Pith Number

pith:4UZOYOLD

pith:2009:4UZOYOLD74QWLMPKALMGGZQWCC

not attested not anchored not stored refs pending

Modularity lifting theorems for Galois representations of unitary type

Lucio Guerberoff

arxiv:0906.4189 v3 · 2009-06-23 · math.NT · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4UZOYOLD74QWLMPKALMGGZQWCC}

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	2026-05-17T23:53:20.004366Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e532ec3963ff2165b1ea02d863661610af78f1dca9be8c6080413c19e929e406

Aliases

arxiv: 0906.4189 · arxiv_version: 0906.4189v3 · doi: 10.48550/arxiv.0906.4189 · pith_short_12: 4UZOYOLD74QW · pith_short_16: 4UZOYOLD74QWLMPK · pith_short_8: 4UZOYOLD

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/4UZOYOLD74QWLMPKALMGGZQWCC \
  | 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: e532ec3963ff2165b1ea02d863661610af78f1dca9be8c6080413c19e929e406

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c554f3a5131bf0e5b48556587d43562eac488f9e0c95d5335599c5d831a42cb",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-06-23T08:26:31Z",
    "title_canon_sha256": "ba13896b70efaa26513954aa7b023976ede95f83d64e2d108fbbcc144c0df960"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.4189",
    "kind": "arxiv",
    "version": 3
  }
}