# Hilbert pillar IV — full warrant resolution — 2026-05-09

**Date:** 2026-05-09 (UTC)
**Author:** blackops + fox
**Method:** `arborist warrant-resolve --use-aliases --write` after registering 4
geometry-domain term aliases (#000042) bridging Hilbert 1902 Townsend
vocabulary to modern claim-pack record names
**Shards:** `~/.arborist/shards/000.db` (claim-pack records) +
`~/.arborist/crawl/textbook_hilbert-foundations-geometry-1902.db` (PG TeX surface)

## Headline

**18 / 18 Hilbert pillar IV records resolve.** Eleven match unaliased,
seven via term-alias OR-expansion. Pillar IV becomes the first complete
warrant-chain vertical: every Hilbert axiom or theorem in the claim-pack
g4 bundle now binds to a primary-source surface chunk via
`derivations.proof_blob` Merkle inclusion proof.

## Aliases registered

All four are `geometry` domain, audit-disciplined per #000042 (each
carries `decision_at` + `decision_by` + `decision_rationale`; smoke-test
`decision_by="blackops 2026-05-09 (smoke)"`).

| Modern term (claim-pack) | Hilbert 1902 term | Discriminating signal |
|---|---|---|
| incidence | connection | "connection" 16 hits in Hilbert TeX; "incidence" zero |
| euclidean parallel postulate | axiom of parallels | Hilbert §5: "Group III: Axiom of Parallels (Euclid's axiom)" |
| non triviality | space axiom | Hilbert §3: "the space axioms of this group" — Group I axiom 8 (4 non-coplanar points) |
| side angle side | included angle | Hilbert §6 Theorem 10: "two sides and the included angle" — `"included angle"` is 1 hit (highly discriminating) |

The first alias unblocked 4 records (Line/Plane/Point-Line/Point-Plane
Incidence). The next three each unblocked 1 record.

## Per-record breakdown

| # | Title | Resolution path |
|---|---|---|
| 1 | Axiom of Line Incidence | via_alias (`incidence ↔ connection`) |
| 2 | Axiom of Plane Incidence | via_alias |
| 3 | Axiom of Point-Line Incidence | via_alias |
| 4 | Axiom of Point-Plane Incidence | via_alias |
| 5 | Axiom of Non-Triviality | via_alias (`non triviality ↔ space axiom`) |
| 6 | Axiom of Betweenness | direct |
| 7 | Axiom of Line Separation | direct |
| 8 | Pasch's Axiom | direct |
| 9 | Axiom of Segment Congruence | direct |
| 10 | Axiom of Angle Congruence | direct |
| 11 | Axiom of Segment Construction | direct |
| 12 | Axiom of Angle Construction | direct |
| 13 | Axiom of Side-Angle-Side (SAS) | via_alias (`side angle side ↔ included angle`) |
| 14 | Euclidean Parallel Postulate | via_alias (`euclidean parallel postulate ↔ axiom of parallels`) |
| 15 | Archimedean Axiom | direct |
| 16 | Completeness Axiom | direct |
| 17 | Pythagorean Theorem | direct |
| 18 | Sum of Angles in Triangle | direct |

## Cluster-wide context

`records_total: 92` · `records_resolved: 18` (20%). The other 74
records cite textbooks not yet in the shard cluster (Mendelson,
Stanley, Brualdi, Knuth, Jech, Kolmogorov, etc.) and stay at
`ANCHOR-WARRANTED` per #000031's honest-ceiling discipline. Phase 4
content acquisition (#000038) gates the next lift.

## Why this matters

Hilbert's `Foundations of Geometry` (1902 Townsend translation) is the
**first textbook the claim-pack ever fully clears**. Every claim that
cites Hilbert can now render with a `· warrant: N proven` tail in the
Q&A surface (#000031 Phase 3 will wire the EVIDENCE-WARRANTED upgrade).

The failure mode #000042 was built to handle — modern vocabulary
("incidence") vs historical translation ("connection") — generalizes
beyond Hilbert. The same mechanism unlocks Boole 1854 ("elective
symbol" → modern "Boolean variable"), Newton 1729 Motte ("alteration of
motion proportional to impressed force" → modern "F = ma"), and
Aristotle's traditional translations once those textbook surfaces land
under #000038.

## Reproducibility

```bash
# Register the four aliases (idempotent — safe to re-run).
for entry in \
  "incidence|connection|Hilbert 1902 Townsend uses 'connection' for what modern texts call 'incidence'" \
  "euclidean parallel postulate|axiom of parallels|Hilbert §5 names this 'Group III: Axiom of Parallels (Euclid's axiom)'" \
  "non triviality|space axiom|Hilbert calls Group I axiom 8 'the space axiom'" \
  "side angle side|included angle|Hilbert §6 Theorem 10: 'two sides and the included angle'"
do
  IFS='|' read -r term alt rat <<< "$entry"
  arborist --shards-dir ~/.arborist/shards alias term add \
    "$term" "$alt" --domain geometry \
    --by "blackops 2026-05-09 (smoke)" \
    --rationale "$rat"
done

# Run the resolver.
arborist --shards-dir ~/.arborist/shards warrant-resolve --use-aliases --write
# → records_total: 92, records_resolved: 18 (Hilbert pillar IV: 18/18)
```

The `+alias` derivations rows distinguish alias-resolved chains from
direct ones (`process_id` field on `derivations` table). Audit reviewers
querying `WHERE process_id LIKE 'warrant-resolver-v1+alias'` see exactly
which records depend on a fox/blackops alias decision.
