Pith Number

pith:OL33PKDY

pith:2011:OL33PKDYQ7S5VENKJI2RPCA7XM

not attested not anchored not stored refs pending

Groupoids and C*-algebras for categories of paths

Jack Spielberg

arxiv:1111.6924 v4 · 2011-11-29 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OL33PKDYQ7S5VENKJI2RPCA7XM}

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	2026-05-18T02:51:34.446138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72f7b7a87887e5da91aa4a3517881fbb0cebcf96c69f863390178087319eb947

Aliases

arxiv: 1111.6924 · arxiv_version: 1111.6924v4 · doi: 10.48550/arxiv.1111.6924 · pith_short_12: OL33PKDYQ7S5 · pith_short_16: OL33PKDYQ7S5VENK · pith_short_8: OL33PKDY

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/OL33PKDYQ7S5VENKJI2RPCA7XM \
  | 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: 72f7b7a87887e5da91aa4a3517881fbb0cebcf96c69f863390178087319eb947

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26ca30fcccd6de05c8d0cd9abb42b58062ad7da7b431b34e16cd0b805ab37aa1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-11-29T18:32:20Z",
    "title_canon_sha256": "0b8dd2d5230255953e16a772717290c437e3bd8ff0bbefe0538aaece87068aa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.6924",
    "kind": "arxiv",
    "version": 4
  }
}