Pith Number

pith:JKTLFNNE

pith:2016:JKTLFNNEX5Z3S7DRYHLSQCOUJG

not attested not anchored not stored refs pending

The number of subsets of integers with no $k$-term arithmetic progression

Hong Liu, J\'ozsef Balogh, Maryam Sharifzadeh

arxiv:1605.03172 v1 · 2016-05-10 · 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{JKTLFNNEX5Z3S7DRYHLSQCOUJG}

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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	2026-05-18T01:15:07.340497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4aa6b2b5a4bf73b97c71c1d72809d449a2b83cbfb04ac2c3f9d7fbaa0f71d71b

Aliases

arxiv: 1605.03172 · arxiv_version: 1605.03172v1 · doi: 10.48550/arxiv.1605.03172 · pith_short_12: JKTLFNNEX5Z3 · pith_short_16: JKTLFNNEX5Z3S7DR · pith_short_8: JKTLFNNE

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/JKTLFNNEX5Z3S7DRYHLSQCOUJG \
  | 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: 4aa6b2b5a4bf73b97c71c1d72809d449a2b83cbfb04ac2c3f9d7fbaa0f71d71b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fea8be0322247c87eb624548754eaf695001de1c0ba840520e0b02ff942e61b9",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-05-10T19:53:26Z",
    "title_canon_sha256": "8770640eea5e4f5d85d6c16a1d111f1f1533254b51caa859900282305e9ce484"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.03172",
    "kind": "arxiv",
    "version": 1
  }
}