Pith Number

pith:4BKXVIUF

pith:2017:4BKXVIUF6K6ZDAESSGFV5AZ4D3

not attested not anchored not stored refs pending

Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator

Artur O. Lopes, Elismar R. Oliveira

arxiv:1710.07511 v3 · 2017-10-20 · math.DS · math.FA · math.OA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4BKXVIUF6K6ZDAESSGFV5AZ4D3}

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	2026-05-18T00:02:36.106437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0557aa285f2bd918092918b5e833c1ee05bc97b143584afa939699a1b3d7065

Aliases

arxiv: 1710.07511 · arxiv_version: 1710.07511v3 · doi: 10.48550/arxiv.1710.07511 · pith_short_12: 4BKXVIUF6K6Z · pith_short_16: 4BKXVIUF6K6ZDAES · pith_short_8: 4BKXVIUF

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/4BKXVIUF6K6ZDAESSGFV5AZ4D3 \
  | 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: e0557aa285f2bd918092918b5e833c1ee05bc97b143584afa939699a1b3d7065

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80bd22f707b4c4864e17c58cdf7d7d875f6225a8814fca547a47ea56d8202567",
    "cross_cats_sorted": [
      "math.FA",
      "math.OA",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-10-20T12:47:30Z",
    "title_canon_sha256": "6815fccc572eb9cd23438d497de420824114788e7158edeec66ed86a17afa19a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.07511",
    "kind": "arxiv",
    "version": 3
  }
}