Pith Number

pith:CO5RA7PT

pith:2016:CO5RA7PT3V4AHRXTYB4FQRVQNJ

not attested not anchored not stored refs pending

On the Density of non-Simple 3-Planar Graphs

Chrysanthi N. Raftopoulou, Michael A. Bekos, Michael Kaufmann

arxiv:1602.04995 v3 · 2016-02-16 · cs.CG · cs.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{CO5RA7PT3V4AHRXTYB4FQRVQNJ}

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	2026-05-18T01:07:20.861462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13bb107df3dd7803c6f3c0785846b06a7737a31bc2193526d8edb694b73d4ab7

Aliases

arxiv: 1602.04995 · arxiv_version: 1602.04995v3 · doi: 10.48550/arxiv.1602.04995 · pith_short_12: CO5RA7PT3V4A · pith_short_16: CO5RA7PT3V4AHRXT · pith_short_8: CO5RA7PT

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/CO5RA7PT3V4AHRXTYB4FQRVQNJ \
  | 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: 13bb107df3dd7803c6f3c0785846b06a7737a31bc2193526d8edb694b73d4ab7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a1fdd12118935a13ad75c17c36aa3c7828972c4016ed86ea1dc3836412fb40f",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2016-02-16T11:45:25Z",
    "title_canon_sha256": "39de28c4f3fe23d519a0ddd249437b7ad9add93aa7b0bc6f01d958d8f6d81237"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.04995",
    "kind": "arxiv",
    "version": 3
  }
}