Pith Number

pith:UEVPC5ZO

pith:2012:UEVPC5ZOLVABAGNH5KDRVABDHN

not attested not anchored not stored refs pending

On Toponogov's comparison theorem for Alexandrov spaces

Urs Lang, Viktor Schroeder

arxiv:1207.3668 v2 · 2012-07-16 · math.MG · 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{UEVPC5ZOLVABAGNH5KDRVABDHN}

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	2026-05-18T03:50:10.309349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a12af1772e5d401019a7ea871a80233b60dfb926d2e8da8b4afe020961c50cc3

Aliases

arxiv: 1207.3668 · arxiv_version: 1207.3668v2 · doi: 10.48550/arxiv.1207.3668 · pith_short_12: UEVPC5ZOLVAB · pith_short_16: UEVPC5ZOLVABAGNH · pith_short_8: UEVPC5ZO

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/UEVPC5ZOLVABAGNH5KDRVABDHN \
  | 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: a12af1772e5d401019a7ea871a80233b60dfb926d2e8da8b4afe020961c50cc3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d622c912ccdc1feb1c10e6269c3b29289af876705142c78a43a86b864ba2efbd",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-07-16T13:08:23Z",
    "title_canon_sha256": "eae92ed33f65c400e92d6eaf12da09a9c8f3d0eb4cacc73988f2c58fa5dba48f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3668",
    "kind": "arxiv",
    "version": 2
  }
}