Pith Number

pith:4CXGYPXN

pith:2012:4CXGYPXNOXMWONJKFMWRCHFBBE

not attested not anchored not stored refs pending

Explicit constructions of extractors and expanders

Fran\c{c}ois Hennecart, Norbert Hegyv\'ari

arxiv:1206.1146 v1 · 2012-06-06 · math.NT · 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{4CXGYPXNOXMWONJKFMWRCHFBBE}

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	2026-05-18T01:57:07.257860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0ae6c3eed75d967352a2b2d111ca10930021a3330be3fe6d8bc824597064005

Aliases

arxiv: 1206.1146 · arxiv_version: 1206.1146v1 · doi: 10.48550/arxiv.1206.1146 · pith_short_12: 4CXGYPXNOXMW · pith_short_16: 4CXGYPXNOXMWONJK · pith_short_8: 4CXGYPXN

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/4CXGYPXNOXMWONJKFMWRCHFBBE \
  | 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: e0ae6c3eed75d967352a2b2d111ca10930021a3330be3fe6d8bc824597064005

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5584529406314b056868d5f48dcedaeae06ecaeecadcae1a51fb70b4f0965cc7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-06-06T08:32:33Z",
    "title_canon_sha256": "6590bc177c3e8e733d60721dd38f819ee038176c47efef3ef0b6bf530395ca86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1146",
    "kind": "arxiv",
    "version": 1
  }
}