Pith Number

pith:NBGUBTXD

pith:2011:NBGUBTXDDBYKQUSYHW73XGEBA7

not attested not anchored not stored refs pending

Approximation by Semigroups of Spherical Operators

Feilong Cao, Yuguang Wang

arxiv:1105.2393 v1 · 2011-05-12 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NBGUBTXDDBYKQUSYHW73XGEBA7}

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	2026-05-18T02:43:00.996820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

684d40cee31870a852583dbfbb988107e1e22565f12e35f0d39b4f4da99e6d3f

Aliases

arxiv: 1105.2393 · arxiv_version: 1105.2393v1 · doi: 10.48550/arxiv.1105.2393 · pith_short_12: NBGUBTXDDBYK · pith_short_16: NBGUBTXDDBYKQUSY · pith_short_8: NBGUBTXD

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/NBGUBTXDDBYKQUSYHW73XGEBA7 \
  | 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: 684d40cee31870a852583dbfbb988107e1e22565f12e35f0d39b4f4da99e6d3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4668cec5770a4edde99367824dedd047de5d59b627143d0ec4633a6fd8d40aa0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-05-12T07:34:03Z",
    "title_canon_sha256": "5f3fb76e301d09b9f54a74e9a14dc6fdc2dd22dccd4d981c87fcde4a28b540b1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2393",
    "kind": "arxiv",
    "version": 1
  }
}