Pith Number

pith:P4MQCCJX

pith:2012:P4MQCCJXXQRRIIJD2DWQ2VD2J4

not attested not anchored not stored refs pending

Subdomain geometry of hyperbolic type metrics

Matti Vuorinen, Riku Kl\'en, Yaxiang Li

arxiv:1212.0115 v1 · 2012-12-01 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P4MQCCJXXQRRIIJD2DWQ2VD2J4}

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	2026-05-18T03:07:02.090510Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f19010937bc23142123d0ed0d547a4f05a6a36a1973aebc20e7f01dc56994f0

Aliases

arxiv: 1212.0115 · arxiv_version: 1212.0115v1 · doi: 10.48550/arxiv.1212.0115 · pith_short_12: P4MQCCJXXQRR · pith_short_16: P4MQCCJXXQRRIIJD · pith_short_8: P4MQCCJX

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/P4MQCCJXXQRRIIJD2DWQ2VD2J4 \
  | 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: 7f19010937bc23142123d0ed0d547a4f05a6a36a1973aebc20e7f01dc56994f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "310f95b05081b33ff7e834d8b7cdf35a05d8ba48a7d1759b656d304504c021d4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-12-01T13:52:56Z",
    "title_canon_sha256": "e7e3a24e0bfed641ed253d41199acded7cad8f874afcf33b3b9c10016f21b519"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0115",
    "kind": "arxiv",
    "version": 1
  }
}