Pith Number

pith:Z56V3ROT

pith:2011:Z56V3ROTYCNEZWAWY6XK57XPJR

not attested not anchored not stored refs pending

Enhanced 2-categories and limits for lax morphisms

Michael Shulman, Stephen Lack

arxiv:1104.2111 v2 · 2011-04-12 · 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{Z56V3ROTYCNEZWAWY6XK57XPJR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T04:02:11.982006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf7d5dc5d3c09a4cd816c7aeaefeef4c4e5036bbe9269491977d367b4245f2b4

Aliases

arxiv: 1104.2111 · arxiv_version: 1104.2111v2 · doi: 10.48550/arxiv.1104.2111 · pith_short_12: Z56V3ROTYCNE · pith_short_16: Z56V3ROTYCNEZWAW · pith_short_8: Z56V3ROT

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/Z56V3ROTYCNEZWAWY6XK57XPJR \
  | 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: cf7d5dc5d3c09a4cd816c7aeaefeef4c4e5036bbe9269491977d367b4245f2b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a814089f69951d300b9cf8895bfcee78c65b9d34fc7cfb860fcc985431f5f386",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2011-04-12T04:37:07Z",
    "title_canon_sha256": "829db5c55f9b5c16e5faca809054d38cd1be23de1ef2f6c2ea6caf932b105c98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2111",
    "kind": "arxiv",
    "version": 2
  }
}