Pith Number

pith:MCZA63BK

pith:2018:MCZA63BKDIV2QRMTALEM5GMLVP

not attested not anchored not stored refs pending

Julia operators and Halmos dilations

P.L. Robinson

arxiv:1803.09329 v1 · 2018-03-25 · 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{MCZA63BKDIV2QRMTALEM5GMLVP}

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.

Cited by

1 paper in Pith

Gravitational redshift as a quantum channel: modeling the effects of gravitational redshift in quantum optics

Receipt and verification

First computed	2026-05-18T00:20:11.984182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60b20f6c2a1a2ba8459302c8ce998babf6f8c8bd5fe83bba572f893b35dd7697

Aliases

arxiv: 1803.09329 · arxiv_version: 1803.09329v1 · doi: 10.48550/arxiv.1803.09329 · pith_short_12: MCZA63BKDIV2 · pith_short_16: MCZA63BKDIV2QRMT · pith_short_8: MCZA63BK

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/MCZA63BKDIV2QRMTALEM5GMLVP \
  | 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: 60b20f6c2a1a2ba8459302c8ce998babf6f8c8bd5fe83bba572f893b35dd7697

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7abb353e3c3a6210b756bf212c00e7967cf716911089185c97f700070b06c74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-03-25T20:16:04Z",
    "title_canon_sha256": "01f08c986eaa614a735739cb9e6ea2b40d63401c56d3ff45964a35196518a5d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.09329",
    "kind": "arxiv",
    "version": 1
  }
}