Pith Number

pith:ZNIKVSCM

pith:2013:ZNIKVSCM2ELVTJ6XF7VC4JDG3A

not attested not anchored not stored refs pending

Congruences for Ramanujan's f and {\omega} functions via generalized Borcherds products

Abel Castillo, Chongli Wang, Jen Berg, Richard Moy, Robert Grizzard, V\'it\v{e}zslav Kala

arxiv:1308.3454 v1 · 2013-08-15 · 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{ZNIKVSCM2ELVTJ6XF7VC4JDG3A}

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	2026-05-18T02:30:32.539255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb50aac84cd11759a7d72fea2e2466d825009cc7f1dc36754e2f90a97fb3987f

Aliases

arxiv: 1308.3454 · arxiv_version: 1308.3454v1 · doi: 10.48550/arxiv.1308.3454 · pith_short_12: ZNIKVSCM2ELV · pith_short_16: ZNIKVSCM2ELVTJ6X · pith_short_8: ZNIKVSCM

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/ZNIKVSCM2ELVTJ6XF7VC4JDG3A \
  | 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: cb50aac84cd11759a7d72fea2e2466d825009cc7f1dc36754e2f90a97fb3987f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93762a5fa0f0713f3b195946cc2773d49d129c1968e6fc9b103dc46abf595d29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-08-15T16:49:20Z",
    "title_canon_sha256": "a51919414465ee67db4cce2de8ce6321e2f51c781a3d190bc4325076efdbedf1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3454",
    "kind": "arxiv",
    "version": 1
  }
}