Pith Number

pith:XE7KYDMY

pith:2012:XE7KYDMYY32ZNNI7ST5F2QIHI5

not attested not anchored not stored refs pending

On the power-bounded operators of classes $C_{0 \cdot}$ and $C_{1 \cdot}$

Patryk Pagacz

arxiv:1206.0492 v1 · 2012-06-03 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XE7KYDMYY32ZNNI7ST5F2QIHI5}

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	2026-05-18T03:54:17.527129Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b93eac0d98c6f596b51f94fa5d410747648b41b93339084dcce4cb650b0d9595

Aliases

arxiv: 1206.0492 · arxiv_version: 1206.0492v1 · doi: 10.48550/arxiv.1206.0492 · pith_short_12: XE7KYDMYY32Z · pith_short_16: XE7KYDMYY32ZNNI7 · pith_short_8: XE7KYDMY

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/XE7KYDMYY32ZNNI7ST5F2QIHI5 \
  | 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: b93eac0d98c6f596b51f94fa5d410747648b41b93339084dcce4cb650b0d9595

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a7fdc527f4f2d9b7c71ba9327cc64e24cc791e221fffde5c75d96eda7bd61ee",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-06-03T21:34:52Z",
    "title_canon_sha256": "8101a785fbd2f92ec0598004f35c227247f2b78291815bb1c75b54933e281bbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0492",
    "kind": "arxiv",
    "version": 1
  }
}