Pith Number

pith:HBCGMLER

pith:2012:HBCGMLERB7LTDJW6HD5IT7FM3B

not attested not anchored not stored refs pending

On the non-planarity of a random subgraph

Alan Frieze, Michael Krivelevich

arxiv:1205.6240 v3 · 2012-05-29 · 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{HBCGMLERB7LTDJW6HD5IT7FM3B}

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	2026-05-18T03:20:09.869847Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3844662c910fd731a6de38fa89fcacd86a7b1f1e6c4858a4156e8a4fdc224d52

Aliases

arxiv: 1205.6240 · arxiv_version: 1205.6240v3 · doi: 10.48550/arxiv.1205.6240 · pith_short_12: HBCGMLERB7LT · pith_short_16: HBCGMLERB7LTDJW6 · pith_short_8: HBCGMLER

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/HBCGMLERB7LTDJW6HD5IT7FM3B \
  | 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: 3844662c910fd731a6de38fa89fcacd86a7b1f1e6c4858a4156e8a4fdc224d52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a9492c3725bb64d79aa9bb5d4e604e76544968dee9bfd25d36537323a87e82d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-29T00:02:40Z",
    "title_canon_sha256": "c6d35cc83b86c982ba288f6158746d1bae074998fa8657c5a1dff07a2022ba6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.6240",
    "kind": "arxiv",
    "version": 3
  }
}