Pith Number

pith:DHNXL563

pith:2009:DHNXL563WFJMJBEQXMQ45C5P57

not attested not anchored not stored refs pending

Wach modules and Iwasawa theory for modular forms

Antonio Lei, David Loeffler, Sarah Livia Zerbes

arxiv:0912.1263 v3 · 2009-12-07 · 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{DHNXL563WFJMJBEQXMQ45C5P57}

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	2026-05-18T00:23:21.771205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

19db75f7dbb152c48490bb21ce8bafeff23bfe63ba913c6916da3225b7af8522

Aliases

arxiv: 0912.1263 · arxiv_version: 0912.1263v3 · doi: 10.48550/arxiv.0912.1263 · pith_short_12: DHNXL563WFJM · pith_short_16: DHNXL563WFJMJBEQ · pith_short_8: DHNXL563

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/DHNXL563WFJMJBEQXMQ45C5P57 \
  | 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: 19db75f7dbb152c48490bb21ce8bafeff23bfe63ba913c6916da3225b7af8522

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d436d9e330db0bc055bd660d00d41212f04638e6c77be811b898ec06ea53c4e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-12-07T15:23:47Z",
    "title_canon_sha256": "157662eb580f9a3ff1853bd1b5388efce86b0e35db6a615dcc2f2d1be66214f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1263",
    "kind": "arxiv",
    "version": 3
  }
}