Pith Number

pith:LE5FSYYV

pith:2010:LE5FSYYVFC3VSKV6WLTL2FQBFQ

not attested not anchored not stored refs pending

Alexandrov meets Kirszbraun

Anton Petrunin, Stephanie Alexander, Vitali Kapovitch

arxiv:1012.5636 v3 · 2010-12-27 · 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{LE5FSYYVFC3VSKV6WLTL2FQBFQ}

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.

Cited by

1 paper in Pith

Inequalities on Six Points in a $\mathrm{CAT}(0)$ Space

Receipt and verification

First computed	2026-07-05T10:12:44.976880Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

593a59631528b7592abeb2e6bd16012c17288462f63661b0ae919ae02f9088dc

Aliases

arxiv: 1012.5636 · arxiv_version: 1012.5636v3 · doi: 10.48550/arxiv.1012.5636 · pith_short_12: LE5FSYYVFC3V · pith_short_16: LE5FSYYVFC3VSKV6 · pith_short_8: LE5FSYYV

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/LE5FSYYVFC3VSKV6WLTL2FQBFQ \
  | 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: 593a59631528b7592abeb2e6bd16012c17288462f63661b0ae919ae02f9088dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef9e39846d250b671566d54ee403c21dd735d9f863088ed02bcf2db3024c21ce",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-12-27T16:54:34Z",
    "title_canon_sha256": "f5a9fa6fe0509a6fb42db281ca66e8fe5689606b3fb3546f6bfdff01e8680762"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5636",
    "kind": "arxiv",
    "version": 3
  }
}