Pith Number

pith:RYPOSMJD

pith:2013:RYPOSMJDPYXAH5DDCO4XIFKSPF

not attested not anchored not stored refs pending

M\"obius Transformation and Einsten Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky

Abraham A. Ungar

arxiv:1303.4785 v1 · 2013-03-19 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RYPOSMJDPYXAH5DDCO4XIFKSPF}

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	2026-05-18T03:30:24.863825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8e1ee931237e2e03f46313b97415527951282382e12db5e2ab92ae83424a8f5a

Aliases

arxiv: 1303.4785 · arxiv_version: 1303.4785v1 · doi: 10.48550/arxiv.1303.4785 · pith_short_12: RYPOSMJDPYXA · pith_short_16: RYPOSMJDPYXAH5DD · pith_short_8: RYPOSMJD

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/RYPOSMJDPYXAH5DDCO4XIFKSPF \
  | 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: 8e1ee931237e2e03f46313b97415527951282382e12db5e2ab92ae83424a8f5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d870b5a1e042a918434e6fb67acf3774fd83b5cafcf5525b30d169f3756b634",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-03-19T22:56:48Z",
    "title_canon_sha256": "ab1b607ea79538b8fcea8d1d24cd41c1f30e395470fc963761a779dac6c25814"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.4785",
    "kind": "arxiv",
    "version": 1
  }
}