Pith Number

pith:DRYJ4WIS

pith:2022:DRYJ4WIS7E7VPYI3K6VUAXU7S5

not attested not anchored not stored refs pending

Dense minors of graphs with independence number two

Paul Seymour, Sergey Norin

arxiv:2206.00186 v1 · 2022-06-01 · 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{DRYJ4WIS7E7VPYI3K6VUAXU7S5}

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	2026-07-05T04:28:13.871456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c709e5912f93f57e11b57ab405e9f977f500eb0f11561dcac2260256fe46c48

Aliases

arxiv: 2206.00186 · arxiv_version: 2206.00186v1 · doi: 10.48550/arxiv.2206.00186 · pith_short_12: DRYJ4WIS7E7V · pith_short_16: DRYJ4WIS7E7VPYI3 · pith_short_8: DRYJ4WIS

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/DRYJ4WIS7E7VPYI3K6VUAXU7S5 \
  | 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: 1c709e5912f93f57e11b57ab405e9f977f500eb0f11561dcac2260256fe46c48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00b719409b3617985483b3663a9208facbeb3f0f486c42126bc897f4a31b29d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-06-01T02:15:41Z",
    "title_canon_sha256": "b2c767d9688f8ffd936e40f0fe5d16ea8ba1ec6683b70d9db3b3ec68da7c61d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2206.00186",
    "kind": "arxiv",
    "version": 1
  }
}