Pith Number

pith:KGQJR3ET

pith:2015:KGQJR3ET7QYK5PL4XTCB5GDYQI

not attested not anchored not stored refs pending

A structure theorem for sets of small popular doubling, revisited

Przemys{\l}aw Mazur

arxiv:1506.00448 v1 · 2015-06-01 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KGQJR3ET7QYK5PL4XTCB5GDYQI}

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	2026-05-18T01:59:54.547230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51a098ec93fc30aebd7cbcc41e98788237fe4a5529205dd6bce758fba344d9d2

Aliases

arxiv: 1506.00448 · arxiv_version: 1506.00448v1 · doi: 10.48550/arxiv.1506.00448 · pith_short_12: KGQJR3ET7QYK · pith_short_16: KGQJR3ET7QYK5PL4 · pith_short_8: KGQJR3ET

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/KGQJR3ET7QYK5PL4XTCB5GDYQI \
  | 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: 51a098ec93fc30aebd7cbcc41e98788237fe4a5529205dd6bce758fba344d9d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29bfb13f77db21c9c6c09cb753ac63c252bdb6defa1c52035b723f9921f72564",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-06-01T11:20:18Z",
    "title_canon_sha256": "27b1fc0361dfe5286294e5c3323f5d04c01d707b82ffede84ba2cc445b8e5531"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.00448",
    "kind": "arxiv",
    "version": 1
  }
}