Pith Number

pith:ZLTG32FJ

pith:2012:ZLTG32FJTTHEPE22O4CW2FDD36

not attested not anchored not stored refs pending

Some Euler-type formulas for planar graphs

Armen Bagdasaryan

arxiv:1207.2345 v1 · 2012-07-10 · cs.DM · 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{ZLTG32FJTTHEPE22O4CW2FDD36}

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	2026-05-18T03:51:24.337139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cae66de8a99cce47935a77056d1463df84c83405a5bed58cd75c012fece77886

Aliases

arxiv: 1207.2345 · arxiv_version: 1207.2345v1 · doi: 10.48550/arxiv.1207.2345 · pith_short_12: ZLTG32FJTTHE · pith_short_16: ZLTG32FJTTHEPE22 · pith_short_8: ZLTG32FJ

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/ZLTG32FJTTHEPE22O4CW2FDD36 \
  | 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: cae66de8a99cce47935a77056d1463df84c83405a5bed58cd75c012fece77886

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "366561e0f8f08209ed46f1e9d7dd5956a49b508676de1bcd13ced8cf5bebc8a3",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-07-10T13:40:06Z",
    "title_canon_sha256": "ad5fed25059c09958266c9ae1f7c3888ca9666603245842ea7a8fb342b3a739f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2345",
    "kind": "arxiv",
    "version": 1
  }
}