# Is there a unified microscopic theory of unconventional superconductivity?

Distinguish shared pairing frameworks from universal mechanisms, and compare symmetry, model calculations and material-specific evidence.

## Scope

A shared mathematical language is available, but it is not yet a demonstrated, quantitatively predictive microscopic explanation of every unconventional superconductor in the sources reviewed here. Three goals should be distinguished: classifying order parameters, identifying a common dominant interaction, and predicting material-specific observables from independently constrained inputs. Success at one level does not establish the others. Scalapino's spin-fluctuation framework is an influential proposed connection across several families, not a proof that every family has an identical mechanism. [R1](#ref-source-eaa3beeed4368f46) [R2](#ref-source-1fe5a46dbbba61a4) [R10](#ref-source-51a15c56a9ac1472)

This question asks what would count as unification and what current examples actually test. It does not assume that cuprates, iron compounds, heavy-fermion materials and every newer platform must reduce to the same minimal Hamiltonian. Conversely, different gap symmetries do not by themselves require unrelated interactions: the same bilayer model can favor different pairing channels when its electronic structure changes. [R1](#ref-source-eaa3beeed4368f46) [R2](#ref-source-1fe5a46dbbba61a4)

## Mathematical assumptions

A schematic linearized singlet pairing equation is

$$
-\frac{T}{N}\sum_{K'}\Gamma^{pp}(K,K')G(K')G(-K')\phi(K')
=\lambda\phi(K).
$$

Here $K$ combines momentum and fermionic Matsubara frequency, $G$ is the normal-state dressed propagator, and $\Gamma^{pp}$ is the irreducible particle–particle vertex in a consistent normalization. Units use $k_B=1$; $N$ denotes the momentum-mesh normalization. Within the specified approximation, a leading eigenvalue reaching one signals a pairing instability. The eigenfunction describes a pairing structure, whereas the vertex and propagators encode more of the microscopic physics. Writing this equation does not solve for those inputs or establish the actual phase-ordering temperature. [R1](#ref-source-eaa3beeed4368f46) [R2](#ref-source-1fe5a46dbbba61a4)

An original two-channel example illustrates the inverse problem. For orthonormal real vectors $v,w$, define the dimensionless kernel

$$
\mathcal K_\mu=0.6\,vv^{\mathsf T}+\mu\,ww^{\mathsf T},\qquad -1\leq\mu\leq0.5.
$$

Every member has the same leading eigenvector $v$ and eigenvalue 0.6, yet its response to a source in the $w$ direction is $(I-\mathcal K_\mu)^{-1}w=w/(1-\mu)$. That response varies from 0.5 to 2 in the stated normalization. Seventy-two independently diagonalized examples verify the construction. The lesson is limited: a leading gap pattern alone need not uniquely identify a kernel. These matrices are not assigned to real materials or claimed to be realizable by distinct microscopic mechanisms; no transition temperature is inferred. [R1](#ref-source-eaa3beeed4368f46)

## A shared interaction can give different gaps

Maier and Scalapino studied a bilayer Hubbard model with $U/t=6$, filling 0.95 and a $2\times4\times4$ dynamic-cluster approximation. Increasing interlayer hopping changes the leading response from $d_{x^2-y^2}$ to sign-changing $s$ pairing. Their selected author text connects this change to intra- versus interlayer spin fluctuations. This is a concrete model example of related interactions producing different gap structures, not a material-by-material demonstration of one universal mechanism. [R2](#ref-source-1fe5a46dbbba61a4)

The same paper explicitly lacks the finite-size scaling needed to determine a thermodynamic transition temperature. Its quoted temperature estimates come from a cluster susceptibility divergence. Moreover, a larger pairing-interaction measure does not alone give the largest estimated transition: quasiparticle renormalization also changes. A unification claim must therefore compare both the interaction and the electronic response, not simply rank the strength of a proposed fluctuation. [R2](#ref-source-1fe5a46dbbba61a4)

