Pith Number

pith:KZALHTLH

pith:2026:KZALHTLHTHQWCARBON3ZYC6L72

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Bogoliubov sum rules and the Knight-shift ellipsoid in noncentrosymmetric superconductors

Yi Zhou

The zero-temperature Knight shift tensor in noncentrosymmetric superconductors equals the normal-state susceptibility times the identity minus the Fermi-surface projector of the spin-locking direction.

arxiv:2605.17030 v1 · 2026-05-16 · cond-mat.supr-con · cond-mat.str-el

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Claims

C1strongest claim

the tensor identity χ_μν(0)=χ_N[δ_μν−Π_μν] independently of pairing symmetry, gap magnitude, and Fermi-surface shape. Because Tr Π=1, the three principal Knight shifts at T=0 lie on a two-dimensional simplex of locking textures, the Knight-shift ellipsoid, whose vertices, edges, and interior classify every canonical pairing class.

C2weakest assumption

The system resides in the strong-locking regime where the residual T=0 Knight shift is completely determined by the Fermi-surface projector Π_μν of the spin-locking direction n̂_k (abstract, paragraph on the central theorem).

C3one line summary

Derives a Bogoliubov sum rule fixing the T=0 Knight shift in noncentrosymmetric superconductors to a Fermi-surface projector of the spin-locking vector, producing a Knight-shift ellipsoid that classifies pairing classes and interprets NMR data.

References

92 extracted · 92 resolved · 1 Pith anchors

[1] to the vertex (0,0,1) of the simplex in Fig. 3. This one-parameter curve is the explicit base- line tested later by Protocol F and by the worked example of Sec. XIV. XI. CORE DIAGNOSTIC: KNIGHT-SHIFT

[2] Step 1: simplex location to pairing class Table VI maps each canonical simplex location to its first-pass diagnosis and to the look-alikes that share the sameT= 0 ellipsoid. The middle column is what

[3] For each, we list the smallest additional measurement or dataset that breaks the degeneracy

[4] Whenever the simplex location implies Παα = 0 for some axisα, the vanishing-projection theorem Eq

[5] XIV runs this diagnos- tic explicitly:

Formal links

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Receipt and verification

First computed	2026-05-20T00:03:36.757753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5640b3cd6799e161022173779c0bcbfebe919008853a915500648d0a52ebae52

Aliases

arxiv: 2605.17030 · arxiv_version: 2605.17030v1 · doi: 10.48550/arxiv.2605.17030 · pith_short_12: KZALHTLHTHQW · pith_short_16: KZALHTLHTHQWCARB · pith_short_8: KZALHTLH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KZALHTLHTHQWCARBON3ZYC6L72 \
  | 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: 5640b3cd6799e161022173779c0bcbfebe919008853a915500648d0a52ebae52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da523f0adf3e0eb69037644d3acbec5af83e7f21ed0e5ced81d3ca34827c6d93",
    "cross_cats_sorted": [
      "cond-mat.str-el"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.supr-con",
    "submitted_at": "2026-05-16T14:58:32Z",
    "title_canon_sha256": "fa1c67488f3d45a2163268f7967eca4ca40852210d35455453c8830622f0bf14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17030",
    "kind": "arxiv",
    "version": 1
  }
}