# Operator 09 — Composition (Stage-0 template)

**Operator.** Composition: given two primes P1, P2 that co-occur so tightly they function as an
emergent UNIT, propose the composite prime P1∘P2 — a distinct pattern with its own name and
structure that neither P1 nor P2 has alone. N-ary. (natural_selection = variation∘selection∘retention
is the archetypal already-named composite.)

**Pre-filter.** Pairs co-occurring in ≥3 shared archetypes with COMPLEMENTARY (not near-alias)
embedding similarity (0.45<cos<0.78). Worklist: `op9_worklist.json` (4,166 pairs). Pilot = a diverse
88-pair sample (per-prime cap 4, to avoid hub-prime domination by feedback/observability/constraint).

**The key discriminator (EMERGENCE rule).** A valid composition prime has EMERGENT structure —
a property or behavior that arises from the combination and belongs to NEITHER part alone, with its
own name. It is NOT: (1) a **mere conjunction** ("P1 and P2 both present" — no emergent unit); (2) a
case where one prime SUBSUMES or is an ASPECT of the other (that's a DAG edge, not a composition);
(3) an already-named composite (alias). Most tight co-occurring pairs collapse — they co-occur
because both are generically useful, not because they fuse into a new thing.

**Model tier.** Sonnet (judging emergence-vs-conjunction needs judgment). Pilot doubles as a
saturation check + tier check.

---

## A. The crank prompt (Stage 2 — sonnet, batched)

> You are applying COMPOSITION to entries from a catalog of "prime abstractions." Each payload line is
> a PAIR of primes P1 + P2 that co-occur tightly across many contexts. Decide whether their
> combination forms an EMERGENT COMPOSITE — a distinct prime with its own name and structure that
> neither P1 nor P2 has alone (like variation+selection+retention → natural_selection).
>
> Output a real composite prime ONLY if it is domain-general, has EMERGENT structure (a property
> arising from the combination, belonging to neither part alone), is NOT already in the corpus, and
> is NOT: a mere conjunction ("both present," no new unit → COLLAPSE "conjunction"); a case where one
> prime is an aspect/subset of the other (→ COLLAPSE "subsumption, not composition"); or an
> already-named composite (→ COLLAPSE alias, name it). Bias HARD toward COLLAPSE — most tight pairs
> co-occur because both are generically useful, not because they fuse.
>
> For EACH pair, output EXACTLY:
>
> ```
> PAIR:      <P1 + P2, copied>
> COMPOSITE: <the emergent composite prime — or NONE>
> EMERGENCE: <the property arising from the combination that neither part has alone — or NONE>
> NEAREST:   <closest existing prime you can name, or NONE>
> VERDICT:   NEW | COLLAPSE
> REASON:    <=12 words>
> ```
>
> **Payload:** `P1 · "one_liner" + P2 · "one_liner" (co-occur×N)`

## B. Collapse test
0. Alias-claim verification on NEAREST + composite name (slug + alias map). Exists → alias.
1. Emergence filter: EMERGENCE=NONE or "both present" → COLLAPSE (conjunction). This is the primary kill.
2. Subsumption filter: if one prime is an aspect of the other → COLLAPSE (that's a DAG edge, feed the
   edge-harvest, not the prime queue).
3. Deterministic slug check on Stage-4 proposed slugs. §D amendment inherited.
4. Survivors (emergent, absent) → sonnet Stage-4, STRONG-only.

## C. Pilot / run — DOUBLES AS SATURATION + TIER CHECK
1. Run the diverse 88-pair pilot (sonnet, 2 batches) + a 15-pair haiku probe.
2. Funnel; verify each survivor is absent + genuinely emergent (not conjunction/subsumption).
3. SATURATION/YIELD: if ≈0 genuine → retire (record any find + subsumption pairs as edge byproduct).
   If ≥1 genuine (op-11/14 precedent for combinatorial ops), surface a widen decision (the full
   ~4,166-pair set ≈ 4–8M, or a larger diverse sample).
4. Manifest + SATURATION row + stubs + runbook/memory/FINDINGS update.

## D. Notes
- Composition BYPRODUCT = subsumption pairs (one prime an aspect of the other) → the DAG-edge harvest
  (already ~272 candidate edges from op-05/13/12).
- Composition is the last of the 14 operators. Like op-11/14 it reaches beyond recombining existing
  structure (it MAKES a new unit), so it may yield where the recombination ops (10/12/13) saturated —
  but most named composites already exist, so expect modest yield.
