Pith Number

pith:WC54VOSE

pith:2012:WC54VOSEXUOQIBD35FICK7TTAW

not attested not anchored not stored refs pending

Bounds for the Rayleigh quotient and the spectrum of self-adjoint operators

Andrew V. Knyazev, Merico E. Argentati, Peizhen Zhu

arxiv:1207.3240 v2 · 2012-07-13 · math.NA · math.FA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WC54VOSEXUOQIBD35FICK7TTAW}

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	2026-05-18T01:01:52.709870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0bbcaba44bd1d04047be950257e7305829e28c10a7388a651946ccb2f97da80

Aliases

arxiv: 1207.3240 · arxiv_version: 1207.3240v2 · doi: 10.48550/arxiv.1207.3240 · pith_short_12: WC54VOSEXUOQ · pith_short_16: WC54VOSEXUOQIBD3 · pith_short_8: WC54VOSE

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/WC54VOSEXUOQIBD35FICK7TTAW \
  | 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: b0bbcaba44bd1d04047be950257e7305829e28c10a7388a651946ccb2f97da80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d359acc67229de2e76d229a36e646494cf261ba2bdc691a57a9802271c19c800",
    "cross_cats_sorted": [
      "math.FA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-07-13T13:32:32Z",
    "title_canon_sha256": "3b53c7a26c4bcd7177474d13662fe13262ebde5847f7e1c9066add7d6f65da1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3240",
    "kind": "arxiv",
    "version": 2
  }
}