Pith Number

pith:CNUUP2ND

pith:2018:CNUUP2NDLOU25S2MSHVKXBKDHG

not attested not anchored not stored refs pending

Ramanujan's theta functions and linear combinations of three triangular numbers

Zhi-Hong Sun

arxiv:1812.03820 v2 · 2018-11-26 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CNUUP2NDLOU25S2MSHVKXBKDHG}

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	2026-05-17T23:58:35.554617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

136947e9a35ba9aecb4c91eaab8543398bcf10e848ba762fd661b736d9b72af8

Aliases

arxiv: 1812.03820 · arxiv_version: 1812.03820v2 · doi: 10.48550/arxiv.1812.03820 · pith_short_12: CNUUP2NDLOU2 · pith_short_16: CNUUP2NDLOU25S2M · pith_short_8: CNUUP2ND

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/CNUUP2NDLOU25S2MSHVKXBKDHG \
  | 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: 136947e9a35ba9aecb4c91eaab8543398bcf10e848ba762fd661b736d9b72af8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26ff87498f06a18b3ac8b32839dc722076548bdc619daa21b334506a98eccbc5",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-11-26T14:12:11Z",
    "title_canon_sha256": "cb42c1ee6db92a238f3d68ae5ab983c19bc0dee18bbcebaee67a61160912f8c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.03820",
    "kind": "arxiv",
    "version": 2
  }
}