AI Mathematician: Towards Fully Automated Frontier Mathematical Research | Paper Citation Record

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Reference 1

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This paper cites Step 3: Hamiltonian Simulation Error Allocation Each term e−ikj Bτ must be simulated with error ≤ ϵ 2 in spectral norm.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research **Step 3: Hamiltonian Simulation Error Allocation** Each term e−ikj Bτ must be simulated with error ≤ ϵ 2 in spectral norm

Reference 2

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Observation 8dfe9766-5462-4491-83a4-ec03eeaaf961 · outbound

This paper cites From Stokes regularity, ∥plim∥L2(Dϵ) ≤C∥g∥ H −1/2.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research From Stokes regularity, ∥plim∥L2(Dϵ) ≤C∥g∥ H −1/2

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Observation b3714c2c-37e4-4c6b-94c5-a9b502543b7b · outbound

This paper cites Thus, there exists a unique solution (u,{φ k})in the specified spaces.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Thus, there exists a unique solution (u,{φ k})in the specified spaces

Reference 5

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Observation 1c89e5d9-f40b-4544-970e-de8604953059 · outbound

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AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

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Observation dc8d0600-efc9-4c63-b5f8-c2153d16663c · outbound

This paper cites Substituting: RHS≤C∥g∥ H −1/2 ·(C eλ−1∥g∥H −1/2 ) = C eλ ∥g∥2 H −1/2.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Substituting: RHS≤C∥g∥ H −1/2 ·(C eλ−1∥g∥H −1/2 ) = C eλ ∥g∥2 H −1/2

Reference 9

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Observation 235eca0b-3982-4104-9533-dc2c6a1cf16c · outbound

This paper cites comment: None type: conjecture Lemma 20.The differencew ε =u lim −u ε satisfies theL 2(Ω)error estimate: ∥wε∥L2(Ω) ≤ Cp eλ ∥g∥H −1/2(∂Ω), whereCis independent of eλ.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research comment: None type: conjecture Lemma 20.The differencew ε =u lim −u ε satisfies theL 2(Ω)error estimate: ∥wε∥L2(Ω) ≤ Cp eλ ∥g∥H −1/2(∂Ω), whereCis independent of eλ

Reference 10

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Observation 496b6461-7805-499e-84f8-d7514b5bf0b6 · outbound

This paper cites Substitute this into the energy identity: Z Ω λ(x)|divw ε|2 + 2µ(x)|D(wε)|2 dx= eλ∥divu ε∥2 L2(Dε).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Substitute this into the energy identity: Z Ω λ(x)|divw ε|2 + 2µ(x)|D(wε)|2 dx= eλ∥divu ε∥2 L2(Dε)

Reference 11

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Observation 81294eb8-c088-4893-921d-bdb1ac269f59 · outbound

This paper cites Thus: Energy integral≤ C eλ ∥g∥2 H −1/2(∂Ω).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Thus: Energy integral≤ C eλ ∥g∥2 H −1/2(∂Ω)

Reference 12

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Observation 0024c547-c0f7-4647-b31b-c6d8234c320e · outbound

This paper cites Under boundary conditions orthogonal to rigid motions, there existsC K >0such that: ∥wε∥2 H 1(Ω) ≤C K Z Ω |D(wε)|2 +|divw ε|2 dx.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Under boundary conditions orthogonal to rigid motions, there existsC K >0such that: ∥wε∥2 H 1(Ω) ≤C K Z Ω |D(wε)|2 +|divw ε|2 dx

Reference 13

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Observation 17a50fae-2abb-4b9f-9b05-6d4600822e2d · outbound

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Observation b4104d10-fa3a-488a-bb67-2df0b586e500 · outbound

This paper cites error” w:=u ϵ −u lim satisfies in Ωϵ the homogeneous Lamé system with zero Neumann data on ∂Ω and a “jump–residue.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research error” w:=u ϵ −u lim satisfies in Ωϵ the homogeneous Lamé system with zero Neumann data on ∂Ω and a “jump–residue

