Pith Number

pith:PSHVYGT2

pith:2011:PSHVYGT26VZB5XQOEP2RFF6KPK

not attested not anchored not stored refs pending

Operator-Valued Measures, Dilations, and the Theory of Frames

Bei Liu, David R. Larson, Deguang Han, Rui Liu

arxiv:1110.5833 v2 · 2011-10-26 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PSHVYGT26VZB5XQOEP2RFF6KPK}

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	2026-05-18T03:50:35.474193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c8f5c1a7af5721ede0e23f51297ca7a8783133fc3e2af19e356f8db087360e0

Aliases

arxiv: 1110.5833 · arxiv_version: 1110.5833v2 · doi: 10.48550/arxiv.1110.5833 · pith_short_12: PSHVYGT26VZB · pith_short_16: PSHVYGT26VZB5XQO · pith_short_8: PSHVYGT2

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/PSHVYGT26VZB5XQOEP2RFF6KPK \
  | 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: 7c8f5c1a7af5721ede0e23f51297ca7a8783133fc3e2af19e356f8db087360e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc85bb2a426da357e0ea12b14ac8255e3590290222f79a151b75d29995091300",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-10-26T16:30:32Z",
    "title_canon_sha256": "a8ee1fd364238f9a15b847102185967ee489a950132bed26bc14f57c152307af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5833",
    "kind": "arxiv",
    "version": 2
  }
}