## Model results depend on the question asked

Qin and colleagues' 2020 study concerns nearest-neighbor hopping only, moderate-to-strong interactions around $U/t=6$–8, and hole doping approximately 0.1–0.2. Its nonsuperconducting conclusion is restricted to that regime; the paper explicitly does not rule out superconductivity everywhere in the Hubbard model. Constrained-path auxiliary-field Monte Carlo introduces a trial-state-dependent systematic error, checked against narrow-cylinder DMRG. The comparison is valuable but does not turn the approximation into an exact solution of all sizes. [R3](#ref-source-74cc3f39d62d38b0)

Xu and colleagues instead include next-neighbor hopping, using $U/t=8$ and $t'/t=-0.2$ on the hole-doped side; a particle–hole mapping gives the positive-sign comparison for electron doping. The checked author manuscript combines twist averaging with a thermodynamic extrapolation followed by removal of the applied pairing field. It reports ground-state pairing coexisting with partially filled stripes and explicitly states that it has not predicted transition temperatures. A dome in a zero-temperature order parameter is not a calculated or measured $T_c$ dome. These studies ask different parameter-dependent questions, so their headlines should not be treated as direct contradictions. [R4](#ref-source-e7b3ac50f76789ac)

## Recent numerical evidence and its limits

Gu and colleagues' June 2026 neural-state paper reports stripe configurations and variational-energy improvements for specified Hubbard systems. Its final accuracy discussion says that $d$-wave correlations strengthen as the calculation improves and that further controlled calculations are needed for superconductivity conclusions. It should not be cited as a definitive absence-of-superconductivity proof. Periodic boundaries remove open edges, but they do not eliminate finite-size or variational errors. [R5](#ref-source-b417dbe2d449c0bb)

An August 2026 preprint by Rende and colleagues uses a translationally symmetric variational ansatz at $U/t=8$, $t'/t=-0.2$ and one-eighth hole doping. It reports long-distance pairing correlations and a finite extrapolated order parameter. Its discussion leaves thermodynamic coexistence with long-range stripe order unresolved. This is a dated preprint result with explicit ansatz and scaling assumptions, not an exact solution or a universal theory. Uniform one-body density in a symmetric state also does not preclude stripe signatures in correlation functions. [R6](#ref-source-095247a10e506437)

## Experimental criteria

Phase-sensitive observations constrain the order parameter, while identifying the dominant microscopic pairing interaction requires additional evidence. The original tricrystal-ring work provides a symmetry test in YBa₂Cu₃O₇−δ; that observation alone does not uniquely invert the pairing vertex. A stronger mechanism test compares momentum, frequency, orbital and temperature dependence across independent probes, together with changes induced by a controlled tuning parameter. Agreement should include observations not used to fit the proposed explanation. [R1](#ref-source-eaa3beeed4368f46) [R9](#ref-source-2e4d7fdb6c1797b7)

Several interactions can cooperate or compete. The checked nematic-fluctuation theory predicts enhancement under specified weak-coupling assumptions, rather than a universal pairing symmetry. The FeSe/SrTiO₃ interfacial-mode study considers enhancement on top of a magnetic pairing baseline. Those examples caution against treating magnetic, charge, orbital and lattice effects as mutually exclusive labels. Their presence or proximity in a phase diagram is not by itself a causal measurement of their contribution to pairing. [R7](#ref-source-24dd77640a555a0f) [R8](#ref-source-f9fe6e9bc3792dcc)

## Limits and disputes

A convincing unification should state its range of materials, independently constrained Hamiltonian, treatment of correlations and competing orders, and measurable predictions with errors. Cross-method agreement at one parameter point supports that point, not every lattice or composition. Numerical energy accuracy also does not automatically guarantee accurate long-distance response. The cited Hubbard studies are examples for evaluating this logic; they are not an exhaustive survey or a final settlement of all model phase diagrams. [R3](#ref-source-74cc3f39d62d38b0) [R4](#ref-source-e7b3ac50f76789ac) [R5](#ref-source-b417dbe2d449c0bb) [R10](#ref-source-51a15c56a9ac1472)

## Discovery implications

Compare proposed mechanisms through discriminating predictions: which changes in structure, filling, pressure or disorder alter the gap, collective response and competing phases together? Preserve failures and alternative explanations, and distinguish a broadly useful organizing principle from a quantitatively validated material theory. This research program can guide discovery even while a universal microscopic account remains unestablished within the reviewed evidence. [R1](#ref-source-eaa3beeed4368f46) [R7](#ref-source-24dd77640a555a0f) [R10](#ref-source-51a15c56a9ac1472)

## Related topics

Continue with [spin-fluctuation pairing](/scwiki/spin-fluctuation-pairing), [nematic fluctuations](/scwiki/nematic-fluctuation-pairing), [cuprates](/scwiki/cuprates), [iron-based superconductors](/scwiki/iron-based-superconductors), and [theoretical tools](/scwiki/theoretical-tools).

