Pith Number

pith:O32RUDQB

pith:2016:O32RUDQB52LT67NDULS2GLH2YA

not attested not anchored not stored refs pending

Expected values of parameters associated with the minimum rank of a graph

Bryan Shader, Leslie Hogben, Ryan R. Martin, Tracy Hall

arxiv:1605.05692 v2 · 2016-05-18 · 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{O32RUDQB52LT67NDULS2GLH2YA}

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	2026-05-18T01:14:12.049001Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76f51a0e01ee973f7da3a2e5a32cfac03f570543c02d7b9cb2b1533b6cec890e

Aliases

arxiv: 1605.05692 · arxiv_version: 1605.05692v2 · doi: 10.48550/arxiv.1605.05692 · pith_short_12: O32RUDQB52LT · pith_short_16: O32RUDQB52LT67ND · pith_short_8: O32RUDQB

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/O32RUDQB52LT67NDULS2GLH2YA \
  | 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: 76f51a0e01ee973f7da3a2e5a32cfac03f570543c02d7b9cb2b1533b6cec890e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b7f7784a96f90c2129eab6300473a8783df5841efe2a30260dc86b10730d41f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-05-18T18:43:32Z",
    "title_canon_sha256": "f1c3a7e72dcdf84af76c53f3b71293ee4e521744585a30e56894bc78df8bdfe4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.05692",
    "kind": "arxiv",
    "version": 2
  }
}