Pith Number

pith:LUSHBVJR

pith:2013:LUSHBVJRSCNHR3I4F6TRU7DD6L

not attested not anchored not stored refs pending

On higher congruences between automorphic forms

Kenneth Kramer, Krzysztof Klosin, Tobias Berger

arxiv:1302.2381 v1 · 2013-02-11 · 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{LUSHBVJRSCNHR3I4F6TRU7DD6L}

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	2026-05-18T03:34:01.377285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d2470d531909a78ed1c2fa71a7c63f2c536749e827de7519662dcf75edeb49e

Aliases

arxiv: 1302.2381 · arxiv_version: 1302.2381v1 · doi: 10.48550/arxiv.1302.2381 · pith_short_12: LUSHBVJRSCNH · pith_short_16: LUSHBVJRSCNHR3I4 · pith_short_8: LUSHBVJR

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/LUSHBVJRSCNHR3I4F6TRU7DD6L \
  | 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: 5d2470d531909a78ed1c2fa71a7c63f2c536749e827de7519662dcf75edeb49e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dc8c0067e97e93330890237fc12961b5690f503dd06b3380f6b3a1684b1f88f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-11T00:46:06Z",
    "title_canon_sha256": "622254159df24423e8fcb5ab92b7a79a1a5654fa235f0bd8e48d2b0657d61823"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.2381",
    "kind": "arxiv",
    "version": 1
  }
}