Pith Number

pith:4VLEY7JD

pith:2025:4VLEY7JD6Q4SKCE7TNWDAJ5LTN

not attested not anchored not stored refs pending

Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor

Teng Zhang

arxiv:2507.14940 v1 · 2025-07-20 · 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{4VLEY7JD6Q4SKCE7TNWDAJ5LTN}

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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.

Cited by

1 paper in Pith

AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates

Receipt and verification

First computed	2026-07-05T11:40:15.728037Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5564c7d23f43925089f9b6c3027ab9b7b5c9542f87f249db4dec8ce732137ea

Aliases

arxiv: 2507.14940 · arxiv_version: 2507.14940v1 · doi: 10.48550/arxiv.2507.14940 · pith_short_12: 4VLEY7JD6Q4S · pith_short_16: 4VLEY7JD6Q4SKCE7 · pith_short_8: 4VLEY7JD

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/4VLEY7JD6Q4SKCE7TNWDAJ5LTN \
  | 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: e5564c7d23f43925089f9b6c3027ab9b7b5c9542f87f249db4dec8ce732137ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c6c63456346a00340d04f7d32a35803d544244d96530f3f4c8271b2d8fcd996",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2025-07-20T12:29:14Z",
    "title_canon_sha256": "a2b56a1436a8039c47c16de47ea1fa12431841041c82fce4e297683785abb65f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.14940",
    "kind": "arxiv",
    "version": 1
  }
}