Pith Number

pith:BD434QRP

pith:2010:BD434QRPHLPEWQ4NRWB2CSNFLZ

not attested not anchored not stored refs pending

On the Structure of Sets of Large Doubling

Allison Lewko, Mark Lewko

arxiv:1003.4561 v4 · 2010-03-24 · math.CA · 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{BD434QRPHLPEWQ4NRWB2CSNFLZ}

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	2026-05-18T04:27:47.681919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08f9be422f3ade4b438d8d83a149a55e624e6a946210e0b5d58d523c6c1ad306

Aliases

arxiv: 1003.4561 · arxiv_version: 1003.4561v4 · doi: 10.48550/arxiv.1003.4561 · pith_short_12: BD434QRPHLPE · pith_short_16: BD434QRPHLPEWQ4N · pith_short_8: BD434QRP

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/BD434QRPHLPEWQ4NRWB2CSNFLZ \
  | 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: 08f9be422f3ade4b438d8d83a149a55e624e6a946210e0b5d58d523c6c1ad306

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd1bfa54d2f782186b8f4124c87165d4dd9519ee134dc4bf0a317a82e2839313",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-03-24T00:49:43Z",
    "title_canon_sha256": "b76cc35572fef359e0236c9dfba82dc7f85dc529f556854da4a1ba5ccb826899"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.4561",
    "kind": "arxiv",
    "version": 4
  }
}