Pith Number

pith:JWUH47VK

pith:2015:JWUH47VKKCFIADT2P3GPYUSBCV

not attested not anchored not stored refs pending

Quaternionic Kleinian modular groups and arithmetic hyperbolic orbifolds over the quaternions

Alberto Verjovsky, Fabio Vlacci, Juan Pablo D\'iaz

arxiv:1503.07214 v1 · 2015-03-24 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JWUH47VKKCFIADT2P3GPYUSBCV}

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	2026-05-18T02:20:28.055397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4da87e7eaa508a800e7a7eccfc5241154386b43fc2730b1a6913fb79245f380d

Aliases

arxiv: 1503.07214 · arxiv_version: 1503.07214v1 · doi: 10.48550/arxiv.1503.07214 · pith_short_12: JWUH47VKKCFI · pith_short_16: JWUH47VKKCFIADT2 · pith_short_8: JWUH47VK

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/JWUH47VKKCFIADT2P3GPYUSBCV \
  | 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: 4da87e7eaa508a800e7a7eccfc5241154386b43fc2730b1a6913fb79245f380d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ab43f11f04db4af6980e070f6652cca45bee75ef03d58ecf6c2484cbb286637",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-03-24T21:51:06Z",
    "title_canon_sha256": "24f98e22b7c97deb9a636618948080f7c877aa7b029fa6836b5cc1ebafec4d6d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.07214",
    "kind": "arxiv",
    "version": 1
  }
}