Pith Number

pith:VLVZV435

pith:2012:VLVZV435A3SWR6DHO65URAHK57

not attested not anchored not stored refs pending

Some arithmetic groups that do not act on the circle

Dave Witte Morris

arxiv:1210.3671 v1 · 2012-10-13 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VLVZV435A3SWR6DHO65URAHK57}

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	2026-05-18T03:43:17.473805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaeb9af37d06e568f86777bb4880eaeffa7098e583f7dee02e9fdf81d65ff704

Aliases

arxiv: 1210.3671 · arxiv_version: 1210.3671v1 · doi: 10.48550/arxiv.1210.3671 · pith_short_12: VLVZV435A3SW · pith_short_16: VLVZV435A3SWR6DH · pith_short_8: VLVZV435

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/VLVZV435A3SWR6DHO65URAHK57 \
  | 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: aaeb9af37d06e568f86777bb4880eaeffa7098e583f7dee02e9fdf81d65ff704

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc08ccfe49547131e05d3c511f3338048ec5ffe5b41fd684a9b4b6d90759429b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-10-13T03:11:42Z",
    "title_canon_sha256": "51bf08a65cd77a73597ac2368691737896933a5d48975ed8b0f45abd8d6fb1ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.3671",
    "kind": "arxiv",
    "version": 1
  }
}