Pith Number

pith:N732Z3JM

pith:2026:N732Z3JMP2MQVGVVRH6LK5WBMV

not attested not anchored not stored refs pending

Erd\H{o}s Problem 684 at Density One: Small-prime Parts of Binomial Coefficients and Gaussian Fluctuations

Eric Li (Trinity College, United Kingdom), University of Cambridge

arxiv:2606.08216 v1 · 2026-06-06 · math.NT · 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{N732Z3JMP2MQVGVVRH6LK5WBMV}

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	2026-06-09T01:05:30.326748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ff7aced2c7e990a9ab589fcb576c165452218d26c11cf286a2a692a6f129bcb

Aliases

arxiv: 2606.08216 · arxiv_version: 2606.08216v1 · doi: 10.48550/arxiv.2606.08216 · pith_short_12: N732Z3JMP2MQ · pith_short_16: N732Z3JMP2MQVGVV · pith_short_8: N732Z3JM

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/N732Z3JMP2MQVGVVRH6LK5WBMV \
  | 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: 6ff7aced2c7e990a9ab589fcb576c165452218d26c11cf286a2a692a6f129bcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "294360b8f3d7a5c293beb2ccaedde6a3687a30f0feab732ec71407f0e83128f1",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-06-06T15:10:08Z",
    "title_canon_sha256": "d36ae5d43297e452c0e055a7b81b5dd0b9ba36096f2b0bc3e7e3c92fb8a10f35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08216",
    "kind": "arxiv",
    "version": 1
  }
}