Pith Number

pith:75NNXQKA

pith:2023:75NNXQKATJIYQJ3NEHUEF54FLD

not attested not anchored not stored refs pending

Winding number criterion for the origin to belong to the numerical range of a matrix on a loop of matrices

Cheng Guo, Shanhui Fan

arxiv:2311.00849 v1 · 2023-11-01 · math.FA · math-ph · math.MP · math.OA · math.SP · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{75NNXQKATJIYQJ3NEHUEF54FLD}

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	2026-07-05T07:08:16.516180Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff5adbc1409a5188276d21e842f78558d55060a1812512584a9a27c725529a84

Aliases

arxiv: 2311.00849 · arxiv_version: 2311.00849v1 · doi: 10.48550/arxiv.2311.00849 · pith_short_12: 75NNXQKATJIY · pith_short_16: 75NNXQKATJIYQJ3N · pith_short_8: 75NNXQKA

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/75NNXQKATJIYQJ3NEHUEF54FLD \
  | 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: ff5adbc1409a5188276d21e842f78558d55060a1812512584a9a27c725529a84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "501c96287f77efae5d292cc284782be5400b0579649896ffe12f1c3582c6d481",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OA",
      "math.SP",
      "physics.optics"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2023-11-01T20:59:10Z",
    "title_canon_sha256": "ef8bc3aaa9527579ce4f22b4eeb1374a1ff6a6c7d5acb3d4e148602b7a6ec876"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.00849",
    "kind": "arxiv",
    "version": 1
  }
}