Pith Number

pith:7RJY7RXL

pith:2023:7RJY7RXLBOIGQPAG6XC25ZXHDU

not attested not anchored not stored refs pending

Sumsets and entropy revisited

Ben Green, Freddie Manners, Terence Tao

arxiv:2306.13403 v3 · 2023-06-23 · 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{7RJY7RXLBOIGQPAG6XC25ZXHDU}

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	2026-06-03T01:05:02.919837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc538fc6eb0b90683c06f5c5aee6e71d2ce98e8018a229bdb208dfb2775cde63

Aliases

arxiv: 2306.13403 · arxiv_version: 2306.13403v3 · doi: 10.48550/arxiv.2306.13403 · pith_short_12: 7RJY7RXLBOIG · pith_short_16: 7RJY7RXLBOIGQPAG · pith_short_8: 7RJY7RXL

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/7RJY7RXLBOIGQPAG6XC25ZXHDU \
  | 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: fc538fc6eb0b90683c06f5c5aee6e71d2ce98e8018a229bdb208dfb2775cde63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8492deadb272230a73fa7d6011e26a066d287d885cc4ebbac9be5b08e4d0b3e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2023-06-23T09:35:11Z",
    "title_canon_sha256": "a1b453eff67f054bcfacdea1160d8db18ae70656cf32c194c239cc092d697232"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.13403",
    "kind": "arxiv",
    "version": 3
  }
}