Pith Number

pith:U66LL2O6

pith:2010:U66LL2O6PCRGT5JVSRAZQX55M3

not attested not anchored not stored refs pending

Group actions on topological graphs

Alex Kumjian, John Quigg, Valentin Deaconu

arxiv:1007.2616 v3 · 2010-07-15 · 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{U66LL2O6PCRGT5JVSRAZQX55M3}

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	2026-05-18T04:28:48.333571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7bcb5e9de78a269f5359441985fbd66e9cc481ce8d8cea7c02b7dc669df7408

Aliases

arxiv: 1007.2616 · arxiv_version: 1007.2616v3 · doi: 10.48550/arxiv.1007.2616 · pith_short_12: U66LL2O6PCRG · pith_short_16: U66LL2O6PCRGT5JV · pith_short_8: U66LL2O6

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/U66LL2O6PCRGT5JVSRAZQX55M3 \
  | 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: a7bcb5e9de78a269f5359441985fbd66e9cc481ce8d8cea7c02b7dc669df7408

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e48c2aa19ac2f7d542a0308d545e68b46a6986e9b8b88fb171b4968355189bf0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-07-15T16:55:19Z",
    "title_canon_sha256": "93b2146a46303f1b0813bc32315d113c45da31340deeb31bc91ad98ac03b00bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.2616",
    "kind": "arxiv",
    "version": 3
  }
}