Pith Number

pith:U3AXKDDV

pith:2025:U3AXKDDVO5MQYZX2YZLTZCR3RF

not attested not anchored not stored refs pending

The familial nature of enrichment over virtual double categories

Soichiro Fujii, Stephen Lack

arxiv:2507.05529 v1 · 2025-07-07 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U3AXKDDVO5MQYZX2YZLTZCR3RF}

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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

Exponentiable virtual double categories and presheaves for double categories

Receipt and verification

First computed	2026-07-05T11:33:31.789188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6c1750c7577590c66fac6573c8a3b894825e89266edc5a29c367a329a2fc2c7

Aliases

arxiv: 2507.05529 · arxiv_version: 2507.05529v1 · doi: 10.48550/arxiv.2507.05529 · pith_short_12: U3AXKDDVO5MQ · pith_short_16: U3AXKDDVO5MQYZX2 · pith_short_8: U3AXKDDV

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/U3AXKDDVO5MQYZX2YZLTZCR3RF \
  | 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: a6c1750c7577590c66fac6573c8a3b894825e89266edc5a29c367a329a2fc2c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "257af2cbbba210a632cb4746ecd32991221ce10ee7b88827aa3c3fbf855b57ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-07-07T23:02:02Z",
    "title_canon_sha256": "3cf7caf0ace5c38c89d0246cba26770e7c4f2beaa88af43c07448b921433afcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.05529",
    "kind": "arxiv",
    "version": 1
  }
}