Pith Number

pith:I5GSMNNI

pith:2005:I5GSMNNITOARU7CVTJXOYSYW33

not attested not anchored not stored refs pending

Majorization for Changes in Angles Between Subspaces, Ritz Values, and Graph Laplacian Spectra

A. V. Knyazev, M. E. Argentati

arxiv:math/0508591 v3 · 2005-08-30 · math.NA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I5GSMNNITOARU7CVTJXOYSYW33}

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	2026-05-18T03:29:51.511049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

474d2635a89b811a7c559a6eec4b16def4b36e0cd140cff98f6dae04b1338644

Aliases

arxiv: math/0508591 · arxiv_version: math/0508591v3 · doi: 10.48550/arxiv.math/0508591 · pith_short_12: I5GSMNNITOAR · pith_short_16: I5GSMNNITOARU7CV · pith_short_8: I5GSMNNI

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/I5GSMNNITOARU7CVTJXOYSYW33 \
  | 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: 474d2635a89b811a7c559a6eec4b16def4b36e0cd140cff98f6dae04b1338644

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ecc54f3ec432bef1392f04038bb34de68d3f7a29b5ab5e73e4b433e540f55ac",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NA",
    "submitted_at": "2005-08-30T03:34:22Z",
    "title_canon_sha256": "928c25b2c28413fc9ef3e6f3c4826ed59c3982f626a43b0f34ae60ce4b02a834"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508591",
    "kind": "arxiv",
    "version": 3
  }
}