Pith Number

pith:IMZW4FNU

pith:2019:IMZW4FNUH4YO7YBMJHOJ7N2JW6

not attested not anchored not stored refs pending

Odd cycles in subgraphs of sparse pseudorandom graphs

Joonkyung Lee, Mathias Schacht, S\"oren Berger

arxiv:1906.05100 v1 · 2019-06-12 · 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{IMZW4FNUH4YO7YBMJHOJ7N2JW6}

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	2026-05-17T23:43:29.485944Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43336e15b43f30efe02c49dc9fb749b79c9db0e6d6e6af2437db24394d83cd0f

Aliases

arxiv: 1906.05100 · arxiv_version: 1906.05100v1 · doi: 10.48550/arxiv.1906.05100 · pith_short_12: IMZW4FNUH4YO · pith_short_16: IMZW4FNUH4YO7YBM · pith_short_8: IMZW4FNU

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/IMZW4FNUH4YO7YBMJHOJ7N2JW6 \
  | 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: 43336e15b43f30efe02c49dc9fb749b79c9db0e6d6e6af2437db24394d83cd0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c047fceda4bdf9bf2b51504496fe9169fb5e5faa0f38cfb9af74228da46bf63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-06-12T12:55:45Z",
    "title_canon_sha256": "24b5b6b78cba9cff67c88a39910500972eb6b65b09e7728736eb688b405594b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.05100",
    "kind": "arxiv",
    "version": 1
  }
}