Pith Number

pith:RQSKALNR

pith:2012:RQSKALNRN5OJJ45RDWEF4KGX5M

not attested not anchored not stored refs pending

Optimal Riemannian metric for a volumorphism and a mean ergodic theorem in complete global Alexandrov nonpositively curved spaces

Tony Liimatainen

arxiv:1206.0368 v1 · 2012-06-02 · math.DG · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RQSKALNRN5OJJ45RDWEF4KGX5M}

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	2026-05-18T03:38:23.475182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c24a02db16f5c94f3b11d885e28d7eb1629c482f1bddba268f81a5337b6511f

Aliases

arxiv: 1206.0368 · arxiv_version: 1206.0368v1 · doi: 10.48550/arxiv.1206.0368 · pith_short_12: RQSKALNRN5OJ · pith_short_16: RQSKALNRN5OJJ45R · pith_short_8: RQSKALNR

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/RQSKALNRN5OJJ45RDWEF4KGX5M \
  | 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: 8c24a02db16f5c94f3b11d885e28d7eb1629c482f1bddba268f81a5337b6511f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7297b52e4752af5946d758d807b3936e2bcf7db6af7646a32eff83cb6d68b81f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-06-02T12:11:03Z",
    "title_canon_sha256": "e6be59c779d42a0476467a6075105b4be1e4cb6162483a6f145ce9b50edc7003"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0368",
    "kind": "arxiv",
    "version": 1
  }
}