Pith Number

pith:AEBZWW7B

pith:2011:AEBZWW7BXLQNYHFFLZAGY57RTQ

not attested not anchored not stored refs pending

Beyond the Expanders

Marianna Bolla

arxiv:1101.5926 v2 · 2011-01-31 · math.CO · stat.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AEBZWW7BXLQNYHFFLZAGY57RTQ}

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	2026-05-18T04:27:27.860371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01039b5be1bae0dc1ca55e406c77f19c1140ba1431f5df3e5a3df5e23fe6d17a

Aliases

arxiv: 1101.5926 · arxiv_version: 1101.5926v2 · doi: 10.48550/arxiv.1101.5926 · pith_short_12: AEBZWW7BXLQN · pith_short_16: AEBZWW7BXLQNYHFF · pith_short_8: AEBZWW7B

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/AEBZWW7BXLQNYHFFLZAGY57RTQ \
  | 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: 01039b5be1bae0dc1ca55e406c77f19c1140ba1431f5df3e5a3df5e23fe6d17a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cf65b760b9a6e98be05bad12c6dd8038f007d22fbd6f414a72c263260d7277f",
    "cross_cats_sorted": [
      "stat.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-01-31T11:54:54Z",
    "title_canon_sha256": "dbb2eaa78aa4b193e322323eb4c8554e2ba147b951c7687a4293c6347b31e224"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5926",
    "kind": "arxiv",
    "version": 2
  }
}