Pith Number

pith:R4Z6XZVN

pith:2012:R4Z6XZVNSQDGVQ7XPLYC32LN5B

not attested not anchored not stored refs pending

Modularity Lifting Theorems beyond the Taylor-Wiles Method. II

David Geraghty, Frank Calegari

arxiv:1209.6293 v2 · 2012-09-27 · 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{R4Z6XZVNSQDGVQ7XPLYC32LN5B}

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	2026-05-18T00:40:16.690642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f33ebe6ad94066ac3f77af02de96de87670fadbd70c8c17f8f5ba3fb4ce6573

Aliases

arxiv: 1209.6293 · arxiv_version: 1209.6293v2 · doi: 10.48550/arxiv.1209.6293 · pith_short_12: R4Z6XZVNSQDG · pith_short_16: R4Z6XZVNSQDGVQ7X · pith_short_8: R4Z6XZVN

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/R4Z6XZVNSQDGVQ7XPLYC32LN5B \
  | 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: 8f33ebe6ad94066ac3f77af02de96de87670fadbd70c8c17f8f5ba3fb4ce6573

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7fa9c4baa1a46e9c542589ca79fb2b7395128a0d6eaaa9aad21fd3aecb6f12b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-09-27T17:27:17Z",
    "title_canon_sha256": "4275d65622ad007aae948b2a0a0fadbab2c170702364fe64e2b7a502dcfae4e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.6293",
    "kind": "arxiv",
    "version": 2
  }
}