Pith Number

pith:HRPEIDKT

pith:2009:HRPEIDKTHYWOK3DZSRWUHT2B5C

not attested not anchored not stored refs pending

The spectrum of random k-lifts of large graphs (with possibly large k)

Roberto Imbuzeiro Oliveira

arxiv:0911.4741 v1 · 2009-11-24 · math.CO · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HRPEIDKTHYWOK3DZSRWUHT2B5C}

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	2026-05-18T04:14:06.018786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c5e440d533e2ce56c79946d43cf41e88654f9317ee747ce9d8fe902f7a5b333

Aliases

arxiv: 0911.4741 · arxiv_version: 0911.4741v1 · doi: 10.48550/arxiv.0911.4741 · pith_short_12: HRPEIDKTHYWO · pith_short_16: HRPEIDKTHYWOK3DZ · pith_short_8: HRPEIDKT

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/HRPEIDKTHYWOK3DZSRWUHT2B5C \
  | 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: 3c5e440d533e2ce56c79946d43cf41e88654f9317ee747ce9d8fe902f7a5b333

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42271f25d3a0e703612c88844831424286bf121464a6cfb307cee361c5c30594",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-11-24T23:52:18Z",
    "title_canon_sha256": "100deca2e64df89c62a7811fcdf2a48f9df27ff5654c72129e1ef09b8f0e28a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4741",
    "kind": "arxiv",
    "version": 1
  }
}