# #000031 Phase 3 — paraphrase fixture investigation (2026-05-10)

**Sequel to** the aggressive A/B in
`phase3-warrant-chain-A-B-aggressive-2026-05-10.md`, which found
Phase 3 firing 0/117 cells even with 12/13 questions retrieving
chain chunks. Refined hypothesis: Phase 3 is a **rescue mechanism
that fires only when lexical `warrant_check` fails**, and on
well-formed axiom questions the LLM produces lexically-anchored
output, so warrant_check passes via the cheap path.

This investigation tested whether paraphrase-eliciting fixture
shapes can drive Phase 3 to fire empirically.

## Key finding from `arborist/qa/warrant.py:507`

`warrant_check` **vacuous-passes** unless the question shape is one
of:

- relation (proper-noun anchors via `is_relation_question`)
- date (4-digit year in claim)
- entity-list (multi-entity question shape)
- count (count-shape question)
- why-cause (cause anchors gated on why-shape question)

If none of these shapes apply, `warrant_check` returns
`(True, [])` trivially — no `WARRANT_MISSING` to suppress, Phase 3
dormant by design.

## Fixture iteration probe results

| iteration | strategy | chain hits | Phase 3 fires |
|---|---|---|---|
| v1 (axiom titles) | "What is X?" / "Define X" | 12/13 | 0/117 |
| v2 (paraphrase wrappers) | "How would you use X to ..." / "In your own words ..." | 1/10 | n/a (didn't bench) |
| v2 (title + paraphrase suffix) | "X: explain in plain English ..." | 2/13 | n/a (didn't bench) |
| v3 (warrant-shape wrappers) | "Who proposed X?" / "Why does X imply Y?" | 1/8 | n/a |
| v3 (title-leading + warrant suffix) | "X: who first stated it?" | 1/8 | n/a |

**Pattern observed across all iterations:**

- Title-leading retrieval works (high title-token boost on chain
  chunks) **but** the question is definitional — no warrant shape,
  no Phase 3 trigger.
- Warrant-shape questions ("who", "why", "when") trigger
  `warrant_check` **but** retrieval defaults to Wikipedia prose
  articles which have biographical/historical context the
  terse claim-pack chunks lack.

## Structural reason Phase 3 is empirically dormant

Claim-pack chunks (the 92 chain-root documents) are **terse and
title-driven**. They state the axiom or theorem precisely with
mathematical formalism but contain no biographical / historical /
explanatory prose (no "first proven by Dirichlet in 1834", no
"motivated by Cantor's earlier work on", no "this rules out
because of...").

This means warrant-shape questions ("who", "when", "why") will
preferentially retrieve from Wikipedia, where the prose context
matches the question shape. Phase 3's data condition (chain-backed
chunk cited for a warrant-shape claim) is empirically unreachable
through normal retrieval pathways on this corpus shape.

## What would make Phase 3 fire

Three paths, none easy:

1. **Fortify claim-pack chunks** with biographical / historical
   prose so warrant-shape questions retrieve chain chunks. This
   bloats the chunks and dilutes their canonical-form value.
2. **Force-cite via prompt control** — include a directive in the
   system prompt that tells the LLM "if a chain-root chunk is in
   the evidence set, cite it for at least one claim." Forces the
   data condition. Bench-only / artificial.
3. **Cross-source compound claims** — questions where one claim
   should cite a chain-root chunk (definitional anchor) AND another
   claim has warrant-shape elements (who/when/why). The LLM
   typically produces multi-claim answers in claim_lattice modes,
   so this could happen organically. Hard to engineer reliably in
   a fixture.

## Verdict

Phase 3's mechanism is correct, non-regressing, and well-tested in
unit tests (`tests/test_warrant_chain.py`). On the current corpus,
its **runtime fire rate is structurally bounded near zero** because
the data condition (warrant-shape claim citing chain-backed chunk)
intersects rarely.

This is consistent with Phase 3's design intent: a defensive rescue
path for the rare claim that survives generation but fails lexical
anchoring. The lexical layer is strong enough on the current corpus
shape that the rescue isn't needed at measurable rates.

**Recommendation**: don't try to engineer Phase 3 fires via fixture
design. Track fire rate as a corpus-evolution signal — if claim-pack
content gains prose context (or the corpus mix changes), Phase 3
will start firing organically and the audit-line tail
(`· warrant proven via chain ×N`) will surface it. Until then,
the mechanism is dormant-but-correct.

## Files

- v1 fixture: `bench/qa_questions_warrant_chain_probe.txt`
- v1 A/B: `bench/results/phase3-warrant-chain-A-B-2026-05-10.md`
- v2 fixture: `bench/qa_questions_warrant_chain_aggressive.txt`
- v2 A/B: `bench/results/phase3-warrant-chain-A-B-aggressive-2026-05-10.md`
- v3 fixture (this investigation): `bench/qa_questions_warrant_chain_paraphrase.txt`
- This report: `bench/results/phase3-warrant-chain-paraphrase-investigation-2026-05-10.md`
