Pith Number

pith:IQZDUJQK

pith:2017:IQZDUJQKFE7WUPUUVDSTTEGISE

not attested not anchored not stored refs pending

On the Whitney extension property for continuously differentiable horizontal curves in sub-Riemannian manifolds

CaGE), Ludovic Sacchelli (CMAP, Mario Sigalotti (CMAP

arxiv:1708.02795 v3 · 2017-08-09 · math.MG · math.DG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IQZDUJQKFE7WUPUUVDSTTEGISE}

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	2026-05-17T23:57:50.939689Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44323a260a293f6a3e94a8e53990c8913e0707dd122dfedda57fa47875c0cc71

Aliases

arxiv: 1708.02795 · arxiv_version: 1708.02795v3 · doi: 10.48550/arxiv.1708.02795 · pith_short_12: IQZDUJQKFE7W · pith_short_16: IQZDUJQKFE7WUPUU · pith_short_8: IQZDUJQK

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/IQZDUJQKFE7WUPUUVDSTTEGISE \
  | 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: 44323a260a293f6a3e94a8e53990c8913e0707dd122dfedda57fa47875c0cc71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0f588f6e4ba10c1d9f47e552e63921cd7d2c41553884c183782d327591323b1",
    "cross_cats_sorted": [
      "math.DG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2017-08-09T12:01:35Z",
    "title_canon_sha256": "45b521ff583f3446aa65c5cf0f65e61a5a2115a62605127819ef57995e3e075c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.02795",
    "kind": "arxiv",
    "version": 3
  }
}