Pith Number

pith:UB2SCH5M

pith:2017:UB2SCH5MF4XJO4RYPQUEFU7ENA

not attested not anchored not stored refs pending

Poincar{\'e} and Sobolev inequalities for differential forms in Heisenberg groups

Annalisa Baldi, Bruno Franchi, Pierre Pansu (LM-Orsay)

arxiv:1711.09786 v1 · 2017-11-27 · 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{UB2SCH5MF4XJO4RYPQUEFU7ENA}

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	2026-05-18T00:29:34.458142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a075211fac2f2e9772387c2842d3e4683c8b9198c67a90f6388e5d2cad0561d3

Aliases

arxiv: 1711.09786 · arxiv_version: 1711.09786v1 · doi: 10.48550/arxiv.1711.09786 · pith_short_12: UB2SCH5MF4XJ · pith_short_16: UB2SCH5MF4XJO4RY · pith_short_8: UB2SCH5M

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/UB2SCH5MF4XJO4RYPQUEFU7ENA \
  | 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: a075211fac2f2e9772387c2842d3e4683c8b9198c67a90f6388e5d2cad0561d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "563b5a84c1303a29c2c1ed015a4647404b9cbdd108ee34b1ee03dece82e772c1",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2017-11-27T15:51:44Z",
    "title_canon_sha256": "a08be97eefea4949bbea24e3ddc5ffa78a42745a84526067f79c32c38267f536"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.09786",
    "kind": "arxiv",
    "version": 1
  }
}