Pith Number

pith:52UWUMGR

pith:2023:52UWUMGRUSODY4KNLLFTPL4324

not attested not anchored not stored refs pending

Distinguishing graphs by their spectra, Smith normal forms and complements

Aida Abiad, Carlos A. Alfaro, Ralihe R. Villagr\'an

arxiv:2304.07217 v1 · 2023-04-14 · 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{52UWUMGRUSODY4KNLLFTPL4324}

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	2026-07-05T06:01:06.808880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eea96a30d1a49c3c714d5acb37af9bd7164a54227b5e5c6006cf902b3e0347b8

Aliases

arxiv: 2304.07217 · arxiv_version: 2304.07217v1 · doi: 10.48550/arxiv.2304.07217 · pith_short_12: 52UWUMGRUSOD · pith_short_16: 52UWUMGRUSODY4KN · pith_short_8: 52UWUMGR

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/52UWUMGRUSODY4KNLLFTPL4324 \
  | 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: eea96a30d1a49c3c714d5acb37af9bd7164a54227b5e5c6006cf902b3e0347b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec437c20cf975b07d1153776e20f4d190edf373aee6fb2ba1aa4c1090761720e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-04-14T15:58:03Z",
    "title_canon_sha256": "a1bffbe85ecb6c3e0aed06329e897060ed5c4f3ed319d775b445d072e08f2982"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.07217",
    "kind": "arxiv",
    "version": 1
  }
}