Pith Number

pith:QHZ7TN4H

pith:2015:QHZ7TN4HRJOEPQA52ZZ2QS3VB5

not attested not anchored not stored refs pending

A structure theorem for sets of small popular doubling

Przemys{\l}aw Mazur

arxiv:1506.00445 v1 · 2015-06-01 · 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{QHZ7TN4HRJOEPQA52ZZ2QS3VB5}

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	2026-05-18T01:59:54.559960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81f3f9b7878a5c47c01dd673a84b750f6f3537f21be06600635541a2c8fe9587

Aliases

arxiv: 1506.00445 · arxiv_version: 1506.00445v1 · doi: 10.48550/arxiv.1506.00445 · pith_short_12: QHZ7TN4HRJOE · pith_short_16: QHZ7TN4HRJOEPQA5 · pith_short_8: QHZ7TN4H

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/QHZ7TN4HRJOEPQA52ZZ2QS3VB5 \
  | 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: 81f3f9b7878a5c47c01dd673a84b750f6f3537f21be06600635541a2c8fe9587

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70e90f4e6e1e7bf65bbfd1f8af3118802dc43df3b96d594fb036bd073fcf3cc2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-06-01T11:16:08Z",
    "title_canon_sha256": "9b5e4b2a7449f504e09bbe1a72c6d40fa9a07d4e6d2d575732799e7c6ba61aa1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.00445",
    "kind": "arxiv",
    "version": 1
  }
}