## Material cases

No sample-specific material records are included in this article. Model results are not experimental transition temperatures.

## Sources

### Ref source-eaa3beeed4368f46

[R1] A common thread: The pairing interaction for unconventional superconductors (2012). [DOI 10.1103/RevModPhys.84.1383](https://doi.org/10.1103/RevModPhys.84.1383). Publication: journal-article. Check: author-review-scoped-check. Checked: 2026-10-18. Selected manuscript text pp. 4, 18–20, 39–46; p. 41 Eq. (13) visually checked. Full 87-page review and final-version equivalence not audited. Independent two-patch algebra is an illustration, not reproduction of a Hubbard calculation.
### Ref source-1fe5a46dbbba61a4

[R2] Pair structure and the pairing interaction in a bilayer Hubbard model for unconventional superconductivity (2011). [DOI 10.1103/PhysRevB.84.180513](https://doi.org/10.1103/PhysRevB.84.180513). Publication: journal-article. Check: selected-author-model-and-figure-check. Checked: 2026-10-19. Journal published 28 November 2011. Author v2 dated 19 July 2011: selected pp. 1–3; Figure 4 and the finite-size limitation on p. 3 visually checked. The PDF interior recompile date is not the publication date. Final full-text equivalence and raw DCA reproduction remain open.
### Ref source-74cc3f39d62d38b0

[R3] Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model (2020). [DOI 10.1103/PhysRevX.10.031016](https://doi.org/10.1103/PhysRevX.10.031016). Publication: journal-article. Check: selected-final-model-and-method-text. Checked: 2026-10-19. Published 21 July 2020. Selected final pp. 1–4 read: nearest-neighbor-only model, interaction/doping window, constrained-path systematic error and ordered limits. No local PDF visual check, complete appendices or QMC reproduction is claimed.
### Ref source-e7b3ac50f76789ac

[R4] Coexistence of superconductivity with partially filled stripes in the Hubbard model (2024). [DOI 10.1126/science.adh7691](https://doi.org/10.1126/science.adh7691). Publication: journal-article. Check: selected-author-model-extrapolation-and-limits. Checked: 2026-10-19. Journal identity linked by the author archive. Selected author v1 of 15 March 2023: pp. 2–4 and 6–7, with Figure 6 on p. 6 visually checked. Ground-state order, next-neighbor hopping and twist averaging retained. Final full-text/supplement comparison and solver reproduction remain open.
### Ref source-b417dbe2d449c0bb

[R5] Solving the Hubbard model with neural quantum states (2026). [DOI 10.1038/s41467-026-74028-6](https://doi.org/10.1038/s41467-026-74028-6). Publication: journal-article. Check: selected-final-stripe-results-and-accuracy-limits. Checked: 2026-10-19. Published 22 June 2026. Selected final pp. 5–6 and beginning of methods; p. 6 accuracy discussion and Figures 5–6 visually checked. Authors explicitly require further controlled calculations of superconducting correlations. Full supplement and model training were not reproduced.
### Ref source-095247a10e506437

[R6] Superconductivity in the t-t′ Hubbard Model from Symmetry-Preserving Neural-Network Quantum States (2026). [DOI 10.48550/arXiv.2608.12465](https://doi.org/10.48550/arXiv.2608.12465). Publication: preprint. Check: selected-preprint-ansatz-correlations-and-limits. Checked: 2026-10-19. arXiv v1 submitted 12 August 2026; PDF interior dated 14 August. Selected pp. 2–6 read; p. 5 Figure 4, Table I and correlation normalization visually checked. Specific parameter regime, finite-size extrapolation and unresolved thermodynamic stripe coexistence retained. Preprint status; no full methods/code reproduction or journal acceptance verified.
### Ref source-24dd77640a555a0f

