Pith Number

pith:YTJ47UHY

pith:2010:YTJ47UHYXLOOGA6BDPRBPVX54R

not attested not anchored not stored refs pending

Cycles in Sparse Graphs II

Benny Sudakov, Jacques Verstraete

arxiv:1010.5309 v1 · 2010-10-26 · 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{YTJ47UHYXLOOGA6BDPRBPVX54R}

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	2026-05-18T04:38:39.042276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4d3cfd0f8badce303c11be217d6fde4753ac799e258a80f3ceb65bedc9bfb9f

Aliases

arxiv: 1010.5309 · arxiv_version: 1010.5309v1 · doi: 10.48550/arxiv.1010.5309 · pith_short_12: YTJ47UHYXLOO · pith_short_16: YTJ47UHYXLOOGA6B · pith_short_8: YTJ47UHY

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/YTJ47UHYXLOOGA6BDPRBPVX54R \
  | 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: c4d3cfd0f8badce303c11be217d6fde4753ac799e258a80f3ceb65bedc9bfb9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b39391a0e2d2f1a3b6c4af1a22a17dd39e6959cd45ca93953a1579fa76084d96",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-10-26T03:42:58Z",
    "title_canon_sha256": "d00e436bf923a5094a0d3ee7062effd42b6e0a3497340387cfe2a0fc7b1ca870"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.5309",
    "kind": "arxiv",
    "version": 1
  }
}