Pith Number

pith:SMKDMG6O

pith:2009:SMKDMG6OO2DYYRSZNQ2Q6V5MKN

not attested not anchored not stored refs pending

More on the phi = beta Conjecture and Eigenvalues of Random Graph Lifts

Doron Puder, Edward Lui

arxiv:0909.1231 v2 · 2009-09-07 · 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{SMKDMG6OO2DYYRSZNQ2Q6V5MKN}

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	2026-05-18T04:34:38.190484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9314361bce76878c46596c350f57ac535aab7d5f2922b1c9b6ee5b295362fddc

Aliases

arxiv: 0909.1231 · arxiv_version: 0909.1231v2 · doi: 10.48550/arxiv.0909.1231 · pith_short_12: SMKDMG6OO2DY · pith_short_16: SMKDMG6OO2DYYRSZ · pith_short_8: SMKDMG6O

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/SMKDMG6OO2DYYRSZNQ2Q6V5MKN \
  | 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: 9314361bce76878c46596c350f57ac535aab7d5f2922b1c9b6ee5b295362fddc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "315ab653cc720d9fc14c5ffbf42b4c2931435b0d1266e9f9f0412a11c2f7ae0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-09-07T12:12:45Z",
    "title_canon_sha256": "b5a242496f2e3e258988e5be9dbb073f239e58938c5bb50dbe3d5f80420d7114"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1231",
    "kind": "arxiv",
    "version": 2
  }
}