ticket #000042: 4 geometry aliases resolve all 18 Hilbert pillar IV records
Smoke-test alias rationale was published with #000042, but two of the three trailing records ("non triviality", "side-angle-side") needed their own per-concept aliases since Hilbert 1902's vocabulary differs in more than one place. Map of registered aliases (geometry domain): incidence -> connection (4 records lifted) euclidean parallel postulate -> axiom of parallels (1) non triviality -> space axiom (1) side angle side -> included angle (1) Hilbert pillar IV is now the first complete warrant-chain vertical: 18/18 records bind to a primary-source surface chunk via Merkle inclusion proof. 11 direct + 7 via-alias derivations rows. Bench journal under bench/results/hilbert-pillar-iv-fully-resolved-2026-05-09.md records reproducibility steps + per-alias signal data so a future shift can extend the same pattern to Boole 1854, Newton 1729 Motte, and Aristotle's traditional translations once #000038 lands those surfaces. Cluster-wide remains 18/92 (20%); the other 74 records cite textbooks not yet ingested. Phase 4 content acquisition (#000038) gates next lift.
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# Hilbert pillar IV — full warrant resolution — 2026-05-09
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**Date:** 2026-05-09 (UTC)
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**Author:** blackops + fox
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**Method:** `arborist warrant-resolve --use-aliases --write` after registering 4
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geometry-domain term aliases (#000042) bridging Hilbert 1902 Townsend
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vocabulary to modern claim-pack record names
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**Shards:** `~/.arborist/shards/000.db` (claim-pack records) +
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`~/.arborist/crawl/textbook_hilbert-foundations-geometry-1902.db` (PG TeX surface)
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## Headline
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**18 / 18 Hilbert pillar IV records resolve.** Eleven match unaliased,
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seven via term-alias OR-expansion. Pillar IV becomes the first complete
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warrant-chain vertical: every Hilbert axiom or theorem in the claim-pack
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g4 bundle now binds to a primary-source surface chunk via
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`derivations.proof_blob` Merkle inclusion proof.
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## Aliases registered
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All four are `geometry` domain, audit-disciplined per #000042 (each
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carries `decision_at` + `decision_by` + `decision_rationale`; smoke-test
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`decision_by="blackops 2026-05-09 (smoke)"`).
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| Modern term (claim-pack) | Hilbert 1902 term | Discriminating signal |
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|---|---|---|
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| incidence | connection | "connection" 16 hits in Hilbert TeX; "incidence" zero |
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| euclidean parallel postulate | axiom of parallels | Hilbert §5: "Group III: Axiom of Parallels (Euclid's axiom)" |
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| non triviality | space axiom | Hilbert §3: "the space axioms of this group" — Group I axiom 8 (4 non-coplanar points) |
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| side angle side | included angle | Hilbert §6 Theorem 10: "two sides and the included angle" — `"included angle"` is 1 hit (highly discriminating) |
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The first alias unblocked 4 records (Line/Plane/Point-Line/Point-Plane
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Incidence). The next three each unblocked 1 record.
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## Per-record breakdown
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| # | Title | Resolution path |
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|---|---|---|
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| 1 | Axiom of Line Incidence | via_alias (`incidence ↔ connection`) |
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| 2 | Axiom of Plane Incidence | via_alias |
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| 3 | Axiom of Point-Line Incidence | via_alias |
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| 4 | Axiom of Point-Plane Incidence | via_alias |
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| 5 | Axiom of Non-Triviality | via_alias (`non triviality ↔ space axiom`) |
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| 6 | Axiom of Betweenness | direct |
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| 7 | Axiom of Line Separation | direct |
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| 8 | Pasch's Axiom | direct |
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| 9 | Axiom of Segment Congruence | direct |
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| 10 | Axiom of Angle Congruence | direct |
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| 11 | Axiom of Segment Construction | direct |
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| 12 | Axiom of Angle Construction | direct |
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| 13 | Axiom of Side-Angle-Side (SAS) | via_alias (`side angle side ↔ included angle`) |
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| 14 | Euclidean Parallel Postulate | via_alias (`euclidean parallel postulate ↔ axiom of parallels`) |
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| 15 | Archimedean Axiom | direct |
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| 16 | Completeness Axiom | direct |
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| 17 | Pythagorean Theorem | direct |
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| 18 | Sum of Angles in Triangle | direct |
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## Cluster-wide context
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`records_total: 92` · `records_resolved: 18` (20%). The other 74
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records cite textbooks not yet in the shard cluster (Mendelson,
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Stanley, Brualdi, Knuth, Jech, Kolmogorov, etc.) and stay at
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`ANCHOR-WARRANTED` per #000031's honest-ceiling discipline. Phase 4
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content acquisition (#000038) gates the next lift.
