Pith Number

pith:2S7TWFYD

pith:2022:2S7TWFYDI3F2Z7NR7XLSDKKP62

not attested not anchored not stored refs pending

On binomial sums, additive energies, and lazy random walks

Vjekoslav Kova\v{c}

arxiv:2206.01591 v5 · 2022-06-03 · math.CA · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2S7TWFYDI3F2Z7NR7XLSDKKP62}

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	2026-07-05T06:21:12.914977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4bf3b170346cbacfdb1fdd721a94ff6a50e8ab3c639dd1b8c33a1d92d9614d3

Aliases

arxiv: 2206.01591 · arxiv_version: 2206.01591v5 · doi: 10.48550/arxiv.2206.01591 · pith_short_12: 2S7TWFYDI3F2 · pith_short_16: 2S7TWFYDI3F2Z7NR · pith_short_8: 2S7TWFYD

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/2S7TWFYDI3F2Z7NR7XLSDKKP62 \
  | 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: d4bf3b170346cbacfdb1fdd721a94ff6a50e8ab3c639dd1b8c33a1d92d9614d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5c813506c3ab3812948a5590d7793c9e91a189c39a5377389a931edff185017",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2022-06-03T14:21:21Z",
    "title_canon_sha256": "177d9c6efe03f987f2948cca06e695eeb1bc5e98d44e0d46ca3851e0b9ff38b3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2206.01591",
    "kind": "arxiv",
    "version": 5
  }
}