Pith Number

pith:YYJEBKKN

pith:2018:YYJEBKKN6XEB2LJIB4TOQ3XZIN

not attested not anchored not stored refs pending

Congruences Modulo Powers of 3 for 3- and 9-Colored Generalized Frobenius Partitions

Liuquan Wang

arxiv:1801.07949 v1 · 2018-01-24 · math.CO · 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{YYJEBKKN6XEB2LJIB4TOQ3XZIN}

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	2026-05-18T00:25:10.478878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c61240a94df5c81d2d280f26e86ef9437a6d7e9970d52c66901d292c17977dd6

Aliases

arxiv: 1801.07949 · arxiv_version: 1801.07949v1 · doi: 10.48550/arxiv.1801.07949 · pith_short_12: YYJEBKKN6XEB · pith_short_16: YYJEBKKN6XEB2LJI · pith_short_8: YYJEBKKN

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/YYJEBKKN6XEB2LJIB4TOQ3XZIN \
  | 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: c61240a94df5c81d2d280f26e86ef9437a6d7e9970d52c66901d292c17977dd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1b7cc208c2078899658e860a501c09ada00dcd9c3a58175e86a134587d024ac",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-01-24T12:12:38Z",
    "title_canon_sha256": "422ae279e489e71f7aacdc2f1c55caa63e800ed9283094db749b9fab4aacc8b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.07949",
    "kind": "arxiv",
    "version": 1
  }
}