Pith Number

pith:5POVKWS7

pith:2025:5POVKWS7TG6JFACIUOUDQR4UQN

not attested not anchored not stored refs pending

The algebraic internal groupoid model of Martin-L\"{o}f type theory

Calum Hughes

arxiv:2503.17319 v2 · 2025-03-21 · math.CT · math.LO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5POVKWS7TG6JFACIUOUDQR4UQN}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

A Model of Type Theory in Groupoid Assemblies

Receipt and verification

First computed	2026-07-05T11:14:05.893105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebdd555a5f99bc928048a3a8384794837b85e27aa9e939f3cba910da525e8918

Aliases

arxiv: 2503.17319 · arxiv_version: 2503.17319v2 · doi: 10.48550/arxiv.2503.17319 · pith_short_12: 5POVKWS7TG6J · pith_short_16: 5POVKWS7TG6JFACI · pith_short_8: 5POVKWS7

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5POVKWS7TG6JFACIUOUDQR4UQN \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ebdd555a5f99bc928048a3a8384794837b85e27aa9e939f3cba910da525e8918

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "274714e26e20e7c4abff2e78b881cf73bee93c5b2eb51bdef02ecb06eb82ea48",
    "cross_cats_sorted": [
      "math.LO"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-03-21T17:13:40Z",
    "title_canon_sha256": "8157ea9e82dfd31f20645a0694e2e930c6d9f5b2e689034eea19df7b6f726fa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2503.17319",
    "kind": "arxiv",
    "version": 2
  }
}