Pith Number

pith:ZGZZLV4L

pith:2017:ZGZZLV4LOOZVY7VPPFY6CCWA32

not attested not anchored not stored refs pending

A Dirichlet approximation theorem for group actions

Clayton Petsche, Jeffrey D. Vaaler

arxiv:1705.00562 v2 · 2017-05-01 · 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{ZGZZLV4LOOZVY7VPPFY6CCWA32}

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	2026-05-18T00:16:03.217096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9b395d78b73b35c7eaf7971e10ac0dea5a06ea59ab131d2a96a2006b6276f1b

Aliases

arxiv: 1705.00562 · arxiv_version: 1705.00562v2 · doi: 10.48550/arxiv.1705.00562 · pith_short_12: ZGZZLV4LOOZV · pith_short_16: ZGZZLV4LOOZVY7VP · pith_short_8: ZGZZLV4L

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/ZGZZLV4LOOZVY7VPPFY6CCWA32 \
  | 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: c9b395d78b73b35c7eaf7971e10ac0dea5a06ea59ab131d2a96a2006b6276f1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9147ebfe8d168f16493bdb7247b370edfe2ac907759aa4498a998607477b2e6d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-05-01T15:28:48Z",
    "title_canon_sha256": "376d4924d0d659cdec9e478b0c86ea44f7990e181d2f4aeb4d2ca45f28ce4899"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.00562",
    "kind": "arxiv",
    "version": 2
  }
}