Pith Number

pith:ZDZ33VKF

pith:2009:ZDZ33VKFZ3Z24II7V2XRWGT2JO

not attested not anchored not stored refs pending

Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator

Alexander K. Motovilov, Christiane Tretter, Sergio Albeverio

arxiv:0909.1211 v1 · 2009-09-07 · math.SP · math-ph · math.FA · math.MP · 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{ZDZ33VKFZ3Z24II7V2XRWGT2JO}

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	2026-05-18T04:10:09.233203Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8f3bdd545cef3ae211faeaf1b1a7a4ba7477dc5ed45517bd4bb16f6877f73ba

Aliases

arxiv: 0909.1211 · arxiv_version: 0909.1211v1 · doi: 10.48550/arxiv.0909.1211 · pith_short_12: ZDZ33VKFZ3Z2 · pith_short_16: ZDZ33VKFZ3Z24II7 · pith_short_8: ZDZ33VKF

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/ZDZ33VKFZ3Z24II7V2XRWGT2JO \
  | 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: c8f3bdd545cef3ae211faeaf1b1a7a4ba7477dc5ed45517bd4bb16f6877f73ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5209090f9afd7032c9d3fc2956b6f4aca89ad0585aa9e0fb786c4e23969d5ecc",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2009-09-07T10:45:44Z",
    "title_canon_sha256": "4b402d8e945ff8bb61f2848a936d2c3baa33e3605e1dae77b040d645554a3ac5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1211",
    "kind": "arxiv",
    "version": 1
  }
}