Pith Number

pith:QQDWDIFN

pith:2011:QQDWDIFNKHZ4KDINKNSEYPMR2I

not attested not anchored not stored refs pending

A note on control theorems for quaternionic Hida families of modular forms

Matteo Longo, Stefano Vigni

arxiv:1110.1977 v1 · 2011-10-10 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QQDWDIFNKHZ4KDINKNSEYPMR2I}

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	2026-05-18T04:11:19.198151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

840761a0ad51f3c50d0d53644c3d91d21859e011ba65c666a5ea4381122f6c91

Aliases

arxiv: 1110.1977 · arxiv_version: 1110.1977v1 · doi: 10.48550/arxiv.1110.1977 · pith_short_12: QQDWDIFNKHZ4 · pith_short_16: QQDWDIFNKHZ4KDIN · pith_short_8: QQDWDIFN

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/QQDWDIFNKHZ4KDINKNSEYPMR2I \
  | 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: 840761a0ad51f3c50d0d53644c3d91d21859e011ba65c666a5ea4381122f6c91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ee61818046563434fb66b1d7576cea7e3bd7502e165a9c9c9042637b02c4480",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-10-10T09:53:13Z",
    "title_canon_sha256": "5cf1e9c7a60c59a66ff70575e775f5cff128440ebcc8347813a5d73932e9f0f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1977",
    "kind": "arxiv",
    "version": 1
  }
}