Pith Number

pith:IXLZ5DIW

pith:2025:IXLZ5DIWRKKXFXH2FLYFGLVFYK

not attested not anchored not stored refs pending

Pairs of Clark Unitary Operators on the Bidisk and their Taylor Joint Spectra

Alan Sola, Constanze Liaw, Kelly Bickel, Palak Arora

arxiv:2511.05306 v2 · 2025-11-07 · math.CV · 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{IXLZ5DIWRKKXFXH2FLYFGLVFYK}

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	2026-05-20T00:00:27.485946Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45d79e8d168a9572dcfa2af0532ea5c2918e0b6cd0f1843e49bb08891a2ea192

Aliases

arxiv: 2511.05306 · arxiv_version: 2511.05306v2 · doi: 10.48550/arxiv.2511.05306 · pith_short_12: IXLZ5DIWRKKX · pith_short_16: IXLZ5DIWRKKXFXH2 · pith_short_8: IXLZ5DIW

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/IXLZ5DIWRKKXFXH2FLYFGLVFYK \
  | 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: 45d79e8d168a9572dcfa2af0532ea5c2918e0b6cd0f1843e49bb08891a2ea192

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5727f10f5d943d309b6156efd890457bc70029e31b795dea06e10bea476b460f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2025-11-07T15:06:14Z",
    "title_canon_sha256": "9af8559a2ac774221e1e61939067895e194a9e0601c95eb8c029c567280a15b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.05306",
    "kind": "arxiv",
    "version": 2
  }
}