Pith Number

pith:I6N5ZSNP

pith:2015:I6N5ZSNPFQ6MM73KSX2LZMHJWJ

not attested not anchored not stored refs pending

Ramanujan-type Congruences for $\ell$-Regular Partitions Modulo $3, 5, 11$ and $13$

Hai-Tao Jin, Li Zhang

arxiv:1509.07591 v1 · 2015-09-25 · 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{I6N5ZSNPFQ6MM73KSX2LZMHJWJ}

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	2026-05-18T01:32:02.411440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

479bdcc9af2c3cc67f6a95f4bcb0e9b252647dd1f7dab2aec76f174a3cdf352d

Aliases

arxiv: 1509.07591 · arxiv_version: 1509.07591v1 · doi: 10.48550/arxiv.1509.07591 · pith_short_12: I6N5ZSNPFQ6M · pith_short_16: I6N5ZSNPFQ6MM73K · pith_short_8: I6N5ZSNP

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/I6N5ZSNPFQ6MM73KSX2LZMHJWJ \
  | 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: 479bdcc9af2c3cc67f6a95f4bcb0e9b252647dd1f7dab2aec76f174a3cdf352d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "021c456035dd5645ebb75a63d1d3de88340fc51688bc68c98f987ed0fb53655a",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-25T05:42:40Z",
    "title_canon_sha256": "22458bd0a1824855915c584905b3eae2fbe3cd6550cd10f5800eaa4024e5aed3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.07591",
    "kind": "arxiv",
    "version": 1
  }
}