[R7] Enhancement of Superconductivity near a Nematic Quantum Critical Point (2015). [DOI 10.1103/PhysRevLett.114.097001](https://doi.org/10.1103/PhysRevLett.114.097001). Publication: journal-article. Check: primary-equations-scoped-check. Checked: 2026-10-18. Lederer et al. published selected pp.1–3 web text Eqs.3,6,11; authorv3 p.2 visually checked. Controlled weak coupling and nematic form factor versus gap symmetry. Publisher direct download401; full supplement and model reproduction open. Angular overlaps here are independent illustrations.
### Ref source-f9fe6e9bc3792dcc

[R8] Interfacial mode coupling as the origin of the enhancement of Tc in FeSe films on SrTiO3 (2014). [DOI 10.1038/nature13894](https://doi.org/10.1038/nature13894). Publication: journal-article. Check: selected-author-results-and-figure-check. Checked: 2026-10-19. Nature publication 13 November 2014; identified author v6 revised 11 May 2015. Selected pp. 3–6, Figure 2 p. 14 visually checked and Figure 4 continuation p. 17 visually checked. Gap closing 58±7 K is a mean-field fit, not zero resistance; predicted enhancement assumes a magnetic baseline. Full supplementary growth/ARPES methods, final-version comparison and raw fitting remain open.
### Ref source-2e4d7fdb6c1797b7

[R9] Pairing Symmetry and Flux Quantization in a Tricrystal Superconducting Ring of YBa2Cu3O7-delta (1994). [DOI 10.1103/PhysRevLett.73.593](https://doi.org/10.1103/PhysRevLett.73.593). Publication: journal-article. Check: publisher-original-abstract. Checked: 2026-10-18. Published 25 July 1994. The original abstract reports scanning SQUID observations at 4.2 K in rings with different junction counts. The complete original article and raw flux maps have not been reviewed here.
### Ref source-51a15c56a9ac1472

[R10] Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms (2015). [DOI 10.1103/PhysRevX.5.041041](https://doi.org/10.1103/PhysRevX.5.041041). Publication: journal-article. Check: selected-published-qmc-dmrg-convergence-check. Checked: 2026-10-19. Published 14 December 2015. Selected pages 1–4, 7–8 and 10; the DMRG convergence discussion on page 8 visually checked. The review retains constrained-path and particle-hole conditions, finite-cylinder limits and method-specific errors. Full tables, datasets and all algorithms have not been reproduced.

## Claim evidence and conditions

### scwiki-n2-claim-scope-1

A shared mathematical language is available, but it is not yet a demonstrated, quantitatively predictive microscopic explanation of every unconventional superconductor in the sources reviewed here. Three goals should be distinguished: classifying order parameters, identifying a common dominant interaction, and predicting material-specific observables from independently constrained inputs. Success at one level does not establish the others. Scalapino's spin-fluctuation framework is an influential proposed connection across several families, not a proof that every family has an identical mechanism.

Evidence: hypothesis. Sources: source-eaa3beeed4368f46, source-1fe5a46dbbba61a4, source-51a15c56a9ac1472.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-scope-2

This question asks what would count as unification and what current examples actually test. It does not assume that cuprates, iron compounds, heavy-fermion materials and every newer platform must reduce to the same minimal Hamiltonian. Conversely, different gap symmetries do not by themselves require unrelated interactions: the same bilayer model can favor different pairing channels when its electronic structure changes.

Evidence: hypothesis. Sources: source-eaa3beeed4368f46, source-1fe5a46dbbba61a4.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-mathematical-assumptions-3

Here $K$ combines momentum and fermionic Matsubara frequency, $G$ is the normal-state dressed propagator, and $\Gamma^{pp}$ is the irreducible particle–particle vertex in a consistent normalization. Units use $k_B=1$; $N$ denotes the momentum-mesh normalization. Within the specified approximation, a leading eigenvalue reaching one signals a pairing instability. The eigenfunction describes a pairing structure, whereas the vertex and propagators encode more of the microscopic physics. Writing this equation does not solve for those inputs or establish the actual phase-ordering temperature.

