Pith Number

pith:ZV4UYGCX

pith:2015:ZV4UYGCX77RFBIAP6TLE2LO3UA

not attested not anchored not stored refs pending

Thickness and Outerthickness for Embedded Graphs

Baogang Xu, Xiaoya Zha

arxiv:1512.04995 v1 · 2015-12-15 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZV4UYGCX77RFBIAP6TLE2LO3UA}

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	2026-05-18T01:24:13.783625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd794c1857ffe250a00ff4d64d2ddba01f420c9b18793e5bd75b6f139a0ba1c3

Aliases

arxiv: 1512.04995 · arxiv_version: 1512.04995v1 · doi: 10.48550/arxiv.1512.04995 · pith_short_12: ZV4UYGCX77RF · pith_short_16: ZV4UYGCX77RFBIAP · pith_short_8: ZV4UYGCX

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/ZV4UYGCX77RFBIAP6TLE2LO3UA \
  | 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: cd794c1857ffe250a00ff4d64d2ddba01f420c9b18793e5bd75b6f139a0ba1c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dad47a59bf52d5173dfe7c504036f3b8c9c2da7500cedae51b137e435c27e509",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-15T22:32:40Z",
    "title_canon_sha256": "aa9adb99f3f2d3fce64a2c477357b2a3cd771d9e6d7a2c83c7ddba94266b15a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04995",
    "kind": "arxiv",
    "version": 1
  }
}