Pith Number

pith:24EXCCKA

pith:2015:24EXCCKAJDGYZ6DG5A7L24GILW

not attested not anchored not stored refs pending

Levels of generalized expansiveness

Jie Li, Ruifeng Zhang

arxiv:1503.03387 v1 · 2015-03-11 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{24EXCCKAJDGYZ6DG5A7L24GILW}

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	2026-05-18T02:25:03.718469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d70971094048cd8cf866e83ebd70c85d9d74431bbef86cd5cb2b329ea046bf57

Aliases

arxiv: 1503.03387 · arxiv_version: 1503.03387v1 · doi: 10.48550/arxiv.1503.03387 · pith_short_12: 24EXCCKAJDGY · pith_short_16: 24EXCCKAJDGYZ6DG · pith_short_8: 24EXCCKA

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/24EXCCKAJDGYZ6DG5A7L24GILW \
  | 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: d70971094048cd8cf866e83ebd70c85d9d74431bbef86cd5cb2b329ea046bf57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4257969e7a50ab29582a85589da6af777762dfbba776bdd6bb04220fc9bdd08d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-03-11T15:50:41Z",
    "title_canon_sha256": "aa9bbdf8e3b1ebbc3822db30156898618dca7aa93a02b1778fe0340f1d351df6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.03387",
    "kind": "arxiv",
    "version": 1
  }
}