Pith Number

pith:4SS53NI2

pith:2015:4SS53NI2XO2WQ3YJYYSB64STKH

not attested not anchored not stored refs pending

Excluding A Grid Minor In Planar Digraphs

Neil Robertson, Paul Seymour, Robin Thomas, Thor Johnson

arxiv:1510.00473 v1 · 2015-10-02 · 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{4SS53NI2XO2WQ3YJYYSB64STKH}

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	2026-05-18T01:31:12.973414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4a5ddb51abbb5686f09c6241f725351ca696e610848711dfdf1ca9f1af4c422

Aliases

arxiv: 1510.00473 · arxiv_version: 1510.00473v1 · doi: 10.48550/arxiv.1510.00473 · pith_short_12: 4SS53NI2XO2W · pith_short_16: 4SS53NI2XO2WQ3YJ · pith_short_8: 4SS53NI2

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/4SS53NI2XO2WQ3YJYYSB64STKH \
  | 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: e4a5ddb51abbb5686f09c6241f725351ca696e610848711dfdf1ca9f1af4c422

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "898c4349b1fb2c5f1861443bdad5dfa05962d06045aee86c2eef154a937b9a12",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-10-02T02:34:05Z",
    "title_canon_sha256": "a48e6f228b5678f9177e23d33c97a845d7758f140d91f6f4f42b80e28602efbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00473",
    "kind": "arxiv",
    "version": 1
  }
}