Pith Number

pith:SGIK2JQO

pith:2012:SGIK2JQOJMKM7FVOXBMHKFWJAE

not attested not anchored not stored refs pending

Multivariable Lubin-Tate (\phi,\Gamma)-modules and filtered \phi-modules

Laurent Berger

arxiv:1211.4431 v2 · 2012-11-19 · 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{SGIK2JQOJMKM7FVOXBMHKFWJAE}

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	2026-05-18T03:27:34.269256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9190ad260e4b14cf96aeb8587516c901021ca012c2b4ba24f78752ac06878d04

Aliases

arxiv: 1211.4431 · arxiv_version: 1211.4431v2 · doi: 10.48550/arxiv.1211.4431 · pith_short_12: SGIK2JQOJMKM · pith_short_16: SGIK2JQOJMKM7FVO · pith_short_8: SGIK2JQO

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/SGIK2JQOJMKM7FVOXBMHKFWJAE \
  | 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: 9190ad260e4b14cf96aeb8587516c901021ca012c2b4ba24f78752ac06878d04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c798585996c4128263cbba71b70272ee449651aadca9c754d9cfdce7d975fd4f",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-11-19T14:19:01Z",
    "title_canon_sha256": "5c2e351cfdc918ec0550efe8921615dcc8b1642abaf646f4a64e64589be0ff8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4431",
    "kind": "arxiv",
    "version": 2
  }
}