Evidence: theory. Sources: source-eaa3beeed4368f46, source-1fe5a46dbbba61a4.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-mathematical-assumptions-6

Every member has the same leading eigenvector $v$ and eigenvalue 0.6, yet its response to a source in the $w$ direction is $(I-\mathcal K_\mu)^{-1}w=w/(1-\mu)$. That response varies from 0.5 to 2 in the stated normalization. Seventy-two independently diagonalized examples verify the construction. The lesson is limited: a leading gap pattern alone need not uniquely identify a kernel. These matrices are not assigned to real materials or claimed to be realizable by distinct microscopic mechanisms; no transition temperature is inferred.

Evidence: theory. Sources: source-eaa3beeed4368f46.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-a-shared-interaction-can-give-different-gaps-1

Maier and Scalapino studied a bilayer Hubbard model with $U/t=6$, filling 0.95 and a $2\times4\times4$ dynamic-cluster approximation. Increasing interlayer hopping changes the leading response from $d_{x^2-y^2}$ to sign-changing $s$ pairing. Their selected author text connects this change to intra- versus interlayer spin fluctuations. This is a concrete model example of related interactions producing different gap structures, not a material-by-material demonstration of one universal mechanism.

Evidence: theory. Sources: source-1fe5a46dbbba61a4.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-a-shared-interaction-can-give-different-gaps-2

The same paper explicitly lacks the finite-size scaling needed to determine a thermodynamic transition temperature. Its quoted temperature estimates come from a cluster susceptibility divergence. Moreover, a larger pairing-interaction measure does not alone give the largest estimated transition: quasiparticle renormalization also changes. A unification claim must therefore compare both the interaction and the electronic response, not simply rank the strength of a proposed fluctuation.

Evidence: theory. Sources: source-1fe5a46dbbba61a4.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-model-results-depend-on-the-question-asked-1

Qin and colleagues' 2020 study concerns nearest-neighbor hopping only, moderate-to-strong interactions around $U/t=6$–8, and hole doping approximately 0.1–0.2. Its nonsuperconducting conclusion is restricted to that regime; the paper explicitly does not rule out superconductivity everywhere in the Hubbard model. Constrained-path auxiliary-field Monte Carlo introduces a trial-state-dependent systematic error, checked against narrow-cylinder DMRG. The comparison is valuable but does not turn the approximation into an exact solution of all sizes.

Evidence: theory. Sources: source-74cc3f39d62d38b0.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-model-results-depend-on-the-question-asked-2

Xu and colleagues instead include next-neighbor hopping, using $U/t=8$ and $t'/t=-0.2$ on the hole-doped side; a particle–hole mapping gives the positive-sign comparison for electron doping. The checked author manuscript combines twist averaging with a thermodynamic extrapolation followed by removal of the applied pairing field. It reports ground-state pairing coexisting with partially filled stripes and explicitly states that it has not predicted transition temperatures. A dome in a zero-temperature order parameter is not a calculated or measured $T_c$ dome. These studies ask different parameter-dependent questions, so their headlines should not be treated as direct contradictions.

Evidence: theory. Sources: source-e7b3ac50f76789ac.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-recent-numerical-evidence-and-its-limits-1

Gu and colleagues' June 2026 neural-state paper reports stripe configurations and variational-energy improvements for specified Hubbard systems. Its final accuracy discussion says that $d$-wave correlations strengthen as the calculation improves and that further controlled calculations are needed for superconductivity conclusions. It should not be cited as a definitive absence-of-superconductivity proof. Periodic boundaries remove open edges, but they do not eliminate finite-size or variational errors.

Evidence: theory. Sources: source-b417dbe2d449c0bb.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-recent-numerical-evidence-and-its-limits-2

An August 2026 preprint by Rende and colleagues uses a translationally symmetric variational ansatz at $U/t=8$, $t'/t=-0.2$ and one-eighth hole doping. It reports long-distance pairing correlations and a finite extrapolated order parameter. Its discussion leaves thermodynamic coexistence with long-range stripe order unresolved. This is a dated preprint result with explicit ansatz and scaling assumptions, not an exact solution or a universal theory. Uniform one-body density in a symmetric state also does not preclude stripe signatures in correlation functions.

