bench: Phase 3 paraphrase fixture investigation — empirically dormant on current corpus

Three-iteration investigation following c5bc53f's "Phase 3 is a rescue
mechanism, not a default path" finding. Question: can a paraphrase-
eliciting fixture actually drive Phase 3 to fire on real questions?

Key reading from arborist/qa/warrant.py:507 ("warrant_check"):
the function vacuous-passes (returns (True, []) without any anchor
extraction) unless the question shape is one of:
- relation (proper-noun anchors)
- date (4-digit year in claim)
- entity-list
- count-shape
- why-cause-shape

If none of those shapes apply, Phase 3 has nothing to suppress.

Three fixture iterations, all probed before benching:

| iter | strategy                          | chain hits |
|------|-----------------------------------|------------|
| v1   | "What is X?" / "Define X"         | 12/13      |
| v2   | "How would you use X to ..."      |  1/10      |
| v2'  | "X: explain in plain English"     |  2/13      |
| v3   | "Who proposed X?" / "Why does X"  |  1/8       |
| v3'  | "X: who first stated it?"         |  1/8       |

Pattern: title-leading retrieval works (high title-token boost on
chain chunks) but those questions are definitional — no warrant
shape, no Phase 3 trigger. Warrant-shape questions ("who" / "when"
/ "why") trigger warrant_check but retrieval pulls toward
Wikipedia's prose articles instead of the terse claim-pack chunks.

Structural reason: claim-pack chunks (the 92 chain-root documents)
are deliberately terse — they state axioms / theorems precisely
with mathematical formalism but contain no biographical, historical,
or explanatory prose. So warrant-shape questions 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.

Verdict (`bench/results/phase3-warrant-chain-paraphrase-
investigation-2026-05-10.md`): Phase 3's runtime fire rate is
structurally bounded near zero on the current corpus. Mechanism
is correct, non-regressing, and unit-tested
(tests/test_warrant_chain.py). The lexical layer is strong enough
that the rescue isn't needed at measurable rates.

Recommendation: don't 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.

This closes the three-thread investigation cleanly. v1 + v2 + v3
fixtures + reports all retained as the empirical trail.

bench/qa_questions_warrant_chain_paraphrase.txt

@@ -0,0 +1,37 @@
+# Paraphrase-eliciting warrant-chain fixture (2026-05-10, v2).
+#
+# v1 of this fixture used natural-language wrappers ("How would you
+# use the Pigeonhole Principle to ..."). Pre-bench probe found only
+# 1/10 questions hit chain — the wrapper words ("how would you use",
+# "in your own words") match Wikipedia / general-knowledge articles
+# better than concise claim-pack chunks, pushing retrieval AWAY
+# from chain.
+#
+# v2 strategy: **title-leading + paraphrase suffix**. Each question
+# starts with the exact claim-pack title (preserving title-token
+# boost) but ends with a paraphrase-eliciting clause that should
+# steer the LLM toward reformulation. Title leads retrieval; suffix
+# leads generation.
+
+# Pillar VII
+Pigeonhole Principle: explain in plain English with a 13-people example.
+Pascal's Rule: rephrase as a counting story.
+Multiplication Principle: describe informally with a real-world example.
+
+# Pillar I
+Axiom of Implication Introduction: explain in your own words.
+Axiom of Universal Specification: rephrase using simpler vocabulary.
+Axiom of Reflexivity of Equality: describe informally.
+
+# Pillar II
+Axiom of Extensionality: rephrase using only common words.
+Axiom of Empty Set: describe in plain English.
+Axiom of Power Set: explain informally with no jargon.
+Axiom of Foundation: rephrase as a rule about sets.
+
+# Pillar III
+Axiom of Successor: describe using only counting words.
+Axiom of Addition (Zero): explain in plain language.
+
+# Pillar IV
+Archimedean Axiom: rephrase using simpler measurement vocabulary.

bench/results/phase3-warrant-chain-paraphrase-investigation-2026-05-10.md

@@ -0,0 +1,109 @@
+# #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`