Pith Number

pith:B2FIIN7X

pith:2016:B2FIIN7X4Q6DI22THVR2XVJZQT

not attested not anchored not stored refs pending

Double-quantitative $\gamma^{\ast}-$fuzzy coverings approximation operators

Guangming Lang

arxiv:1611.08103 v1 · 2016-11-24 · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B2FIIN7X4Q6DI22THVR2XVJZQT}

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	2026-05-18T00:56:44.380162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e8a8437f7e43c346b533d63abd53984dac5ddfe81529aad47d7f7a4920e8908

Aliases

arxiv: 1611.08103 · arxiv_version: 1611.08103v1 · doi: 10.48550/arxiv.1611.08103 · pith_short_12: B2FIIN7X4Q6D · pith_short_16: B2FIIN7X4Q6DI22T · pith_short_8: B2FIIN7X

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/B2FIIN7X4Q6DI22THVR2XVJZQT \
  | 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: 0e8a8437f7e43c346b533d63abd53984dac5ddfe81529aad47d7f7a4920e8908

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51abc80822fc8873d8029518df9846314bc902dcbe24297c419a8379e90466ad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2016-11-24T09:06:57Z",
    "title_canon_sha256": "fe1314cef08a54557c088dca05b3db981ec950bb93df811fc5f889e73456a637"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.08103",
    "kind": "arxiv",
    "version": 1
  }
}