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AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

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AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

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Observation 3a04add8-7e41-42f2-b5ea-cc1fe0600848 · outbound

This paper cites 49 comment: Nonetype: lemma Lemma 25.(Uniform Coercivity of the Elasticity Bilinear Form) Let (λ, µ)satisfy the admissibility λ+ 2µ d >0,µ >0.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research 49 comment: Nonetype: lemma Lemma 25.(Uniform Coercivity of the Elasticity Bilinear Form) Let (λ, µ)satisfy the admissibility λ+ 2µ d >0,µ >0

Reference 19

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Observation eccf26f4-dc52-4007-8819-c5c834f8feac · outbound

This paper cites Hence for anyu∈H 1(Ωε;R d), aε(u, u) = Z Ωε Q(D(u))dx≥c 0 Z Ωε |D(u)|2 dx.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Hence for anyu∈H 1(Ωε;R d), aε(u, u) = Z Ωε Q(D(u))dx≥c 0 Z Ωε |D(u)|2 dx

Reference 21

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Observation 4360bf6b-9ce9-4516-9e17-30a4e1847195 · outbound

This paper cites By Conjecture 1 above, for allu∈V ε, ∥u∥2 H 1(Ωε) ≤C 2 ∥D(u)∥2 L2(Ωε), withCindependent ofε.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research By Conjecture 1 above, for allu∈V ε, ∥u∥2 H 1(Ωε) ≤C 2 ∥D(u)∥2 L2(Ωε), withCindependent ofε

Reference 22

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Observation 79ce6f63-fa1a-4de7-91b5-4157cc8d43d5 · outbound

This paper cites uniform extension + Korn on the fixed domain + pull-back,.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research uniform extension + Korn on the fixed domain + pull-back,

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Observation 7397e930-3f5f-49a5-9006-7896f4bf1a49 · outbound

This paper cites By the periodicity, the uniform separation of holes, and the Lipschitz regularity of ∂Ω, one constructs (e.g.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research By the periodicity, the uniform separation of holes, and the Lipschitz regularity of ∂Ω, one constructs (e.g

Reference 24

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Observation fd74b89e-21f2-4140-aaf9-f13ad27b65b5 · outbound

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Observation 7bbb0fc1-dde1-4440-a13f-d6995c27abe2 · outbound

This paper cites Take anyu∈V ε and setU:=E εu∈V.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Take anyu∈V ε and setU:=E εu∈V

Reference 26

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Observation 5bad17ca-2e11-487a-9ada-58e739e3f371 · outbound

This paper cites Define w:=u e −u lim, φ:= divu e.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Define w:=u e −u lim, φ:= divu e

Reference 27

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Observation 6622dbb7-8822-4eae-9d4a-5e369508415c · outbound

This paper cites Putting these together, the left-hand side becomes −˜µ R D |∇w|2 −( ˜λ+ ˜µ) R D |φ|2 and the right- hand side is− R D plimφ.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Putting these together, the left-hand side becomes −˜µ R D |∇w|2 −( ˜λ+ ˜µ) R D |φ|2 and the right- hand side is− R D plimφ

Reference 30

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Observation f0e7aedf-c051-464b-acf8-01a9c01ca232 · outbound

This paper cites Let V=D and set V ∗ =H −1(D).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Let V=D and set V ∗ =H −1(D)

Reference 31

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Reference 34

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Observation c38b67eb-a976-40fe-844b-e14f483db44b · outbound

