Pith Number

pith:VXSWTTUJ

pith:2013:VXSWTTUJBCL6ZMLAXK6HVNM25T

not attested not anchored not stored refs pending

On the Study of Hyperbolic Triangles and Circles by Hyperbolic Barycentric Coordinates in Relativistic Hyperbolic Geometry

Abraham A. Ungar

arxiv:1305.4990 v1 · 2013-05-22 · 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{VXSWTTUJBCL6ZMLAXK6HVNM25T}

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	2026-05-18T03:25:13.813169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ade569ce890897ecb160babc7ab59aecc2d532cee917e4a3d5f21aface6ca1af

Aliases

arxiv: 1305.4990 · arxiv_version: 1305.4990v1 · doi: 10.48550/arxiv.1305.4990 · pith_short_12: VXSWTTUJBCL6 · pith_short_16: VXSWTTUJBCL6ZMLA · pith_short_8: VXSWTTUJ

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/VXSWTTUJBCL6ZMLAXK6HVNM25T \
  | 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: ade569ce890897ecb160babc7ab59aecc2d532cee917e4a3d5f21aface6ca1af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6398280c848f884187e2c321e47d75e79092811e8629f1a2fcfe5bc3acb2db1a",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-05-22T00:15:04Z",
    "title_canon_sha256": "9c32aac2c54226ee02ef98686744ec7f79cd905ab51f43d70409ca1e183bb188"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4990",
    "kind": "arxiv",
    "version": 1
  }
}