Pith Number

pith:WTW6CQC4

pith:2011:WTW6CQC4SD3DO7YMTN2C7YLZ4F

not attested not anchored not stored refs pending

Iwasawa theory and p-adic L-functions over $\mathbf{Z}_p^2$-extensions

David Loeffler, Sarah Livia Zerbes

arxiv:1108.5954 v3 · 2011-08-30 · 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{WTW6CQC4SD3DO7YMTN2C7YLZ4F}

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	2026-05-18T02:32:55.413497Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4ede1405c90f6377f0c9b742fe179e15d884391a597ddfa34d3663b771b1d64

Aliases

arxiv: 1108.5954 · arxiv_version: 1108.5954v3 · doi: 10.48550/arxiv.1108.5954 · pith_short_12: WTW6CQC4SD3D · pith_short_16: WTW6CQC4SD3DO7YM · pith_short_8: WTW6CQC4

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/WTW6CQC4SD3DO7YMTN2C7YLZ4F \
  | 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: b4ede1405c90f6377f0c9b742fe179e15d884391a597ddfa34d3663b771b1d64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdb7256ba42f20dad5eaf4a69c39cc847bba31149d420050e07ea8fb42ec75f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-30T13:18:14Z",
    "title_canon_sha256": "7f1e885a572711e26e65d3026364dba472ee6d63d0fc294e456078a863ea80c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5954",
    "kind": "arxiv",
    "version": 3
  }
}