This paper cites Combining the two estimates, |L(φ)| ≤C′ [λ∥divu∥+µ∥∇u∥]· ∥φ∥ H 1/2(∂D) , so by duality ∥σ(u)N∥ H −1/2(∂D) = sup φ̸=0 |L(φ)| ∥φ∥H 1/2 ≤C[λ∥divu∥ L2(D) +µ∥∇u∥ L2(D)], as claimed.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Combining the two estimates, |L(φ)| ≤C′ [λ∥divu∥+µ∥∇u∥]· ∥φ∥ H 1/2(∂D) , so by duality ∥σ(u)N∥ H −1/2(∂D) = sup φ̸=0 |L(φ)| ∥φ∥H 1/2 ≤C[λ∥divu∥ L2(D) +µ∥∇u∥ L2(D)], as claimed

Reference 35

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Reference 38

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Observation 6d7b21d2-8fdb-49c5-9d67-4a313a5dcd85 · outbound

This paper cites [Correct]The agent correctly employes mathematical inequality techniques to complete the derivation and gets a reasonable conclusion.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research [Correct]The agent correctly employes mathematical inequality techniques to complete the derivation and gets a reasonable conclusion

Reference 39

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Observation 77d7bc26-0882-4feb-8eb1-19b95f75a0cc · outbound

This paper cites [Vague]The process here is lack of details of theorem derivation.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research [Vague]The process here is lack of details of theorem derivation

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:09.904445Z

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Reference 42

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Observation 45dd6bbd-2608-4c99-a8f4-2a2ed4c49c02 · outbound

This paper cites comment: Nonetype: lemma Lemma 34.Let D⊂R d (d≥2 ) be a bounded Lipschitz domain with outward unit normalN, and let the Lamé parameters satisfy ˜µ >0and ˜λ+ 2˜µ/d >0.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research comment: Nonetype: lemma Lemma 34.Let D⊂R d (d≥2 ) be a bounded Lipschitz domain with outward unit normalN, and let the Lamé parameters satisfy ˜µ >0and ˜λ+ 2˜µ/d >0

Reference 43

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Observation 9bf913d7-4ad9-4719-97ed-3baca2731d09 · outbound

This paper cites Let T:H 1(D)− →H1/2(∂D) be any bounded right-inverse of the trace map (such an extension operator exists on Lipschitz domains).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Let T:H 1(D)− →H1/2(∂D) be any bounded right-inverse of the trace map (such an extension operator exists on Lipschitz domains)

Reference 44

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Observation c61c97fd-8f2e-465a-90d6-c47a01f0e078 · outbound

This paper cites Using Cauchy–Schwarz and the two energy bounds above, |⟨τ, g⟩| ≤ ∥∇u∥L2(D)∥∇G∥L2(D) +∥f∥ H −1 ∥G∥H 1(D) ≤(C 1C2 +C 2)∥f∥ H −1(D)∥g∥H 1/2(∂D).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Using Cauchy–Schwarz and the two energy bounds above, |⟨τ, g⟩| ≤ ∥∇u∥L2(D)∥∇G∥L2(D) +∥f∥ H −1 ∥G∥H 1(D) ≤(C 1C2 +C 2)∥f∥ H −1(D)∥g∥H 1/2(∂D)

Reference 45

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Observation be1467e0-a7e7-47b8-8e94-8209de6837fa · outbound

This paper cites normal-trace.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research normal-trace

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:08.504701Z

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Observation fff10af0-f560-4dd4-8213-4a4b1b2d7b2e · outbound

This paper cites Fix any φ∈H 1 2 (∂D;R d) and choose an H 1-extension v:=Eφ∈H 1(D;R d)with v|∂D =φ,∥v∥ H 1(D) ≤C ext∥φ∥H 1 2 (∂D).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Fix any φ∈H 1 2 (∂D;R d) and choose an H 1-extension v:=Eφ∈H 1(D;R d)with v|∂D =φ,∥v∥ H 1(D) ≤C ext∥φ∥H 1 2 (∂D)

Reference 47

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Observation 099dfca1-02bb-411f-9032-3cb8f8c2022c · outbound

