Pith Number

pith:Q6OSB33G

pith:2013:Q6OSB33G745X6TZQMOLVX5ZTPQ

not attested not anchored not stored refs pending

Congruences for 9-regular partitions modulo 3

William J. Keith

arxiv:1306.0136 v2 · 2013-06-01 · 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{Q6OSB33G745X6TZQMOLVX5ZTPQ}

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	2026-05-18T03:21:42.970471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

879d20ef66ff3b7f4f3063975bf7337c0e5d9983c4315261460d2e3806698b61

Aliases

arxiv: 1306.0136 · arxiv_version: 1306.0136v2 · doi: 10.48550/arxiv.1306.0136 · pith_short_12: Q6OSB33G745X · pith_short_16: Q6OSB33G745X6TZQ · pith_short_8: Q6OSB33G

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/Q6OSB33G745X6TZQMOLVX5ZTPQ \
  | 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: 879d20ef66ff3b7f4f3063975bf7337c0e5d9983c4315261460d2e3806698b61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a8f6cf25d9c793dfb7751f4fdbf70e3ebf6021218fd3d7c16f76dfc677375e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-01T18:36:33Z",
    "title_canon_sha256": "2c1f86881dc4c0f0085a95d609640e5dccfa807c3cf8ac0a61e67332038acd01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0136",
    "kind": "arxiv",
    "version": 2
  }
}