Pith Number

pith:N4YTN7WJ

pith:2026:N4YTN7WJYC5LWNBLKZ7XDAFHX3

not attested not anchored not stored refs pending

Improved Bounds for numerical radius and $a$-numerical radius in ${C}^*$-algebras

Arobinda Ghosh, Riddhick Birbonshi, Saikat Mahapatra

arxiv:2606.10659 v1 · 2026-06-09 · 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{N4YTN7WJYC5LWNBLKZ7XDAFHX3}

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	2026-06-10T01:10:32.896427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f3136fec9c0babb342b567f7180a7bec240998293f1b5141bac8c5820906bb6

Aliases

arxiv: 2606.10659 · arxiv_version: 2606.10659v1 · doi: 10.48550/arxiv.2606.10659 · pith_short_12: N4YTN7WJYC5L · pith_short_16: N4YTN7WJYC5LWNBL · pith_short_8: N4YTN7WJ

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/N4YTN7WJYC5LWNBLKZ7XDAFHX3 \
  | 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: 6f3136fec9c0babb342b567f7180a7bec240998293f1b5141bac8c5820906bb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "214587c0b294f29ac7963c2c2fcd196de7a3f7f9b7c66e01269ad5253343688e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-06-09T10:08:05Z",
    "title_canon_sha256": "b08db1490a065b3e0033d00cec472b2c04e4e04bdaa109edb9ae312881a5d22d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.10659",
    "kind": "arxiv",
    "version": 1
  }
}