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## Why this matters
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Hilbert's `Foundations of Geometry` (1902 Townsend translation) is the
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**first textbook the claim-pack ever fully clears**. Every claim that
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cites Hilbert can now render with a `· warrant: N proven` tail in the
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Q&A surface (#000031 Phase 3 will wire the EVIDENCE-WARRANTED upgrade).
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The failure mode #000042 was built to handle — modern vocabulary
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("incidence") vs historical translation ("connection") — generalizes
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beyond Hilbert. The same mechanism unlocks Boole 1854 ("elective
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symbol" → modern "Boolean variable"), Newton 1729 Motte ("alteration of
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motion proportional to impressed force" → modern "F = ma"), and
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Aristotle's traditional translations once those textbook surfaces land
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under #000038.
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## Reproducibility
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```bash
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# Register the four aliases (idempotent — safe to re-run).
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for entry in \
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"incidence|connection|Hilbert 1902 Townsend uses 'connection' for what modern texts call 'incidence'" \
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"euclidean parallel postulate|axiom of parallels|Hilbert §5 names this 'Group III: Axiom of Parallels (Euclid's axiom)'" \
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"non triviality|space axiom|Hilbert calls Group I axiom 8 'the space axiom'" \
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"side angle side|included angle|Hilbert §6 Theorem 10: 'two sides and the included angle'"
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do
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IFS='|' read -r term alt rat <<< "$entry"
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arborist --shards-dir ~/.arborist/shards alias term add \
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"$term" "$alt" --domain geometry \
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--by "blackops 2026-05-09 (smoke)" \
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--rationale "$rat"
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done
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# Run the resolver.
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arborist --shards-dir ~/.arborist/shards warrant-resolve --use-aliases --write
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# → records_total: 92, records_resolved: 18 (Hilbert pillar IV: 18/18)
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```
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The `+alias` derivations rows distinguish alias-resolved chains from
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direct ones (`process_id` field on `derivations` table). Audit reviewers
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querying `WHERE process_id LIKE 'warrant-resolver-v1+alias'` see exactly
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which records depend on a fox/blackops alias decision.
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@ -61,7 +61,7 @@ Newest first. Update on every open/close.
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| ID | Title | Status | Opened | Directive |
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|----------|------------------------------------------------|-----------------------|------------|-----------|
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| #000042 | Term-aliases table (vocabulary-mismatch bridge) | closed · landed 2026-05-09 (smoke-test alias incidence↔connection geometry resolves 4 stuck Hilbert records) | 2026-05-09 | — |
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| #000042 | Term-aliases table (vocabulary-mismatch bridge) | closed · landed 2026-05-09; 4 smoke aliases (geometry) resolve **all 18 Hilbert pillar IV records** (11 direct + 7 via alias) | 2026-05-09 | — |
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| #000041 | Citation-aliases table (PD substitutes for proprietary cites) | closed · mechanism landed 2026-05-09; rows added via fox decisions per #000038 | 2026-05-09 | — |
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| #000040 | Phase 5 resolver fix — phrase + content-token cascade (Hilbert terminology mismatch surfaced) | closed · cascade landed 2026-05-09; lift blocked by 1902-vs-modern vocab; follow-up #000042 | 2026-05-09 | — |
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| #000039 | Optional `sqlite-vec` retrieval backend (A/B vs FTS5, hybrid not replacement) | open · awaiting go/no-go (doc-only Phase 0) | 2026-05-09 | — |
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@ -1,6 +1,6 @@
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# Ticket #000042 — Term-aliases table (vocabulary-mismatch bridge)
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**Status:** closed · mechanism landed 2026-05-09 with smoke-test alias (incidence ↔ connection geometry) — 4 stuck Hilbert records now resolve via alias-expanded cascade
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**Status:** closed · mechanism + 4 smoke aliases landed 2026-05-09 — **all 18 Hilbert pillar IV records resolve** (11 unaliased, 7 alias-resolved). Aliases registered: `incidence ↔ connection`, `euclidean parallel postulate ↔ axiom of parallels`, `non triviality ↔ space axiom`, `side angle side ↔ included angle` (all geometry domain)
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**Opened:** 2026-05-09
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**Scope:** Add an `arborist term_aliases` table that maps a
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`(term, domain)` pair to an alternate term used in older /
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