Pith Number

pith:Z7CN75ZV

pith:2012:Z7CN75ZVZY5B7CYTS2UMTLSTN3

not attested not anchored not stored refs pending

Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions

Pere Ara, Ruy Exel

arxiv:1210.6931 v2 · 2012-10-25 · 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{Z7CN75ZVZY5B7CYTS2UMTLSTN3}

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	2026-05-18T03:06:34.658957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfc4dff735ce3a1f8b1396a8c9ae536edfce6b0b8adb1ec4e44254d3703835ea

Aliases

arxiv: 1210.6931 · arxiv_version: 1210.6931v2 · doi: 10.48550/arxiv.1210.6931 · pith_short_12: Z7CN75ZVZY5B · pith_short_16: Z7CN75ZVZY5B7CYT · pith_short_8: Z7CN75ZV

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/Z7CN75ZVZY5B7CYTS2UMTLSTN3 \
  | 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: cfc4dff735ce3a1f8b1396a8c9ae536edfce6b0b8adb1ec4e44254d3703835ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0441c2570d3e5612cc84776613c97494a8606f620dfa85b5b326cee053589af2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-10-25T18:08:22Z",
    "title_canon_sha256": "f2031c258490fed784c0ef65e4e3641bdf23a9400895989fcbb9001f0e654a0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6931",
    "kind": "arxiv",
    "version": 2
  }
}