Pith Number

pith:EH2QEC3I

pith:2025:EH2QEC3IEDUJ2ATZ67BM25F3DC

not attested not anchored not stored refs pending

The joint numerical range of three hermitian $4\times 4$ matrices

Ilya Spitkovsky, Karol \.Zyczkowski, Konrad Szyma\'nski, Piotr Pikul, Stephan Weis

The joint numerical range of three Hermitian 4x4 matrices has non-generic boundaries classifiable into fifteen types based on non-elliptic faces.

arxiv:2510.27670 v2 · 2025-10-31 · 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{EH2QEC3IEDUJ2ATZ67BM25F3DC}

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.

Claims

C1strongest claim

Fifteen possible classes regarding the numbers of non-elliptic faces in the boundary of W are identified and an explicit example is presented for each class. A nonempty intersection of three mutually distinct one-dimensional faces is a corner point.

C2weakest assumption

The analysis assumes that varying only the number of non-elliptic faces fully captures all possible non-generic boundary structures for three Hermitian 4x4 matrices without additional geometric features or degeneracies arising, as implied by the identification of exactly fifteen classes in the abstract.

C3one line summary

Classifies non-generic joint numerical ranges of three Hermitian 4x4 matrices into 15 classes with examples, proves corner points from face intersections, and compares the separable numerical range boundary for entanglement analysis.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:33.693262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21f5020b6820e89d0279f7c2cd74bb18bf4e2c645dcd5f6640d54b8551b340cb

Aliases

arxiv: 2510.27670 · arxiv_version: 2510.27670v2 · doi: 10.48550/arxiv.2510.27670 · pith_short_12: EH2QEC3IEDUJ · pith_short_16: EH2QEC3IEDUJ2ATZ · pith_short_8: EH2QEC3I

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/EH2QEC3IEDUJ2ATZ67BM25F3DC \
  | 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: 21f5020b6820e89d0279f7c2cd74bb18bf4e2c645dcd5f6640d54b8551b340cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b0ca76368843f9bde409238c67887f2f3dc5eb5a8453de398e5c519d0fd2b71",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-10-31T17:34:54Z",
    "title_canon_sha256": "6d09b7415bc569144ecc77c49e27eb3b82d358ac234f5ee7488c01e00858d270"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.27670",
    "kind": "arxiv",
    "version": 2
  }
}