Evidence: theory. Sources: source-095247a10e506437.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-experimental-criteria-1

Phase-sensitive observations constrain the order parameter, while identifying the dominant microscopic pairing interaction requires additional evidence. The original tricrystal-ring work provides a symmetry test in YBa₂Cu₃O₇−δ; that observation alone does not uniquely invert the pairing vertex. A stronger mechanism test compares momentum, frequency, orbital and temperature dependence across independent probes, together with changes induced by a controlled tuning parameter. Agreement should include observations not used to fit the proposed explanation.

Evidence: experiment. Sources: source-eaa3beeed4368f46, source-2e4d7fdb6c1797b7.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-experimental-criteria-2

Several interactions can cooperate or compete. The checked nematic-fluctuation theory predicts enhancement under specified weak-coupling assumptions, rather than a universal pairing symmetry. The FeSe/SrTiO₃ interfacial-mode study considers enhancement on top of a magnetic pairing baseline. Those examples caution against treating magnetic, charge, orbital and lattice effects as mutually exclusive labels. Their presence or proximity in a phase diagram is not by itself a causal measurement of their contribution to pairing.

Evidence: experiment. Sources: source-24dd77640a555a0f, source-f9fe6e9bc3792dcc.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-limits-and-disputes-1

A convincing unification should state its range of materials, independently constrained Hamiltonian, treatment of correlations and competing orders, and measurable predictions with errors. Cross-method agreement at one parameter point supports that point, not every lattice or composition. Numerical energy accuracy also does not automatically guarantee accurate long-distance response. The cited Hubbard studies are examples for evaluating this logic; they are not an exhaustive survey or a final settlement of all model phase diagrams.

Evidence: hypothesis. Sources: source-74cc3f39d62d38b0, source-e7b3ac50f76789ac, source-b417dbe2d449c0bb, source-51a15c56a9ac1472.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

### scwiki-n2-claim-discovery-implications-1

Compare proposed mechanisms through discriminating predictions: which changes in structure, filling, pressure or disorder alter the gap, collective response and competing phases together? Preserve failures and alternative explanations, and distinguish a broadly useful organizing principle from a quantitatively validated material theory. This research program can guide discovery even while a universal microscopic account remains unestablished within the reviewed evidence.

Evidence: hypothesis. Sources: source-eaa3beeed4368f46, source-24dd77640a555a0f, source-51a15c56a9ac1472.

Conditions: Retain model parameters, finite-size and trial-state limits, source version and publication status. Ground-state pairing and symmetry are not material Tc or unique mechanism measurements.

Verification scope: Selected primary text/figures and inherited named review scopes; independent inverse-kernel example only. No many-body solver or material mechanism reproduced.

## Approved scope items

N2. Checked: 2026-10-19. Selected bilayer and Hubbard primary methods, three recent numerical figures and explicit convergence limits, inherited phase-sensitive and interaction evidence, and 72 independent inverse-kernel examples.

- Complete scientific acceptance remains open.
- Author manuscripts retain explicit final-version comparison limits; the August 2026 result is a preprint.
- No full many-body calculation, training run, raw experimental analysis or universal mechanism is independently reproduced.
- This selection is not an exhaustive survey of unconventional superconductors or all Hubbard parameter regimes.
- A shared gap or ground-state order parameter does not determine a material transition temperature.

## Revision and review

Article ID: scwiki-n2. Revision: ca6ec5ab17ca48859684. Updated: 2026-10-18T20:19:01.320054+00:00.

Review scope: Selected bilayer and Hubbard primary methods, three recent numerical figures and explicit convergence limits, inherited phase-sensitive and interaction evidence, and 72 independent inverse-kernel examples.

- Complete scientific acceptance remains open.
- Author manuscripts retain explicit final-version comparison limits; the August 2026 result is a preprint.
- No full many-body calculation, training run, raw experimental analysis or universal mechanism is independently reproduced.
- This selection is not an exhaustive survey of unconventional superconductors or all Hubbard parameter regimes.
- A shared gap or ground-state order parameter does not determine a material transition temperature.

Source: [02_BATCH_2_IN_PLAN.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/02_BATCH_2_IN_PLAN.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 502293e5ed2fe8463b61a6c5b78a2c33bc33f3265bd36fe534fa2c469e42ff48.