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Paper Citation Record · LEDGER

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data

As of 5 August 2026, this Paper Citation Record lists 7 of 7 outbound references and 0 inbound Pith citation observations for arXiv:2605.29669.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2605.29669 v2

Coverage vector

measured 7 of 7 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-29T05:32:50.381010Z

measured 7 of 7 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

7 of 7 outbound references displayed

  • verified exact0
  • verified fuzzy0
  • unresolved6
  • parse uncertain0
  • malformed identifier1
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fadd34ff-8c83-44fa-b1a0-c47396e9c94d · outbound

This paper cites an unresolved cited work.

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data Unresolved cited work

Reference 1

Resolution
unresolved
no resolver link, observed 2026-06-29T05:32:50.381010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T05:32:50.381010Z digest=sha256:916d59899a7f01b918b6a8b147e76c8e82ccf8795ddb8acf1ecc731e1550fc7c

Observation d142abdc-c447-49f6-98f4-7d06843c91c4 · outbound

This paper cites If{A n}are random matrices, we interpret ∥An∥op =o P(1)⇐ ⇒ ∥A n∥op P − →0.

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data If{A n}are random matrices, we interpret ∥An∥op =o P(1)⇐ ⇒ ∥A n∥op P − →0

Reference 2

Resolution
malformed identifier
no resolver link, observed 2026-06-29T05:32:50.381010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T05:32:50.381010Z digest=sha256:2a97f2ff32f602d5c1e97f5ce26cae5ea705f7a3437916dfd22a74d3ff779a27

Observation 13467c44-1fd3-4785-a4bf-716e57001134 · outbound

This paper cites Write logQ m = log Γ(m+ 1 2)−log Γ(m) − 1 2 logm.

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data Write logQ m = log Γ(m+ 1 2)−log Γ(m) − 1 2 logm

Reference 3

Resolution
unresolved
no resolver link, observed 2026-06-29T05:32:50.381010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T05:32:50.381010Z digest=sha256:a64be089aac102a9d0b3b5a05eb10c957f50560f41220643c6ea13640f112cb3

Observation f92e1ae4-4afe-4f5a-adf6-1d7b8ba52fc5 · outbound

This paper cites The logarithmic terms simplify to mlog 1 + 1 2m − 1 2.

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data The logarithmic terms simplify to mlog 1 + 1 2m − 1 2

Reference 4

Resolution
unresolved
no resolver link, observed 2026-06-29T05:32:50.381010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T05:32:50.381010Z digest=sha256:df9d559036d3abe1fcd1b5ac31435c41ddaa4e4c2ad2a929e928322d6449142a

Observation b2511ddc-6cdb-4b97-a56a-fcb0cf74710b · outbound

This paper cites Further, the difference− 1 360(m+ 1 2 )3 + 1 360m3 isO(m −4) (since the leading term cancels and the remainder begins at orderm −4).

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data Further, the difference− 1 360(m+ 1 2 )3 + 1 360m3 isO(m −4) (since the leading term cancels and the remainder begins at orderm −4)

Reference 5

Resolution
unresolved
no resolver link, observed 2026-06-29T05:32:50.381010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T05:32:50.381010Z digest=sha256:27aef51f44e4e88f47aee0d2500c881887045a9cd4f223c1b828e734f3577ef0

Observation 35262b4b-5933-43e1-862e-b60d96c8ce5e · outbound

This paper cites The matricesYΠ s andY ♯ s have operator normO P(1):Y ♯ 0 Πs is bounded by Proposition 31, and the quadratic term has norm |cσ|θ2 0 2 ∥a⊙2∥ ∥Πsq∥=O P(1) by Lemmas 55 and 56.

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data The matricesYΠ s andY ♯ s have operator normO P(1):Y ♯ 0 Πs is bounded by Proposition 31, and the quadratic term has norm |cσ|θ2 0 2 ∥a⊙2∥ ∥Πsq∥=O P(1) by Lemmas 55 and 56

Reference 6

Resolution
unresolved
no resolver link, observed 2026-06-29T05:32:50.381010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T05:32:50.381010Z digest=sha256:f337863dcc6c840ada184ea5628ecb7e9706fefaacf3cd353dabdea9e7c695d7

Observation 1b120ecc-92c2-41bd-b6e8-de4207d37d8b · outbound

This paper cites Define its Hermite coefficients ζ(i) k :=E[σ (i)(ξ)hk(ξ)], k∈N, 82 and the diagonal matricesD k := diag(ζ(1) k ,.

Eigen-Spike Emergence and Quadratic Equivalents for Conjugate Kernels on Nonlinearly Separable Data Define its Hermite coefficients ζ(i) k :=E[σ (i)(ξ)hk(ξ)], k∈N, 82 and the diagonal matricesD k := diag(ζ(1) k ,

Reference 7

Resolution
unresolved
no resolver link, observed 2026-06-29T05:32:50.381010Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T05:32:50.381010Z digest=sha256:867aab9db14d3d4f2bc450c1b4d327db7bc04f23709190d06b8acb23ba95b358

Pith citing papers

No inbound Pith citation observations are available.