Pith Number

pith:M4HDI7EJ

pith:2020:M4HDI7EJRCNKZG3DH5RXM3SLTY

not attested not anchored not stored refs pending

The maximal number of $3$-term arithmetic progressions in finite sets in different geometries

Itai Benjamini, Shoni Gilboa

arxiv:2011.04410 v4 · 2020-11-09 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M4HDI7EJRCNKZG3DH5RXM3SLTY}

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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	2026-07-05T05:39:10.089463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

670e347c89889aac9b633f63766e4b9e361cfc46f5b6378d6793b4601d003a8e

Aliases

arxiv: 2011.04410 · arxiv_version: 2011.04410v4 · doi: 10.48550/arxiv.2011.04410 · pith_short_12: M4HDI7EJRCNK · pith_short_16: M4HDI7EJRCNKZG3D · pith_short_8: M4HDI7EJ

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/M4HDI7EJRCNKZG3DH5RXM3SLTY \
  | 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: 670e347c89889aac9b633f63766e4b9e361cfc46f5b6378d6793b4601d003a8e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d0140ac4d695405337cb4f8d48327a88d7a3392c0a07bbc453324002b1eb1c3",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-11-09T13:25:25Z",
    "title_canon_sha256": "e8f7bd415aea3de645abe5f45657644fa412695877598c859fc8555abc671936"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.04410",
    "kind": "arxiv",
    "version": 4
  }
}