Pith Number

pith:RGQA44IQ

pith:2016:RGQA44IQCLIOGJCO6TBLPQNAPR

not attested not anchored not stored refs pending

Long cycles in locally expanding graphs, with applications

Michael Krivelevich

arxiv:1609.06851 v2 · 2016-09-22 · 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{RGQA44IQCLIOGJCO6TBLPQNAPR}

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	2026-05-18T00:44:15.889835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

89a00e711012d0e3244ef4c2b7c1a07c7a685205b6daab21c373dfac3f50f9e1

Aliases

arxiv: 1609.06851 · arxiv_version: 1609.06851v2 · doi: 10.48550/arxiv.1609.06851 · pith_short_12: RGQA44IQCLIO · pith_short_16: RGQA44IQCLIOGJCO · pith_short_8: RGQA44IQ

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/RGQA44IQCLIOGJCO6TBLPQNAPR \
  | 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: 89a00e711012d0e3244ef4c2b7c1a07c7a685205b6daab21c373dfac3f50f9e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44f5a8e028a7b6c9b3fe8d1b0eca963ad304fd0c052da360bc7961e4d41459c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-22T07:47:32Z",
    "title_canon_sha256": "008bb5f4e7c6ddf3bfe117eedaaca5350aca417453fd08924291c4f092526305"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06851",
    "kind": "arxiv",
    "version": 2
  }
}