Pith Number

pith:BAXGLI3B

pith:2018:BAXGLI3B7R5P6AIIG2LFZ52QRE

not attested not anchored not stored refs pending

Relatively bounded operators and the operator E-norms (addition to arXiv:1806.05668)

M.E.Shirokov

arxiv:1811.09659 v1 · 2018-11-23 · math.FA · math-ph · math.MP · math.OA · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BAXGLI3B7R5P6AIIG2LFZ52QRE}

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	2026-05-18T00:00:01.555621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

082e65a361fc7aff010836965cf750893b42526407db8575fc392bb859034403

Aliases

arxiv: 1811.09659 · arxiv_version: 1811.09659v1 · doi: 10.48550/arxiv.1811.09659 · pith_short_12: BAXGLI3B7R5P · pith_short_16: BAXGLI3B7R5P6AII · pith_short_8: BAXGLI3B

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/BAXGLI3B7R5P6AIIG2LFZ52QRE \
  | 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: 082e65a361fc7aff010836965cf750893b42526407db8575fc392bb859034403

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "beb5f6f566ee8114a78250b24e80cc34e39a6159f8471cc9e78738c32c42bcc6",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-11-23T20:16:22Z",
    "title_canon_sha256": "8b4a39fcc0c536746e04bc52de7ae68fc176f76262ee31293819322c56cf5cf5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.09659",
    "kind": "arxiv",
    "version": 1
  }
}