Pith Number

pith:TKRTF5WB

pith:2015:TKRTF5WB4TTVJ3GC6UIYCJJ6KO

not attested not anchored not stored refs pending

A sub-Riemannian Santal\'o formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators

Dario Prandi, Luca Rizzi, Marcello Seri

arxiv:1509.05415 v3 · 2015-09-17 · math.DG · math.AP · math.SP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TKRTF5WB4TTVJ3GC6UIYCJJ6KO}

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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	2026-05-17T23:54:27.207786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9aa332f6c1e4e754ecc2f51181253e538658c75a74d536904d6452b564500693

Aliases

arxiv: 1509.05415 · arxiv_version: 1509.05415v3 · doi: 10.48550/arxiv.1509.05415 · pith_short_12: TKRTF5WB4TTV · pith_short_16: TKRTF5WB4TTVJ3GC · pith_short_8: TKRTF5WB

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/TKRTF5WB4TTVJ3GC6UIYCJJ6KO \
  | 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: 9aa332f6c1e4e754ecc2f51181253e538658c75a74d536904d6452b564500693

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d833a6394994a0f3f11b42830afb4b5c43545ecc91017418a294371981ccd600",
    "cross_cats_sorted": [
      "math.AP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-09-17T20:15:34Z",
    "title_canon_sha256": "20ffdc27f776190a338932a5a4255092300313b5da1794978ca74c54694579c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05415",
    "kind": "arxiv",
    "version": 3
  }
}