Pith Number

pith:4OPHKQQE

pith:2018:4OPHKQQEBM5R5DH6MYEBA7FNYC

not attested not anchored not stored refs pending

Crossed extensions and equivalences of topological 2-groupoids

El-ka\"ioum M. Moutuou

arxiv:1802.02017 v1 · 2018-02-06 · math.AT · math.CT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4OPHKQQEBM5R5DH6MYEBA7FNYC}

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	2026-05-18T00:24:11.171339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e39e7542040b3b1e8cfe6608107cadc094760600d795d83eeafbefe633d2c8b1

Aliases

arxiv: 1802.02017 · arxiv_version: 1802.02017v1 · doi: 10.48550/arxiv.1802.02017 · pith_short_12: 4OPHKQQEBM5R · pith_short_16: 4OPHKQQEBM5R5DH6 · pith_short_8: 4OPHKQQE

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/4OPHKQQEBM5R5DH6MYEBA7FNYC \
  | 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: e39e7542040b3b1e8cfe6608107cadc094760600d795d83eeafbefe633d2c8b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec6ca758070828b9f0e17b53d6d4b7c80dcf0147c2b981d8874513ec6a8de5ea",
    "cross_cats_sorted": [
      "math.CT",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2018-02-06T15:56:06Z",
    "title_canon_sha256": "e452e9d7e800798a6fdafdac64af92bfa5ab36c2e857f05a0da4f2ac67af2c4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.02017",
    "kind": "arxiv",
    "version": 1
  }
}