Pith Number

pith:PGGTPCSE

pith:2026:PGGTPCSE6DTJUXOBDFMCB6X6OS

not attested not anchored not stored refs pending

Decay of weighted cusp counts for congruence subgroups of $SL_2$ over number fields

Shengyuan Zhao

arxiv:2605.17972 v1 · 2026-05-18 · math.NT · math.AG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PGGTPCSE6DTJUXOBDFMCB6X6OS}

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	2026-05-20T00:05:08.830922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

798d378a44f0e69a5dc1195820fafe74b3d1f04ec75cd87c1a89579061ade484

Aliases

arxiv: 2605.17972 · arxiv_version: 2605.17972v1 · doi: 10.48550/arxiv.2605.17972 · pith_short_12: PGGTPCSE6DTJ · pith_short_16: PGGTPCSE6DTJUXOB · pith_short_8: PGGTPCSE

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/PGGTPCSE6DTJUXOBDFMCB6X6OS \
  | 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: 798d378a44f0e69a5dc1195820fafe74b3d1f04ec75cd87c1a89579061ade484

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87785bc4ea52e098c04f957bd0a0a505ddc180ced07240cd5f032dab677a39ce",
    "cross_cats_sorted": [
      "math.AG",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-18T07:28:15Z",
    "title_canon_sha256": "dd09233648eab1ccaba66de74055b12929e9fe59c7d700baa9de276dbca11a37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17972",
    "kind": "arxiv",
    "version": 1
  }
}