Pith Number

pith:ZTOFIJY4

pith:2019:ZTOFIJY4B3AKVSRBVQ4FFHA3LR

not attested not anchored not stored refs pending

Maximally additively reducible subsets of the integers

Gal Gross

arxiv:1908.05220 v1 · 2019-08-14 · 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{ZTOFIJY4B3AKVSRBVQ4FFHA3LR}

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	2026-07-05T09:09:47.743571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccdc54271c0ec0aaca21ac38529c1b5c4ef4fae27b2e6c4b36b8bb00cf2612dd

Aliases

arxiv: 1908.05220 · arxiv_version: 1908.05220v1 · doi: 10.48550/arxiv.1908.05220 · pith_short_12: ZTOFIJY4B3AK · pith_short_16: ZTOFIJY4B3AKVSRB · pith_short_8: ZTOFIJY4

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/ZTOFIJY4B3AKVSRBVQ4FFHA3LR \
  | 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: ccdc54271c0ec0aaca21ac38529c1b5c4ef4fae27b2e6c4b36b8bb00cf2612dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74c34e9c31525a9336326fbb7bad6e9c7130d83b7e17888308aaf78107e3bf4b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-14T16:45:32Z",
    "title_canon_sha256": "7b146f8f9c26ab089cf97c5f2fc50a14c66ac1e8f70d5d957471761005d8b9f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.05220",
    "kind": "arxiv",
    "version": 1
  }
}