Pith Number

pith:5OPJ77EC

pith:2019:5OPJ77ECUY56S3VFOIUYONZL4I

not attested not anchored not stored refs pending

Note on Fourier expansions at cusps

Fran\c{c}ois Brunault, Michael Neururer

arxiv:1905.02946 v1 · 2019-05-08 · 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{5OPJ77ECUY56S3VFOIUYONZL4I}

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	2026-05-17T23:46:44.948990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb9e9ffc82a63be96ea5722987372be213f45cc76cecee1e177335e2a399c3ae

Aliases

arxiv: 1905.02946 · arxiv_version: 1905.02946v1 · doi: 10.48550/arxiv.1905.02946 · pith_short_12: 5OPJ77ECUY56 · pith_short_16: 5OPJ77ECUY56S3VF · pith_short_8: 5OPJ77EC

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/5OPJ77ECUY56S3VFOIUYONZL4I \
  | 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: eb9e9ffc82a63be96ea5722987372be213f45cc76cecee1e177335e2a399c3ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5fe48f663d7bdade9fc37934796d2649ee0f182599d454ba4d9567c3d50b852",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-05-08T07:43:38Z",
    "title_canon_sha256": "92631e0d2a1406bac60e8765aa88c210ba7d08431abd99890e55015040fe4f02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.02946",
    "kind": "arxiv",
    "version": 1
  }
}