This paper cites By the divergence theorem for Lipschitz domains (valid in theH(div)–H 1 duality), one checks for smoothpandφthat Z D σ:∇v+ Z D (divσ)·v= Z ∂D (σ N)·v= Z ∂D (pI N)·φ= Z ∂D p N·φ dS.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research By the divergence theorem for Lipschitz domains (valid in theH(div)–H 1 duality), one checks for smoothpandφthat Z D σ:∇v+ Z D (divσ)·v= Z ∂D (σ N)·v= Z ∂D (pI N)·φ= Z ∂D p N·φ dS

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:08.271631Z

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Observation cc5acbef-20b6-4a4d-b9cf-79058feb58ba · outbound

This paper cites From the definition ofT p and Cauchy–Schwarz one obtains ⟨Tp, φ⟩ ≤ ∥σ∥L2(D)∥∇v∥L2(D)+∥divσ∥ H −1(D)∥v∥H 1(D) ≤ ∥p∥L2(D)+∥∇p∥H −1(D) Cext∥φ∥H 1 2 (∂D).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research From the definition ofT p and Cauchy–Schwarz one obtains ⟨Tp, φ⟩ ≤ ∥σ∥L2(D)∥∇v∥L2(D)+∥divσ∥ H −1(D)∥v∥H 1(D) ≤ ∥p∥L2(D)+∥∇p∥H −1(D) Cext∥φ∥H 1 2 (∂D)

Reference 49

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9846c634-be35-4884-b09f-8a69997ec476 · outbound

This paper cites Thus the pressure in the inclusions is uniformly bounded by the boundary data, with no dependence onε.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Thus the pressure in the inclusions is uniformly bounded by the boundary data, with no dependence onε

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:07.781680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e845be8f-d421-49ed-8af7-6c0d2638893e · outbound

This paper cites Set Ωe := Ω\D e and define w:=u e −u lim on Ωe.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Set Ωe := Ω\D e and define w:=u e −u lim on Ωe

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:07.624598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 558930c5-d970-4146-b79b-d4028a25dbb6 · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 53

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:12:07.457708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e95cef43-b9c7-4a00-a652-c0efc7a93d00 · outbound

This paper cites Fix one inclusion D=D ε,i.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Fix one inclusion D=D ε,i

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:07.261449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4f13d8e7-7a0a-449f-9a4f-88260ad2c167 · outbound

This paper cites Combining the exterior bound of step 2 with the boundary-trace estimate of step 3 yields ∥ue −u lim∥H 1(Ωe) ≤Cmax i ∥ue −u lim∥H 1/2(∂Dε,i) ≤C ′˜λ−1/2∥g∥H −1/2(∂Ω), as claimed.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Combining the exterior bound of step 2 with the boundary-trace estimate of step 3 yields ∥ue −u lim∥H 1(Ωe) ≤Cmax i ∥ue −u lim∥H 1/2(∂Dε,i) ≤C ′˜λ−1/2∥g∥H −1/2(∂Ω), as claimed

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:06.985097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4e7e8b2c-6d4d-43e0-90ff-fc93439f41c4 · outbound

This paper cites By standard Neumann–Stokes theory (e.g.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research By standard Neumann–Stokes theory (e.g

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:06.725039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation abc31366-d523-4809-8301-72c708c128d9 · outbound

This paper cites Set w=u λ −u ∞ and φ= divu λ.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Set w=u λ −u ∞ and φ= divu λ

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:06.481516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 399f6fd8-4c19-4d9c-979e-e91ace355eaf · outbound

This paper cites By Cauchy–Schwarz, (λ+µ)∥φ∥ 2 L2 ≤ ∥p∞∥L2 ∥φ∥L2 ⇒ ∥φ∥L2(D) ≤(λ+µ) −1∥p∞∥L2(D) ≤C 2λ−1∥t∥H −1/2(∂D).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research By Cauchy–Schwarz, (λ+µ)∥φ∥ 2 L2 ≤ ∥p∞∥L2 ∥φ∥L2 ⇒ ∥φ∥L2(D) ≤(λ+µ) −1∥p∞∥L2(D) ≤C 2λ−1∥t∥H −1/2(∂D)

