Pith Number

pith:RPALQFQW

pith:2015:RPALQFQWH3K62W6S4JVVQUTRLF

not attested not anchored not stored refs pending

Cyclic Critical Groups of Graphs

Darren Glass, Ryan Becker

arxiv:1504.05939 v1 · 2015-04-22 · 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{RPALQFQWH3K62W6S4JVVQUTRLF}

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	2026-05-18T02:18:04.665544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8bc0b816163ed5ed5bd2e26b5852715963e81212415e37e6f8337ac817a58881

Aliases

arxiv: 1504.05939 · arxiv_version: 1504.05939v1 · doi: 10.48550/arxiv.1504.05939 · pith_short_12: RPALQFQWH3K6 · pith_short_16: RPALQFQWH3K62W6S · pith_short_8: RPALQFQW

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/RPALQFQWH3K62W6S4JVVQUTRLF \
  | 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: 8bc0b816163ed5ed5bd2e26b5852715963e81212415e37e6f8337ac817a58881

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "269c293ac3e9348a2b67922bb716de07d5ad5e5bdfa4d69b1f57c74a604ca1e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-04-22T19:45:32Z",
    "title_canon_sha256": "b05e8c365c02ffc8394fdc452727472552985a7a409d359616370bf29ed16c7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05939",
    "kind": "arxiv",
    "version": 1
  }
}