Pith Number

pith:CPV756PG

pith:2015:CPV756PGVPLXKRXW46BSGC7ZVN

not attested not anchored not stored refs pending

New representation results for planar graphs

Farhad Shahrokhi

arxiv:1502.06175 v1 · 2015-02-22 · math.CO · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CPV756PGVPLXKRXW46BSGC7ZVN}

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.

Cited by

1 paper in Pith

Short Paths in the Planar Graph Product Structure Theorem

Receipt and verification

First computed	2026-05-18T02:18:31.140331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13ebfef9e6abd77546f6e783230bf9ab7899fa93f6da0a1270a97d914cf56800

Aliases

arxiv: 1502.06175 · arxiv_version: 1502.06175v1 · doi: 10.48550/arxiv.1502.06175 · pith_short_12: CPV756PGVPLX · pith_short_16: CPV756PGVPLXKRXW · pith_short_8: CPV756PG

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/CPV756PGVPLXKRXW46BSGC7ZVN \
  | 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: 13ebfef9e6abd77546f6e783230bf9ab7899fa93f6da0a1270a97d914cf56800

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3ade7caa8362aefb4f4502af5ac816370ddf0c591a1912d03165e3475529561",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-22T04:03:14Z",
    "title_canon_sha256": "78668221b5932c3e42d799ce6ab243c3297909783edd64141799c25d093bb9c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.06175",
    "kind": "arxiv",
    "version": 1
  }
}