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:06.248991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 83a92a10-6b18-4aea-b0ba-70b399383666 · outbound

This paper cites From the energy identity again, µ∥∇w∥2 L2 ≤ ∥p∞∥L2 ∥φ∥L2 ≤C 3λ−1∥t∥2 H −1/2.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research From the energy identity again, µ∥∇w∥2 L2 ≤ ∥p∞∥L2 ∥φ∥L2 ≤C 3λ−1∥t∥2 H −1/2

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:06.077461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0d08a0ba-1522-4f8b-a9a4-91dd037d2afc · outbound

This paper cites Since t7→u λ −u ∞ is linear and the above estimate is uniform for all admissibletandλ≥λ 0, we conclude ∥A−1 λ −B −1∥L(V ∗,V) ≤Cλ −1/2.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Since t7→u λ −u ∞ is linear and the above estimate is uniform for all admissibletandλ≥λ 0, we conclude ∥A−1 λ −B −1∥L(V ∗,V) ≤Cλ −1/2

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:05.835561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3be4e0cf-27de-4c7d-8660-783797735a19 · outbound

This paper cites elastic pressure.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research elastic pressure

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:05.648769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 689118a2-3a0e-40b9-bad3-24b26e6044b0 · outbound

This paper cites Define the trial spaces V:={u∈H 1(D;R d) : Z ∂D u·r= 0∀rigid motionsr}, Q:=L 2 0(D) ={q∈L 2(D) : Z D q= 0}.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Define the trial spaces V:={u∈H 1(D;R d) : Z ∂D u·r= 0∀rigid motionsr}, Q:=L 2 0(D) ={q∈L 2(D) : Z D q= 0}

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:05.455503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a60a679f-0cdb-4376-8feb-cdff4731ecba · outbound

This paper cites A11 A12 A21 A22 # with A11 =a ∞ :V→V ∗, A 12 =−b T :Q→V ∗, A21 =b:V→Q ∗, A 22 =−(1/ ˜λ)s:Q→Q ∗. Equivalently, A(˜λ) =A ∞ −(1/ ˜λ)N, where A∞ =.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research A11 A12 A21 A22 # with A11 =a ∞ :V→V ∗, A 12 =−b T :Q→V ∗, A21 =b:V→Q ∗, A 22 =−(1/ ˜λ)s:Q→Q ∗. Equivalently, A(˜λ) =A ∞ −(1/ ˜λ)N, where A∞ =

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:05.212816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d927d996-6808-4e27-99a7-3e08239f874c · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 64

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:12:04.974853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c0cb7129-1caf-43d1-80e0-a72081a63abd · outbound

This paper cites boundary-trace lemma.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research boundary-trace lemma

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:04.783330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4b098fb3-9d39-43f2-9f4b-fa4fbf87f810 · outbound

This paper cites On each ε–inclusion D we denote by N the outward normal and by t:= (−p limI+ 2˜µD(ulim))N the Stokes-limit traction.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research On each ε–inclusion D we denote by N the outward normal and by t:= (−p limI+ 2˜µD(ulim))N the Stokes-limit traction

Reference 66

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:04.487612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation df370464-2a51-440c-b2f8-29703077bbd3 · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 67

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:12:04.325699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0944b542-5d9b-485b-9cbd-5d7d4f71c6ba · outbound

This paper cites By construction the H 1/2–norm on ∂Dε is the ℓ2–sum of the norms on each inclusion boundary: ∥(uε −u lim −U (1))|∂Dε ∥2 H 1/2(∂Dε) = X cellsD ∥RD 2 ∥2 H 1/2(∂D).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research By construction the H 1/2–norm on ∂Dε is the ℓ2–sum of the norms on each inclusion boundary: ∥(uε −u lim −U (1))|∂Dε ∥2 H 1/2(∂Dε) = X cellsD ∥RD 2 ∥2 H 1/2(∂D)

