Pith Number

pith:ZY7XVE5M

pith:2012:ZY7XVE5M4QUSZFLMCP5ASE2PDR

not attested not anchored not stored refs pending

Clifford-Wolf translations of Homogeneous Randers spheres

Ming Xu, ShaoQiang Deng

arxiv:1204.5232 v1 · 2012-04-23 · 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{ZY7XVE5M4QUSZFLMCP5ASE2PDR}

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	2026-05-18T03:57:13.695651Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce3f7a93ace4292c956c13fa09134f1c6976f528ac388ac18d4973d4d6540ae9

Aliases

arxiv: 1204.5232 · arxiv_version: 1204.5232v1 · doi: 10.48550/arxiv.1204.5232 · pith_short_12: ZY7XVE5M4QUS · pith_short_16: ZY7XVE5M4QUSZFLM · pith_short_8: ZY7XVE5M

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/ZY7XVE5M4QUSZFLMCP5ASE2PDR \
  | 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: ce3f7a93ace4292c956c13fa09134f1c6976f528ac388ac18d4973d4d6540ae9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "baf12fd5007827e0c201bd3f0e110e36ad300d49fc54887ab60cd9a332bb458d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-04-23T23:18:36Z",
    "title_canon_sha256": "0a12d8d937aa138a476d56e80ea4f052fec88e230668735f0c40b5c64eabff36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5232",
    "kind": "arxiv",
    "version": 1
  }
}