Pith Number

pith:PRLP3N7W

pith:2011:PRLP3N7WJ6U36TQYVVIJGE6ISK

not attested not anchored not stored refs pending

Critical slope p-adic L-functions of CM modular forms

Antonio Lei, David Loeffler, Sarah Livia Zerbes

arxiv:1112.5579 v1 · 2011-12-23 · 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{PRLP3N7WJ6U36TQYVVIJGE6ISK}

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	2026-05-18T02:32:55.396062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c56fdb7f64fa9bf4e18ad509313c892bdb01a05d3a5b92b774a52c8faea8183

Aliases

arxiv: 1112.5579 · arxiv_version: 1112.5579v1 · doi: 10.48550/arxiv.1112.5579 · pith_short_12: PRLP3N7WJ6U3 · pith_short_16: PRLP3N7WJ6U36TQY · pith_short_8: PRLP3N7W

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/PRLP3N7WJ6U36TQYVVIJGE6ISK \
  | 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: 7c56fdb7f64fa9bf4e18ad509313c892bdb01a05d3a5b92b774a52c8faea8183

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "463987f3a8f4781dfdaf5f43473d317c53c08acb382eb64bc4001b240218c1dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-23T12:59:43Z",
    "title_canon_sha256": "dca00d5d924c91d662593d08bccfc6199c87caf798cb1c12de596037c3e9eb23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5579",
    "kind": "arxiv",
    "version": 1
  }
}