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:04.134446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e8278b94-bcc8-4f78-b753-8ff98157145e · outbound

This paper cites Define the space V:= v∈H 1(Ω;R d) : Z ∂Ω v·r dS+ NX i=1 Z ∂D iε v·r dS= 0∀rigid motionsr.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Define the space V:= v∈H 1(Ω;R d) : Z ∂Ω v·r dS+ NX i=1 Z ∂D iε v·r dS= 0∀rigid motionsr

Reference 69

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:03.888394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 944a2265-d23d-4a92-b43d-568e60a432a5 · outbound

This paper cites Set euε :=u lim + eλ−1U (1).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Set euε :=u lim + eλ−1U (1)

Reference 70

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:03.663018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3d895fba-a151-4a2d-ac8d-3ed87639e15f · outbound

This paper cites Its traction-jump on∂D e is J (1) e := σ(˜λ,˜µ)(˜ue)N − − σ(λ,µ)(˜ue)N + = ˜λ−1 σ(˜λ,˜µ)(U (1))N| − −σ (λ,µ)(U (1))N| +.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Its traction-jump on∂D e is J (1) e := σ(˜λ,˜µ)(˜ue)N − − σ(λ,µ)(˜ue)N + = ˜λ−1 σ(˜λ,˜µ)(U (1))N| − −σ (λ,µ)(U (1))N| +

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:03.479474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1d2d14c3-19c1-4603-ac1e-30552504be7d · outbound

This paper cites Then w solves the homogeneous Lamé system in Ωe with zero Neumann data on ∂Ω and with traction-jump J (1) e on ∂De.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Then w solves the homogeneous Lamé system in Ωe with zero Neumann data on ∂Ω and with traction-jump J (1) e on ∂De

Reference 72

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:03.303395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b226e054-a621-43a1-b7f6-97a134b2c60d · outbound

This paper cites This completes the proof.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research This completes the proof

Reference 73

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:03.004345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8cc64270-69ee-4721-a295-f7dc72911ba4 · outbound

This paper cites Hence ∥u˜λ −u 0∥H 1(D) ≤ ˜λ−1∥v1∥H 1(D) +C ˜λ−2∥t∥H − 1 2 (∂D).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Hence ∥u˜λ −u 0∥H 1(D) ≤ ˜λ−1∥v1∥H 1(D) +C ˜λ−2∥t∥H − 1 2 (∂D)

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:02.805489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fc560351-2b54-430f-acd6-0bd8ba401cde · outbound

This paper cites elastic pressure.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research elastic pressure

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:02.678845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3e2a4714-5c11-49b6-8c32-5191dfb233f2 · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 76

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:12:02.466161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b0190fef-9ddd-448d-936a-7a02b4d1a7ce · outbound

This paper cites [Vague]The proof here just offers the conclusions but not the detailed process.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research [Vague]The proof here just offers the conclusions but not the detailed process

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:02.137310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 25c6082e-9036-425a-a8fc-96d95bc9107e · outbound

This paper cites Define the closed subspace V0 :={v∈H 1(Ωε;R d) :v= 0on∂D ε, σ(v)N= 0on∂Ω} and the bilinear form a(v, w) := Z Ωε 2µ D(v) :D(w) +λ(divv)(divw) dx.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Define the closed subspace V0 :={v∈H 1(Ωε;R d) :v= 0on∂D ε, σ(v)N= 0on∂Ω} and the bilinear form a(v, w) := Z Ωε 2µ D(v) :D(w) +λ(divv)(divw) dx

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:01.924600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d0fb0343-c908-4356-86da-58a2f1e71c53 · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 79

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:12:01.672312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 72b45005-8856-47cd-ad8c-96bc83e70c6e · outbound

This paper cites Set ψ:=E(φ), z:=w ext −ψ.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Set ψ:=E(φ), z:=w ext −ψ

