Pith Number

pith:L67XV2JE

pith:2026:L67XV2JESMFH477EZFVVULV4VX

not attested not anchored not stored refs pending

On Circular Numerical Ranges of Companion Matrices with Repeated Eigenvalues

Hsin-Yi Lee, Wei-Qiang Huang

arxiv:2607.01099 v1 · 2026-07-01 · 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{L67XV2JESMFH477EZFVVULV4VX}

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	2026-07-02T01:18:29.011397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fbf7ae924930a7e7fe4c96b5a2ebcadf157f23248ba47b674f49e971cd132cc

Aliases

arxiv: 2607.01099 · arxiv_version: 2607.01099v1 · doi: 10.48550/arxiv.2607.01099 · pith_short_12: L67XV2JESMFH · pith_short_16: L67XV2JESMFH477E · pith_short_8: L67XV2JE

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/L67XV2JESMFH477EZFVVULV4VX \
  | 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: 5fbf7ae924930a7e7fe4c96b5a2ebcadf157f23248ba47b674f49e971cd132cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99eaa2ae41ff43af29020d884040d7e12c01c07dde24e3b33adb51e0ab528cfd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-07-01T15:50:51Z",
    "title_canon_sha256": "30804d031119f72041f39b3913918f905972b8430d3ffed6b6ce5ce2eb351e87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.01099",
    "kind": "arxiv",
    "version": 1
  }
}