Pith Number

pith:5H54FINP

pith:2012:5H54FINPH33FRLXUDOEBVGTJJQ

not attested not anchored not stored refs pending

Kropina metrics and Zermelo navigation on Riemannian manifolds

Ryozo Yoshikawa, Sorin V. Sabau

arxiv:1209.0340 v1 · 2012-09-03 · 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{5H54FINPH33FRLXUDOEBVGTJJQ}

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	2026-05-18T03:46:29.318062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9fbc2a1af3ef658aef41b881a9a694c19ee25d141f6c10af4f94ef617f37127

Aliases

arxiv: 1209.0340 · arxiv_version: 1209.0340v1 · doi: 10.48550/arxiv.1209.0340 · pith_short_12: 5H54FINPH33F · pith_short_16: 5H54FINPH33FRLXU · pith_short_8: 5H54FINP

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/5H54FINPH33FRLXUDOEBVGTJJQ \
  | 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: e9fbc2a1af3ef658aef41b881a9a694c19ee25d141f6c10af4f94ef617f37127

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95790966425cb36a796abfdec0a7bf01b22b5a334f9e16a4fa4052bfa4487a76",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-09-03T13:16:53Z",
    "title_canon_sha256": "6197e23c71d4741a4f7b251417d291a7857adef603cc925456805f35992425cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0340",
    "kind": "arxiv",
    "version": 1
  }
}