Pith Number

pith:C4GHEDAJ

pith:2019:C4GHEDAJDBKLDFCM4LOK6QXM6M

not attested not anchored not stored refs pending

Integral factorial ratios: Irreducible examples with height larger than 1

K. Soundararajan

arxiv:1906.06413 v1 · 2019-06-14 · 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{C4GHEDAJDBKLDFCM4LOK6QXM6M}

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.

Cited by

1 paper in Pith

Counting birthday collisions using partitions

Receipt and verification

First computed	2026-07-05T01:14:25.986749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

170c720c091854b1944ce2dcaf42ecf317ad1f12fe0afc7d1763843a20cf71e9

Aliases

arxiv: 1906.06413 · arxiv_version: 1906.06413v1 · doi: 10.48550/arxiv.1906.06413 · pith_short_12: C4GHEDAJDBKL · pith_short_16: C4GHEDAJDBKLDFCM · pith_short_8: C4GHEDAJ

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/C4GHEDAJDBKLDFCM4LOK6QXM6M \
  | 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: 170c720c091854b1944ce2dcaf42ecf317ad1f12fe0afc7d1763843a20cf71e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf84a67ba8b0d6c56fc93f8f78a5acfdc0ecf78fa98d89b5b54728bf539a05b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-06-14T21:40:14Z",
    "title_canon_sha256": "707d25de358ac343de2ed5dccbb5ea586d75a15efb6c45edd97c2ccb04bee5db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.06413",
    "kind": "arxiv",
    "version": 1
  }
}