strictly was the corpus test's own. The 97 existing declarations
("exactly −2", "at most −4") stay true; the corpus contradicts Collects only on a firing that
grew. The enum doc, the guide and the test say it in the same words.

What Common declares

rules	growth	count
the thirteen above	Collects	`1 −
a-sign-times-a-thing-over-its-own-absolute-value-cancels	Collects	`−1 − 2
a-reciprocal-rational-factor-is-a-division	Rearranges	exactly 0 — IsWholeReciprocal is entity is Rational(...), literal only; the guide said it also took a written 1 / c, and was wrong
a-negated-reciprocal-rational-factor-is-a-negated-division	Expands	exactly +2

Six stay Unknown and say why beside the rule: five attach a condition sized by their own
operands, and a + a / b = a(1 + 1/b) is 3 − |a| — two nodes larger at a leaf, a shape the
corpus had never fired. Six shapes join the corpus so every newly declared rule fires on it.

Pins that moved

Re-recorded, not loosened:

• the safe ceiling moves 2 of 5 ordinary inputs, not 1: (x + 1)(x − 1) → x² − 1², and stops
  there because no safe rule folds a numeric power;
• the narrow ceiling brings the difference of squares together — a test asserted only the widest
  could, renamed to what it shows now.

Census: 111 collect, 46 rearrange, 31 expand, 136 unjudged; the safe ceiling admits 157 of
324.

Changed answers

Measured on a build of master (72676b0c) and of this branch, and recorded in
BREAKING-CHANGES.md. Transformation.CanonicalizationOverGraph(budget) — public, safe ceiling by
default — now collects what the sixteen rules collect: (x + y) * (x - y) was (-y + x) * (x + y)
and is -y ^ 2 + x ^ 2, the tree x ^ 2 - y ^ 2 reaches; x + x was left as written and is
2 * x; x + x * y is (1 + y) * x. Entity.Canonicalize() runs the rule pass, not the graph,
and is unchanged on every input probed. Next: the relatives in Power and Factorization (aⁿ·a, a/b/b), each on its own count.

Part of #746.

Checks

Full suite 9579 passed, 0 failed, 14 skipped — one of the 9579 a throwaway census probe, not committed. The Transformations area (822) was run twice more on its own.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura