Pith Number

pith:M7UXW6B6

pith:2022:M7UXW6B6APYWCCBHUOCA7GIKEK

not attested not anchored not stored refs pending

A $p$-adic approach to the existence of level-raising congruences

Jack A. Thorne

arxiv:2212.03591 v2 · 2022-12-07 · 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{M7UXW6B6APYWCCBHUOCA7GIKEK}

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.

Cited by

1 paper in Pith

A Decade of Deep Learning: A Survey on The Magnificent Seven

Receipt and verification

First computed	2026-07-05T07:47:00.145016Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67e97b783e03f1610827a3840f990a22a05718d6dbc3016e4ee9f8de4e162840

Aliases

arxiv: 2212.03591 · arxiv_version: 2212.03591v2 · doi: 10.48550/arxiv.2212.03591 · pith_short_12: M7UXW6B6APYW · pith_short_16: M7UXW6B6APYWCCBH · pith_short_8: M7UXW6B6

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/M7UXW6B6APYWCCBHUOCA7GIKEK \
  | 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: 67e97b783e03f1610827a3840f990a22a05718d6dbc3016e4ee9f8de4e162840

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6639f66de94998d67368937e33579a48abe9a498940355b506dcbb1baec0550f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-12-07T12:12:04Z",
    "title_canon_sha256": "ea2684a9007116120cc2dad55b4033a6791c491df22c4a411e704849611a7e97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.03591",
    "kind": "arxiv",
    "version": 2
  }
}