Pith Number

pith:YZ2EN3JN

pith:2010:YZ2EN3JN6OCN7VPPWLAFRTU7EL

not attested not anchored not stored refs pending

Sub-Riemannian geodesics and heat operator on odd dimensional spheres

Irina Markina, Mauricio Godoy Molina

arxiv:1008.5265 v1 · 2010-08-31 · 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{YZ2EN3JN6OCN7VPPWLAFRTU7EL}

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	2026-05-18T01:35:33.331111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c67446ed2df384dfd5efb2c058ce9f22d65ca764c0f34d395da85a151d622545

Aliases

arxiv: 1008.5265 · arxiv_version: 1008.5265v1 · doi: 10.48550/arxiv.1008.5265 · pith_short_12: YZ2EN3JN6OCN · pith_short_16: YZ2EN3JN6OCN7VPP · pith_short_8: YZ2EN3JN

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/YZ2EN3JN6OCN7VPPWLAFRTU7EL \
  | 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: c67446ed2df384dfd5efb2c058ce9f22d65ca764c0f34d395da85a151d622545

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5ac7f2595e7aa681984a342e5c545dfa6820c7b68354335959bc8d17068883b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2010-08-31T09:36:59Z",
    "title_canon_sha256": "0f27de15356fee558e65e869567b1df507c1afb2556b15ee18ede111e6147b99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.5265",
    "kind": "arxiv",
    "version": 1
  }
}