Pith Number

pith:2F6WACSB

pith:2025:2F6WACSBKDGH4NQQDBIPXRJAYX

not attested not anchored not stored refs pending

Additive sumset sizes with tetrahedral differences

Melvyn B. Nathanson

arxiv:2507.08646 v2 · 2025-07-11 · 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{2F6WACSBKDGH4NQQDBIPXRJAYX}

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	2026-07-05T12:00:28.478427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d17d600a4150cc7e36101850fbc520c5c96228de9f0705922993fcddbf30bd84

Aliases

arxiv: 2507.08646 · arxiv_version: 2507.08646v2 · doi: 10.48550/arxiv.2507.08646 · pith_short_12: 2F6WACSBKDGH · pith_short_16: 2F6WACSBKDGH4NQQ · pith_short_8: 2F6WACSB

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/2F6WACSBKDGH4NQQDBIPXRJAYX \
  | 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: d17d600a4150cc7e36101850fbc520c5c96228de9f0705922993fcddbf30bd84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d7a630cae44bbd446b20933cdec2b2ef7c128776cd97a6d2ff979e63bac0b1b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-07-11T14:50:34Z",
    "title_canon_sha256": "4035c71e6b5ace7afd672aeddfdc53be079bcfaba124de048e7335d78a09237c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.08646",
    "kind": "arxiv",
    "version": 2
  }
}