Pith Number

pith:JGWF5OO4

pith:2012:JGWF5OO4FCUTGPNXQ5TVIBGWNY

not attested not anchored not stored refs pending

Modularity Lifting beyond the Taylor-Wiles Method

David Geraghty, Frank Calegari

arxiv:1207.4224 v2 · 2012-07-17 · 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{JGWF5OO4FCUTGPNXQ5TVIBGWNY}

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	2026-05-18T00:40:16.700012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

49ac5eb9dc28a9333db787675404d66e2b379d0ae7a958d31ac8cb4a39a6d68b

Aliases

arxiv: 1207.4224 · arxiv_version: 1207.4224v2 · doi: 10.48550/arxiv.1207.4224 · pith_short_12: JGWF5OO4FCUT · pith_short_16: JGWF5OO4FCUTGPNX · pith_short_8: JGWF5OO4

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/JGWF5OO4FCUTGPNXQ5TVIBGWNY \
  | 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: 49ac5eb9dc28a9333db787675404d66e2b379d0ae7a958d31ac8cb4a39a6d68b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e7035bcd5b3084f5eb3041d7db2211f38f307b739c2cce5c6422578b6c50b4b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-07-17T22:01:45Z",
    "title_canon_sha256": "6d25adec19167e66ca5a51560a381895264d2230c84a972693b8c63288e97b84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4224",
    "kind": "arxiv",
    "version": 2
  }
}