Pith Number

pith:QEJYQKH2

pith:2019:QEJYQKH2XF7YDMFFR4STGMRYJ7

not attested not anchored not stored refs pending

Congruences involving the $U_{\ell}$ operator for weakly holomorphic modular forms

Dohoon Choi, Subong Lim

arxiv:1902.06456 v1 · 2019-02-18 · 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{QEJYQKH2XF7YDMFFR4STGMRYJ7}

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	2026-05-17T23:53:45.422234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81138828fab97f81b0a58f253332384fd746f262cfddbb30615690bc59899190

Aliases

arxiv: 1902.06456 · arxiv_version: 1902.06456v1 · doi: 10.48550/arxiv.1902.06456 · pith_short_12: QEJYQKH2XF7Y · pith_short_16: QEJYQKH2XF7YDMFF · pith_short_8: QEJYQKH2

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/QEJYQKH2XF7YDMFFR4STGMRYJ7 \
  | 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: 81138828fab97f81b0a58f253332384fd746f262cfddbb30615690bc59899190

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09e6643f43ff7a1f35734852fcd9f0623ece308cbca5f66b5e2acfacce568061",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-02-18T08:31:49Z",
    "title_canon_sha256": "374a9bcfe61fbe4c49362ae04cbe7e19b7caee10e228dc41816d875d37a652a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.06456",
    "kind": "arxiv",
    "version": 1
  }
}