Pith Number

pith:W4L3OZJL

pith:2012:W4L3OZJLARNZIEOM5KVHR2OUY6

not attested not anchored not stored refs pending

Forbidding Kuratowski Graphs as Immersions

Archontia C. Giannopoulou, Dimitrios M. Thilikos, Marcin Kaminski

arxiv:1207.5329 v1 · 2012-07-23 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4L3OZJLARNZIEOM5KVHR2OUY6}

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	2026-05-18T03:50:23.859725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b717b7652b045b9411cceaaa78e9d4c7aa57a7d8d9401eabadd676bd570c4de9

Aliases

arxiv: 1207.5329 · arxiv_version: 1207.5329v1 · doi: 10.48550/arxiv.1207.5329 · pith_short_12: W4L3OZJLARNZ · pith_short_16: W4L3OZJLARNZIEOM · pith_short_8: W4L3OZJL

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/W4L3OZJLARNZIEOM5KVHR2OUY6 \
  | 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: b717b7652b045b9411cceaaa78e9d4c7aa57a7d8d9401eabadd676bd570c4de9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2cb0845b2d7d0de9e2647e39f0bdfde4c4dd603354a16390e72c7fefced34e0",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-23T09:05:57Z",
    "title_canon_sha256": "734245a483203d374aaf4b3e3aff80212718189a26beddc927bcb3bbe41e7085"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5329",
    "kind": "arxiv",
    "version": 1
  }
}