Pith Number

pith:KI5T42O4

pith:2016:KI5T42O4EJG25BHQUF7KUYA5US

not attested not anchored not stored refs pending

Blow-up lemmas for sparse graphs

Hiep H\`an, Julia B\"ottcher, Peter Allen, Yoshiharu Kohayakawa, Yury Person

arxiv:1612.00622 v5 · 2016-12-02 · 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{KI5T42O4EJG25BHQUF7KUYA5US}

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.

Cited by

1 paper in Pith

A rainbow blow-up lemma for almost optimally bounded edge-colourings

Receipt and verification

First computed	2026-07-05T12:00:41.271861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

523b3e69dc224dae84f0a17eaa601da48b53e7748922e328a67fe784c10f15e7

Aliases

arxiv: 1612.00622 · arxiv_version: 1612.00622v5 · doi: 10.48550/arxiv.1612.00622 · pith_short_12: KI5T42O4EJG2 · pith_short_16: KI5T42O4EJG25BHQ · pith_short_8: KI5T42O4

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/KI5T42O4EJG25BHQUF7KUYA5US \
  | 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: 523b3e69dc224dae84f0a17eaa601da48b53e7748922e328a67fe784c10f15e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63d70a9674e5e6fc4b63567c255dcc3bfb21a73c75f23f76f37effafd37333ea",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-02T10:30:22Z",
    "title_canon_sha256": "615531780154d07afb4914fd8c7496cbeac74079fb80ac001ae184994ae0ceaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00622",
    "kind": "arxiv",
    "version": 5
  }
}