Pith Number

pith:AGIGYW3U

pith:2026:AGIGYW3UC2B4K5DBJRZRO7J3RG

not attested not anchored not stored refs resolved

Spectral reconstruction from Euclidean lattice correlators through singular value decomposition

Ryutaro Tsuji, Shoji Hashimoto

Truncating the singular value decomposition of the kernel function reconstructs smeared spectral densities from Euclidean lattice correlators with controlled uncertainties.

arxiv:2605.15674 v1 · 2026-05-15 · hep-lat

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Record completeness

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4 Citations open

5 Replications open

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Claims

C1strongest claim

By retaining only the components associated with the largest singular values, for which the correlator data remain statistically significant, one can reconstruct smeared spectral functions with controlled uncertainties. The systematic error arising from the truncation can also be bounded under reasonable assumptions.

C2weakest assumption

The systematic error from SVD truncation can be bounded under reasonable assumptions about the form or positivity properties of the underlying spectral function.

C3one line summary

SVD truncation of the exp(-ωt) kernel reconstructs smeared spectral functions from lattice correlators with controlled uncertainties and approaches the Mellin transform in the continuum limit.

References

35 extracted · 35 resolved · 6 Pith anchors

[1] M. Bertero, C. D. Mol, and E. R. Pike, Inverse Problems1, 301 (1985), URLhttps://doi. org/10.1088/0266-5611/1/4/004 1985 · doi:10.1088/0266-5611/1/4/004

[2] M. Bertero, C. D. Mol, and E. R. Pike, Inverse Problems4, 573 (1988), URLhttps://doi. org/10.1088/0266-5611/4/3/004 1988 · doi:10.1088/0266-5611/4/3/004

[3] Hadronic Spectral Functions in Lattice QCD 1999 · arXiv:hep-lat/9905034

[4] M. Asakawa, T. Hatsuda, and Y. Nakahara, Prog. Part. Nucl. Phys.46, 459 (2001), hep- lat/0011040 2001

[5] J. Otsuki, M. Ohzeki, H. Shinaoka, and K. Yoshimi, Journal of the Physical Society of Japan 24 10 1 100 101 102 t 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4U0(t) tmax = max = 50.1 tmax = max = 75.1 tmax = max = 2020

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:11.692906Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01906c5b741683c574614c73177d3b89acbf98ef5e62528763ec4c0d31bcfa66

Aliases

arxiv: 2605.15674 · arxiv_version: 2605.15674v1 · doi: 10.48550/arxiv.2605.15674 · pith_short_12: AGIGYW3UC2B4 · pith_short_16: AGIGYW3UC2B4K5DB · pith_short_8: AGIGYW3U

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/AGIGYW3UC2B4K5DBJRZRO7J3RG \
  | 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: 01906c5b741683c574614c73177d3b89acbf98ef5e62528763ec4c0d31bcfa66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef8e3b173b8fb0f71a2e1fe57b168acead6aec1e4e7157aaa7599390231df8ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-lat",
    "submitted_at": "2026-05-15T06:53:32Z",
    "title_canon_sha256": "564970acf26d6ccb7ced8fa327a53b62f63389085afd4f7726a6ec8465febaed"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}