Pith Number

pith:UWG3ZM42

pith:2026:UWG3ZM42W3MJFQYEXA7OBAKJH4

not attested not anchored not stored refs pending

Operator Inequalities in $\Phi$-Product Tensor Algebras: Invariance and Transform Sensitivity

Michael K. Ng, Shih-Yu Chang

arxiv:2606.21667 v1 · 2026-06-19 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UWG3ZM42W3MJFQYEXA7OBAKJH4}

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	2026-06-23T01:13:18.403269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a58dbcb39ab6d892c304b83ee081493f257257551c0a88ec574f93a5119de80b

Aliases

arxiv: 2606.21667 · arxiv_version: 2606.21667v1 · doi: 10.48550/arxiv.2606.21667 · pith_short_12: UWG3ZM42W3MJ · pith_short_16: UWG3ZM42W3MJFQYE · pith_short_8: UWG3ZM42

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/UWG3ZM42W3MJFQYEXA7OBAKJH4 \
  | 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: a58dbcb39ab6d892c304b83ee081493f257257551c0a88ec574f93a5119de80b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7eaa851453972063a96e464c07bbfba4affcaa5502f08e0d0fd5c9f3920a4426",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-19T18:17:48Z",
    "title_canon_sha256": "645226d3b0e7476f90bb5161d4d9eef3d61fd9b4f6d71303c05e7a15b28eb011"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21667",
    "kind": "arxiv",
    "version": 1
  }
}