Pith Number

pith:VDZRX5JH

pith:2015:VDZRX5JH3XMSWGUF6OSNCDOQ5W

not attested not anchored not stored refs pending

Homogeneous space with non virtually abelian discontinuous groups but without any proper SL(2,R)-action

Takayuki Okuda

arxiv:1503.02186 v1 · 2015-03-07 · math.DG · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDZRX5JH3XMSWGUF6OSNCDOQ5W}

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	2026-05-18T02:25:25.666534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8f31bf527ddd92b1a85f3a4d10dd0ed8e71e703cdeb2c7ede37787e2c008fe4

Aliases

arxiv: 1503.02186 · arxiv_version: 1503.02186v1 · doi: 10.48550/arxiv.1503.02186 · pith_short_12: VDZRX5JH3XMS · pith_short_16: VDZRX5JH3XMSWGUF · pith_short_8: VDZRX5JH

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/VDZRX5JH3XMSWGUF6OSNCDOQ5W \
  | 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: a8f31bf527ddd92b1a85f3a4d10dd0ed8e71e703cdeb2c7ede37787e2c008fe4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "398ecf80488e666874f9e969725372835ee45069621e56e29659b1c83e097a08",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-03-07T15:53:17Z",
    "title_canon_sha256": "e901afd57d2a0d12e4ab01c508b7855b0b66c0c87476faa6b8ca26b0a304c635"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02186",
    "kind": "arxiv",
    "version": 1
  }
}