Pith Number

pith:HQF6FQ32

pith:2013:HQF6FQ32NUTWWZM5FPBTHQPGLC

not attested not anchored not stored refs pending

The Alexandrov-Toponogov comparison theorem for radial curvature

Katsuhiro Shiohama, Nobuhiro Innami, Yuya Uneme

arxiv:1302.4500 v1 · 2013-02-19 · 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{HQF6FQ32NUTWWZM5FPBTHQPGLC}

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	2026-05-18T03:33:13.113446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c0be2c37a6d276b659d2bc333c1e658a431d7e84190daf0f04cccef8a8b490d

Aliases

arxiv: 1302.4500 · arxiv_version: 1302.4500v1 · doi: 10.48550/arxiv.1302.4500 · pith_short_12: HQF6FQ32NUTW · pith_short_16: HQF6FQ32NUTWWZM5 · pith_short_8: HQF6FQ32

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/HQF6FQ32NUTWWZM5FPBTHQPGLC \
  | 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: 3c0be2c37a6d276b659d2bc333c1e658a431d7e84190daf0f04cccef8a8b490d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8c886b447bcf528cfc5560b7edb63d3098c0537c131577617d60f1e6d047f51",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-02-19T01:20:20Z",
    "title_canon_sha256": "b611a701003114803c8932911906f4185cbdace0209f7ab161a6deda0e290beb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4500",
    "kind": "arxiv",
    "version": 1
  }
}