Pith Number

pith:GFPNRIUW

pith:2011:GFPNRIUWMOS5WUM3RH3NLHDRWX

not attested not anchored not stored refs pending

Positive Operator Valued Measures: A General Setting for Frames

Bill Moran, Doug Cochran, Stephen Howard

arxiv:1111.1450 v1 · 2011-11-06 · math.FA · 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{GFPNRIUWMOS5WUM3RH3NLHDRWX}

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	2026-05-18T04:09:26.117828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

315ed8a29663a5db519b89f6d59c71b5caf1327249bebce6305c5ea21e4ebc04

Aliases

arxiv: 1111.1450 · arxiv_version: 1111.1450v1 · doi: 10.48550/arxiv.1111.1450 · pith_short_12: GFPNRIUWMOS5 · pith_short_16: GFPNRIUWMOS5WUM3 · pith_short_8: GFPNRIUW

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/GFPNRIUWMOS5WUM3RH3NLHDRWX \
  | 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: 315ed8a29663a5db519b89f6d59c71b5caf1327249bebce6305c5ea21e4ebc04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7a2a2be61154f05ab140b43574ec7da54e9b4e7128be70edb8823993612418a",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-11-06T20:40:58Z",
    "title_canon_sha256": "5eb0a9c42308ec0b0b0c6a70809f8b2a209d7ced783f4324a0469527a024e6f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1450",
    "kind": "arxiv",
    "version": 1
  }
}