Pith Number

pith:KIAZRT7D

pith:2016:KIAZRT7DZTBG5PJZMIRTS6ODCO

not attested not anchored not stored refs pending

Many cliques in $H$-free subgraphs of random graphs

Alexandr Kostochka, Clara Shikhelman, Noga Alon

arxiv:1612.09143 v2 · 2016-12-29 · 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{KIAZRT7DZTBG5PJZMIRTS6ODCO}

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	2026-05-18T00:30:17.282500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

520198cfe3ccc26ebd3962233979c313b567a7909414c8fe4776cb4c7a2a157e

Aliases

arxiv: 1612.09143 · arxiv_version: 1612.09143v2 · doi: 10.48550/arxiv.1612.09143 · pith_short_12: KIAZRT7DZTBG · pith_short_16: KIAZRT7DZTBG5PJZ · pith_short_8: KIAZRT7D

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/KIAZRT7DZTBG5PJZMIRTS6ODCO \
  | 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: 520198cfe3ccc26ebd3962233979c313b567a7909414c8fe4776cb4c7a2a157e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bab34b71f432f9263e9a8acf395a8d07c491af49a8209d5355f2914d001d27c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-29T13:49:27Z",
    "title_canon_sha256": "615ca875b92b94875d77e4ae8c37226dad854c0e2270e4fc33e887b6e5d6e761"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09143",
    "kind": "arxiv",
    "version": 2
  }
}