Pith Number

pith:CNFSHWV3

pith:2015:CNFSHWV353SFKQ4LJLOPW7Z2HL

not attested not anchored not stored refs pending

Explicit Formulas for Partition Pairs and Triples with 3-Cores

Liuquan Wang

arxiv:1507.03099 v1 · 2015-07-11 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CNFSHWV353SFKQ4LJLOPW7Z2HL}

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	2026-05-18T01:36:59.700865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

134b23dabbeee455438b4adcfb7f3a3adefbd036a57cd52dfdd40fa0b1d7bd7b

Aliases

arxiv: 1507.03099 · arxiv_version: 1507.03099v1 · doi: 10.48550/arxiv.1507.03099 · pith_short_12: CNFSHWV353SF · pith_short_16: CNFSHWV353SFKQ4L · pith_short_8: CNFSHWV3

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/CNFSHWV353SFKQ4LJLOPW7Z2HL \
  | 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: 134b23dabbeee455438b4adcfb7f3a3adefbd036a57cd52dfdd40fa0b1d7bd7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c236f9cfc79e24d20418c4395b3b93119c7f9dd0057f5be0790b6d2544262af",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-07-11T11:45:54Z",
    "title_canon_sha256": "ace6e36997fa2f1748d4b0ab459c7910dd4ea10183d2160a10648c18c4e43c81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03099",
    "kind": "arxiv",
    "version": 1
  }
}