# Warrant chain render tail bench — 2026-05-09

**Date:** 2026-05-09 (UTC)
**Author:** blackops + fox
**Commits:** `f0e6baf` (Phase 2 resolver + writer) + `69e0a95`
(Phase 3 render tail + theorem-name resolver)

## Setup

- Shard cluster: `~/.arborist/shards/000-003.db` — 3.47M docs
  including 92 claim-pack records (78 v2 + 14 pillar VII)
- Crawl shards: `~/.arborist/crawl/textbook_*.db` — 9 surface
  textbooks across 6 g4 pillars
- 11 `derivations.process_id='warrant-resolver-v1'` rows in
  shard 000.db, all binding pillar-IV Hilbert axioms to chunks
  in the surface-ingested Hilbert *Foundations of Geometry*

## Method

Six representative questions through `arborist query --top-k 3`
(full QA pipeline: retrieval + body-coverage rerank + title-
relevance + concept-relations + verifier + render layer):

```bash
arborist --shards-dir ~/.arborist/shards query "$q" --top-k 3
```

Looking for the new `· warrant: N proven` tail surfaced by
`_render_warrant_chain_tail` (commit `69e0a95`) when the
answer's cited sources include a claim-pack record with a
`warrant-resolver-v1` derivations row.

## Results

| # | Question | Audit line | Warrant tail? |
|---|---|---|---|
| 1 | `Pasch's axiom` | STRICT · via quote · **warrant: 1 proven**  1/1  2.9s | ✓ |
| 2 | `Hilbert geometry axioms` | STRICT · via quote  13/13  13.9s | ✗ |
| 3 | `axiom of betweenness` | HYBRID · via paraphrase  3/4  4.1s | ✗ |
| 4 | `Bayes theorem` | STRICT · via quote  1/1  8.1s | ✗ |
| 5 | `modus tollens` | UNGROUNDED · via quote  0/1  4.0s | ✗ |
| 6 | `binomial coefficient identity` | HYBRID · via paraphrase  5/7  5.4s | ✗ |

**1 of 6 questions** lit up the warrant tail. That's the
honest signal — only **11 of 92** claim-pack records (~12%)
have warrant chains, and only the question that retrieved a
Hilbert-pillar-IV record AS its cited source surfaced the tail.

## Why each case landed where it did

- **#1 Pasch's axiom (warrant: 1 proven)** — The retrieval
  pipeline cited *both* the Wikipedia "Pasch's axiom" article
  AND the claim-pack pillar-IV record. The claim-pack record
  has a `warrant-resolver-v1` derivations row binding it to
  chunk 1 of the Hilbert textbook. The render layer surfaces
  this chain.
- **#2 Hilbert geometry axioms (no tail)** — STRICT verdict,
  but the cited sources were Wikipedia + crawled Hilbert
  surface — NOT the claim-pack records. The claim-pack records
  ARE in the cluster but didn't make the top-k for this
  multi-axiom question. No claim-pack record cited → no warrant
  chain to surface.
- **#3 axiom of betweenness (no tail)** — Same as #2 — claim-
  pack record not in the cited set.
- **#4 Bayes theorem (no tail)** — Different reason: even if
  the claim-pack Bayes record HAD been cited, Kolmogorov isn't
  surface-ingested, so its `source_reference` doesn't resolve
  to a Merkle-bound surface chunk. ANCHOR-WARRANTED ceiling per
  #000031 §1 honest-ceiling clause.
- **#5 modus tollens (UNGROUNDED, no tail)** — The verifier
  couldn't substring-match the answer's quotes against any
  cited source. Pre-warrant-chain issue; orthogonal to this
  ticket's scope.
- **#6 binomial coefficient identity (no tail)** — Same as #4
  — claim-pack pillar VII records cite Brualdi / Stanley /
  Knuth, none of which are surface-ingested under the current
  manifest.

## What this measurement actually shows

The render-layer tail correctly surfaces when a chain-of-custody
exists from answer → cited source → primary-source surface
chunk via Merkle-proven derivations. It correctly stays silent
in absence of data:

1. **Honest signal floor.** 1/6 lift in the broad sweep matches
   the data substrate (11/92 records have chains). No false
   positives observed on Bayes / Combinatorics queries whose
   cited textbooks aren't ingested.
2. **Targeted lift would be much higher.** A bench specifically
   on the 11 Hilbert-pillar-IV axioms with warrants, asked
   against the augmented shard, would light up the tail on
   ~all of them (modulo which records the retrieval pipeline
   chooses to cite).
3. **The path to higher coverage is content acquisition, not
   code.** Adding Mendelson + Enderton would resolve ~20 more
   records (logic pillar I); adding Stanley + Brualdi + Knuth
   would resolve ~7 pillar VII records; adding Jech would
   resolve ~7 set-theory records. The resolver code is done;
   the manifest needs more textbooks.

## Reproducibility

```bash
# Clear + re-populate derivations
sqlite3 ~/.arborist/shards/000.db \
    "DELETE FROM derivations WHERE process_id='warrant-resolver-v1';"
arborist --shards-dir ~/.arborist/shards warrant-resolve --write
# → records_total=92, records_resolved=11, derivations_written=11

# Run targeted query
arborist --shards-dir ~/.arborist/shards query "Pasch's axiom" --top-k 3
# Look for: "· warrant: 1 proven" on the audit line
```

arborist commit at measurement: `69e0a95`.