Reference 80

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:01.404008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 35e3fb91-5858-4a27-9ffb-4b2e95255c90 · outbound

This paper cites Taking v=z in the last identity and using Cauchy–Schwarz plus coercivity, α∥z∥ 2 H 1(Ωε) ≤ |a(ψ, z)| ≤C a ∥ψ∥H 1(Ωε) ∥z∥H 1(Ωε), whereC a depends only on the Lamé parameters(λ, µ).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Taking v=z in the last identity and using Cauchy–Schwarz plus coercivity, α∥z∥ 2 H 1(Ωε) ≤ |a(ψ, z)| ≤C a ∥ψ∥H 1(Ωε) ∥z∥H 1(Ωε), whereC a depends only on the Lamé parameters(λ, µ)

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:01.154668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ecde4116-5397-4fe5-a5d6-f117d8a25ef3 · outbound

This paper cites Notingφ=w ext|∂Dε = (uε −u lim)|∂Dε, we arrive at the asserted estimate ∥uε −u lim∥H 1(Ωε) ≤C∥u ε −u lim∥H 1/2(∂Dε).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Notingφ=w ext|∂Dε = (uε −u lim)|∂Dε, we arrive at the asserted estimate ∥uε −u lim∥H 1(Ωε) ≤C∥u ε −u lim∥H 1/2(∂Dε)

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:00.947804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 66c0aeaf-16d5-4110-a5b4-5347cf047c3f · outbound

This paper cites 3.Ω\Dis connected and has a Lipschitz boundary∂Ω∪∂D.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research 3.Ω\Dis connected and has a Lipschitz boundary∂Ω∪∂D

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:00.738588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1cf7418c-fda6-48bd-b287-72cb3b1f86ed · outbound

This paper cites 3.Ω\Dis connected and has a Lipschitz boundary∂Ω∪∂D.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research 3.Ω\Dis connected and has a Lipschitz boundary∂Ω∪∂D

Reference 84

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:00.561571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 98034778-47c5-442b-9b11-f59aa4e12883 · outbound

This paper cites By the scalingx=εyone deduces that on eachε-cellε(Y f +k) for allv∈H 1(ε(Yf +k)),∥v∥ H 1(ε(Yf +k)) ≤C 0 ∥v∥L2(ε(Yf +k)) +∥sym∇v∥ L2(ε(Yf +k)).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research By the scalingx=εyone deduces that on eachε-cellε(Y f +k) for allv∈H 1(ε(Yf +k)),∥v∥ H 1(ε(Yf +k)) ≤C 0 ∥v∥L2(ε(Yf +k)) +∥sym∇v∥ L2(ε(Yf +k))

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:00.348234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8bf291a6-a54b-4078-8aec-e49b6d4419f7 · outbound

This paper cites We also choose a finite set of boundary functions {ψb} supported in the ε-neighborhood of ∂Ω so that P k ψk + P b ψb ≡1 on Ω.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research We also choose a finite set of boundary functions {ψb} supported in the ε-neighborhood of ∂Ω so that P k ψk + P b ψb ≡1 on Ω

Reference 86

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:12:00.189860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a4be7dff-94a6-414b-807f-45c92be62d91 · outbound

This paper cites On each interior cell we apply the scaled Korn of Step 1: ∥uk∥H 1(ε(Yf +k)) ≤C 0 [∥ψku∥L2 +∥sym∇(ψ ku)∥L2 ] ≤C 0 ∥u∥L2(suppψ k) +∥ψ k sym∇u∥ L2 +∥u⊗ ∇ψk∥L2.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research On each interior cell we apply the scaled Korn of Step 1: ∥uk∥H 1(ε(Yf +k)) ≤C 0 [∥ψku∥L2 +∥sym∇(ψ ku)∥L2 ] ≤C 0 ∥u∥L2(suppψ k) +∥ψ k sym∇u∥ L2 +∥u⊗ ∇ψk∥L2

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:59.986349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 486be83f-9f83-46a9-a761-9d5ad08d338c · outbound

