Pith Number

pith:Q5NV3RJO

pith:2012:Q5NV3RJOJMS7I544MMUOPJKCIS

not attested not anchored not stored refs pending

The Funk and Hilbert geometries for spaces of constant curvature

Athanase Papadopoulos (IRMA), Sumio Yamada

arxiv:1209.4160 v1 · 2012-09-19 · math.GT · 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{Q5NV3RJOJMS7I544MMUOPJKCIS}

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	2026-05-18T03:45:13.261328Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

875b5dc52e4b25f4779c6328e7a54244840abc653498de5fc641ff4988b05c0a

Aliases

arxiv: 1209.4160 · arxiv_version: 1209.4160v1 · doi: 10.48550/arxiv.1209.4160 · pith_short_12: Q5NV3RJOJMS7 · pith_short_16: Q5NV3RJOJMS7I544 · pith_short_8: Q5NV3RJO

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/Q5NV3RJOJMS7I544MMUOPJKCIS \
  | 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: 875b5dc52e4b25f4779c6328e7a54244840abc653498de5fc641ff4988b05c0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de60eb4d111ce2aef0814fbefca9cc3d8882c5cf28cb6d559cae4366f12de999",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-19T06:40:09Z",
    "title_canon_sha256": "d877aadac4d2660d015c5a3178e44834b37cc0af1b83ee0d3871d4c2d7cf41cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4160",
    "kind": "arxiv",
    "version": 1
  }
}