Pith Number

pith:SO3BOOSR

pith:2012:SO3BOOSRFL3R3Z6FGM4DAMPAJC

not attested not anchored not stored refs pending

Spectra of subdivision-vertex join and subdivision-edge join of two graphs

Xiaogang Liu, Zuhe Zhang

arxiv:1212.0619 v4 · 2012-12-04 · 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{SO3BOOSRFL3R3Z6FGM4DAMPAJC}

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	2026-05-17T23:55:43.596289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93b6173a512af71de7c533383031e0488def5318656f6d1ec60a58c21501d585

Aliases

arxiv: 1212.0619 · arxiv_version: 1212.0619v4 · doi: 10.48550/arxiv.1212.0619 · pith_short_12: SO3BOOSRFL3R · pith_short_16: SO3BOOSRFL3R3Z6F · pith_short_8: SO3BOOSR

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/SO3BOOSRFL3R3Z6FGM4DAMPAJC \
  | 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: 93b6173a512af71de7c533383031e0488def5318656f6d1ec60a58c21501d585

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a91b41a71dc3b41a2f4603cc45a489f8ef348bf19d4b77c5ba8e72cef1b759c4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-04T06:13:21Z",
    "title_canon_sha256": "e9de9a129f8439c7751e5339c9ac5020cb56d1e8b394a2cb42aff00bc6f84527"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0619",
    "kind": "arxiv",
    "version": 4
  }
}