This paper cites This completes the proof.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research This completes the proof

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:59.778648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 15b77e2d-01b0-4e61-901d-431fb14a5f32 · outbound

This paper cites Recall the unfolding operator Tε :L 2(Ωε)→L 2(Ω×Y f ), which on each cellΩ ε ∩ε(k+Y f )is defined by (Tεv)(x, y) =v(εk+εy), x∈ε(k+Y), y∈Y f , zero elsewhere.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Recall the unfolding operator Tε :L 2(Ωε)→L 2(Ω×Y f ), which on each cellΩ ε ∩ε(k+Y f )is defined by (Tεv)(x, y) =v(εk+εy), x∈ε(k+Y), y∈Y f , zero elsewhere

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:59.580869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 815f34fa-5196-4223-a1ac-3fc41482bb9b · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 90

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:11:59.361492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7ceef03b-aafe-40e0-937b-58a0471c7745 · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 91

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:11:59.166299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7d58d4d1-f545-4a2a-b931-c50478589c9d · outbound

This paper cites We set W(x, y) = lim ε→0 ∇yTεuε inL 2(Ω×Y f ).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research We set W(x, y) = lim ε→0 ∇yTεuε inL 2(Ω×Y f )

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:58.966759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 63ffaa7a-c15d-46a0-a17f-f5cb86895e80 · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 93

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:11:58.783745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ddd7289f-f0ac-4585-9ba6-4cfd699caf88 · outbound

This paper cites [Error]The test function space may not be accurate since the divergence of the function is not concluded in this conclusion.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research [Error]The test function space may not be accurate since the divergence of the function is not concluded in this conclusion

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:58.590884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2a2a2b89-1cf4-49ba-8630-9727206f37a6 · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 95

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:11:58.378606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5bba44c8-d13a-46a6-b4c9-6b48269c0104 · outbound

This paper cites Inserting (vε, qε) into the variational equation and passing to the limit by two-scale convergence (unfolding arguments in Lemma A.4) yields for a.e.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Inserting (vε, qε) into the variational equation and passing to the limit by two-scale convergence (unfolding arguments in Lemma A.4) yields for a.e

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:58.196129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation feebffb0-3255-4991-9e82-556f388cc7ae · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 97

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:11:57.979371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 16902a27-ece9-4e14-8500-7f54ab101a3e · outbound

This paper cites [Vague]The conditions for using the theorem need to be verified.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research [Vague]The conditions for using the theorem need to be verified

Reference 98

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:57.761707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b90e3e4a-c662-491e-90ae-103f9e8b875a · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 99

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:11:57.543853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 53b28f11-23df-409f-a34c-93680adc319f · outbound

This paper cites In particular, for any smooth strain field E(x) =D xu0(x), one has by the chain rule ∇xχE(x)(y) = (∂ EχE)(y)[D2 xu0(x)] and hence ∥∇xχDxu0(·)(·/ε)∥L2(Ωε) ≤C∥u 0∥H 2(Ω).

AI Mathematician: Towards Fully Automated Frontier Mathematical Research In particular, for any smooth strain field E(x) =D xu0(x), one has by the chain rule ∇xχE(x)(y) = (∂ EχE)(y)[D2 xu0(x)] and hence ∥∇xχDxu0(·)(·/ε)∥L2(Ωε) ≤C∥u 0∥H 2(Ω)

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:57.336968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f9f8474a-c409-4603-b1ea-693cdeda64b6 · outbound

This paper cites an unresolved cited work.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research Unresolved cited work

Reference 101

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:11:57.151872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f6e59551-9c46-432c-9d04-0a417627241c · outbound

This paper cites [Vague]The derivation process here is in urgent need of proof details.

AI Mathematician: Towards Fully Automated Frontier Mathematical Research [Vague]The derivation process here is in urgent need of proof details

Reference 102

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:11:56.975163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers