Pith Number

pith:C4ZIP7D5

pith:2026:C4ZIP7D5TLAFUB37THOCHX4BDV

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On the Stability of Inverse Conductivity Problem for Polyhedral Inclusions under a Single Measurement

Chun-Hsiang Tsou

Logarithmic stability estimate holds for the Hausdorff distance between convex polyhedral inclusions from a single boundary measurement error.

arxiv:2605.17484 v1 · 2026-05-17 · math.AP

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Claims

C1strongest claim

Combining singularity decomposition for elliptic equations in non-smooth domains, propagation of smallness, and microlocal analysis, we establish a logarithmic stability estimate for the Hausdorff distance between inclusions in terms of the measurement error.

C2weakest assumption

The unknown inclusion is a convex polyhedron and the background medium is homogeneous and isotropic; the analysis relies on the specific singularity structure that these assumptions produce near edges and vertices.

C3one line summary

Proves logarithmic stability estimate for Hausdorff distance of convex polyhedral inclusions in the inverse conductivity problem from one boundary measurement using singularity decomposition, propagation of smallness, and microlocal analysis.

References

47 extracted · 47 resolved · 0 Pith anchors

[1] Alessandrini 1988

[2] G. Alessandrini, L. Rondi, E. Rosset, and S. Vessella. The stability for the cauchy problem for elliptic equations.Inverse Problems, 25:123004, 12 2009 2009

[3] Ammari.An Introduction to Mathematics of Emerging Biomedical Imaging, volume 62 2008

[4] B. Barcelo, E. Fabes, and J.-K. Seo. The inverse conductivity problem with one measurement: Unique- ness for convex polyhedra.Proceedings of the American Mathematical Society, 122:183, 9 1994 1994

[5] H. Bellout, A. Friedman, and V. Isakov. Stability for an inverse problem in potential theory.Transactions of the American Mathematical Society, 332:271–296, 7 1992 1992

Receipt and verification

First computed	2026-05-20T00:04:41.390634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

173287fc7d9ac05a077f99dc23df811d7510daedc569c60a7aa4d119d004be37

Aliases

arxiv: 2605.17484 · arxiv_version: 2605.17484v1 · doi: 10.48550/arxiv.2605.17484 · pith_short_12: C4ZIP7D5TLAF · pith_short_16: C4ZIP7D5TLAFUB37 · pith_short_8: C4ZIP7D5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/C4ZIP7D5TLAFUB37THOCHX4BDV \
  | 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: 173287fc7d9ac05a077f99dc23df811d7510daedc569c60a7aa4d119d004be37

Canonical record JSON

{
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    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-17T14:52:17Z",
    "title_canon_sha256": "0b3c6c5ecb1bdb33a9bef92fed720cb22da8f5433e8509976d903072541c0fee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17484",
    "kind": "arxiv",
    "version": 1
  }
}