Pith Number

pith:NNTXNG5A

pith:2013:NNTXNG5AXGNZ5LYNJBJV3LGYOU

not attested not anchored not stored refs pending

Extremal results in random graphs

Mathias Schacht, Vojt\v{e}ch R\"odl

arxiv:1302.2248 v2 · 2013-02-09 · 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{NNTXNG5AXGNZ5LYNJBJV3LGYOU}

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	2026-05-18T01:20:22.489288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b67769ba0b99b9eaf0d48535dacd8753bb00838a10015a38f3786c0913a7d09

Aliases

arxiv: 1302.2248 · arxiv_version: 1302.2248v2 · doi: 10.48550/arxiv.1302.2248 · pith_short_12: NNTXNG5AXGNZ · pith_short_16: NNTXNG5AXGNZ5LYN · pith_short_8: NNTXNG5A

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/NNTXNG5AXGNZ5LYNJBJV3LGYOU \
  | 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: 6b67769ba0b99b9eaf0d48535dacd8753bb00838a10015a38f3786c0913a7d09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95c4b41b52cc4e3a1ff0cdc058a2329c689f07972b54a13ad67839d4756c548e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-09T17:22:23Z",
    "title_canon_sha256": "10cdf3bb968b687e17e765f9f8718875ffbe37f10918e7ce340688cc13cdc527"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.2248",
    "kind": "arxiv",
    "version": 2
  }
}