Pith Number

pith:XUDQ2RX4

pith:2017:XUDQ2RX4F43EANODXTPH3I32BZ

not attested not anchored not stored refs pending

Duality for Differential Operators of Lie-Rinehart Algebras

Patrick Le Meur, Thierry Lambre

arxiv:1709.03973 v2 · 2017-09-12 · math.RA · math.KT · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XUDQ2RX4F43EANODXTPH3I32BZ}

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	2026-05-17T23:57:36.801868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd070d46fc2f364035c3bcde7da37a0e6cfa06b51d3f1326c16375ee471600ba

Aliases

arxiv: 1709.03973 · arxiv_version: 1709.03973v2 · doi: 10.48550/arxiv.1709.03973 · pith_short_12: XUDQ2RX4F43E · pith_short_16: XUDQ2RX4F43EANOD · pith_short_8: XUDQ2RX4

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/XUDQ2RX4F43EANODXTPH3I32BZ \
  | 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: bd070d46fc2f364035c3bcde7da37a0e6cfa06b51d3f1326c16375ee471600ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7230000d1c8e6e8477de7bd9604aba44dfac0e511a33822b9b71a309525d5b2f",
    "cross_cats_sorted": [
      "math.KT",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2017-09-12T17:57:38Z",
    "title_canon_sha256": "fa90d1124a8f43a66f0bbe5c0cd297e3fbcbac58f354d91b82eccc217440489e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.03973",
    "kind": "arxiv",
    "version": 2
  }
}