Pith Number

pith:OYLQ562G

pith:2015:OYLQ562GRLUCBAKQYAPRUGDXON

not attested not anchored not stored refs pending

Chromatic thresholds in sparse random graphs

Julia B\"ottcher, Peter Allen, Robert Morris, Simon Griffiths, Yoshiharu Kohayakawa

arxiv:1508.03875 v2 · 2015-08-16 · 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{OYLQ562GRLUCBAKQYAPRUGDXON}

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	2026-05-18T01:09:12.669067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76170efb468ae8208150c01f1a1877735753feacc6b85fd1ca359410037cca7c

Aliases

arxiv: 1508.03875 · arxiv_version: 1508.03875v2 · doi: 10.48550/arxiv.1508.03875 · pith_short_12: OYLQ562GRLUC · pith_short_16: OYLQ562GRLUCBAKQ · pith_short_8: OYLQ562G

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/OYLQ562GRLUCBAKQYAPRUGDXON \
  | 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: 76170efb468ae8208150c01f1a1877735753feacc6b85fd1ca359410037cca7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6806ff51c647d1281e142e852d01029464c5e18cb1449989232218ec1d97f7ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-16T22:10:10Z",
    "title_canon_sha256": "29425ded88edf3423d5bc3ee8767b8efa90d70f1556ed4ad1ad8917177c66d16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03875",
    "kind": "arxiv",
    "version": 2
  }
}