Pith Number

pith:SFU5GOLN

pith:2015:SFU5GOLN3AQ3Q2CYWZB5VJM7GE

not attested not anchored not stored refs pending

The Length Spectrum of the Sub-Riemannian Three-Sphere

David Klapheck, Michael VanValkenburgh

arxiv:1507.03041 v2 · 2015-07-10 · 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{SFU5GOLN3AQ3Q2CYWZB5VJM7GE}

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	2026-05-18T00:14:11.620102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9169d3396dd821b86858b643daa59f312d29b375bcf3649af4bd829d6939b71f

Aliases

arxiv: 1507.03041 · arxiv_version: 1507.03041v2 · doi: 10.48550/arxiv.1507.03041 · pith_short_12: SFU5GOLN3AQ3 · pith_short_16: SFU5GOLN3AQ3Q2CY · pith_short_8: SFU5GOLN

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/SFU5GOLN3AQ3Q2CYWZB5VJM7GE \
  | 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: 9169d3396dd821b86858b643daa59f312d29b375bcf3649af4bd829d6939b71f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "257e2ce56e092c68cbeb5f102bf26df51aa5481266ad6e2c1299497b779a4ecb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-07-10T22:36:12Z",
    "title_canon_sha256": "75cac3a8a6b3c122ada678dfc11864e1494fe67cb9eb88be2a0eb928b82982be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03041",
    "kind": "arxiv",
    "version": 2
  }
}