Pith Number

pith:VNDWSTCI

pith:2026:VNDWSTCIJWLCIBDRK73XWYTO33

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Spectral Bounds for Tensors Derived from Trace Functionals and Wasserstein Distance in Tensor Spaces

Hemant Sharma, Nachiketa Mishra

Trace functionals produce eigenvalue bounds for positive semi-definite tensors while defining their Bures-Wasserstein distance.

arxiv:2605.16930 v1 · 2026-05-16 · math.NA · cs.NA

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Claims

C1strongest claim

The paper derives trace-based eigenvalue bounds for PSD tensors and establishes the Bures-Wasserstein distance on tensor spaces, with bounds depending on the PSD condition.

C2weakest assumption

The central derivations assume tensors satisfy the positive semi-definite condition to obtain the stated bounds and metric properties; the analysis of relaxed PSD is presented separately via examples rather than as part of the core derivation.

C3one line summary

Defines trace-based metric and Bures-Wasserstein distance for PSD tensors, derives spectral eigenvalue bounds, and analyzes dependence on PSD condition with examples and complexity.

References

16 extracted · 16 resolved · 0 Pith anchors

[1] Geometry of quantum states: an introduction to quantum entanglement 2017

[2] Pattern Recognition 127 (2022), 108611 2019 · doi:10.1016/j

[3] An Order -p Tensor Factorization with Applications in Imaging 2013 · doi:10.1137/110841229

[4] The infinite-Wasserstein Distance: Local Solutions and Existence of Optimal Transport Maps 2008 · doi:10.1137/07069938x

[5] From matrix to tensor: Multilinear algebra and signal pro- cessing 1998

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:31.353064Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab47694c484d9624047157f77b626eded424baff8c9f3eb88764f6b0b7f155ca

Aliases

arxiv: 2605.16930 · arxiv_version: 2605.16930v1 · doi: 10.48550/arxiv.2605.16930 · pith_short_12: VNDWSTCIJWLC · pith_short_16: VNDWSTCIJWLCIBDR · pith_short_8: VNDWSTCI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VNDWSTCIJWLCIBDRK73XWYTO33 \
  | 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: ab47694c484d9624047157f77b626eded424baff8c9f3eb88764f6b0b7f155ca

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "ffa4451fa0e6f65ae731acef0da8ea722efb3831c0ca087a48492a1957d83b79",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-16T10:55:37Z",
    "title_canon_sha256": "2b329747bd64c4c77228a54ab96fd0c21d86b0d4c5f51f52b8a4e22309da1e71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16930",
    "kind": "arxiv",
    "version": 1
  }
}