{"schemaVersion":"1.0","revision":"fa961ab24277a91737c3","article":{"id":"scwiki-b12","topicId":"scwiki-topic-b12","code":"B12","slug":"multiband-pairing","title":"Multiband and multichannel pairing","summary":"A coupling matrix determines a pairing instability. Multiple bands, interaction channels, transport channels and material phases are different concepts.","aliases":["two-band superconductivity","multichannel superposition","MgB2","Eliashberg kernel","multiband pairing","multichannel pairing","多能带配对","多通道配对"],"evidenceTypes":["theory","experiment"],"relatedCodes":["C2","D4","D7","D11","H8"],"editorialStatus":"scoped-check","contentState":"pilot","modifiedAt":"2026-10-19T00:47:10.029011+00:00","review":{"checkedAt":"2026-10-19","scope":"Inherited D7 source-specific MgB2 checks; Lee author v6 selected results/Figure 2 and model caption; Faeth author v1 selected methods/Figures 2–3; Li–Sawatzky original abstract; 64 reciprocal-kernel cases, 31 PSD controls and bounded counterexamples. Nine exact rational similarity checks and four uncoupled/degenerate boundary cases.","limitations":["Complete scientific acceptance remains open.","Suhl original full text remains metadata-only; the two-band illustration was checked independently, not attributed as a complete historical audit.","Lee/Faeth final-version comparisons, complete supplementary controls and raw spectral fits remain open.","No unique multi-boson decomposition or full frequency-dependent Eliashberg solve is claimed.","At zero interband coupling, a degenerate quadratic instability does not fix a unique relative phase; local eigenvalue checks do not solve nonlinear phase selection."]},"provenance":{"repository":"JackZH26/jzis-superconductivity","commit":"0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf","path":"B_mechanisms/B12_multi_channel_superposition.md","sha256":"f7633eef3b233297e3d3dc010522914b257dc6184c6c03432341c56fe065b2aa","sourceId":"file-60aaa444e141cdcd"},"sourceMap":[{"startLine":1,"endLine":9,"targetSections":["scope","limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":10,"endLine":15,"targetSections":["scope","limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":16,"endLine":30,"targetSections":["mathematical-assumptions"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":31,"endLine":43,"targetSections":["scope","limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":44,"endLine":58,"targetSections":["material-interpretation","material-cases"],"decision":"condensed-and-structured","note":"Selected MgB2 and FeSe records retain primary source/version and criteria. Unsupported quantitative coupling budgets omitted; high-pressure examples are treated in their material articles."},{"startLine":59,"endLine":66,"targetSections":["material-interpretation","material-cases"],"decision":"condensed-and-structured","note":"Selected MgB2 and FeSe records retain primary source/version and criteria. Unsupported quantitative coupling budgets omitted; high-pressure examples are treated in their material articles."},{"startLine":67,"endLine":76,"targetSections":["limits-and-disputes"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":77,"endLine":89,"targetSections":["experimental-criteria"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":90,"endLine":100,"targetSections":[],"decision":"not-published-as-scientific-evidence","note":"Historical audit scores and repeated summaries are not scientific verification. Selected cautions are rewritten in the limits section."},{"startLine":101,"endLine":112,"targetSections":["sources"],"decision":"condensed-and-structured","note":"Edited English adaptation, with source-specific conditions retained. This map identifies editorial scope, not an independent verification of every original claim."},{"startLine":113,"endLine":118,"targetSections":[],"decision":"not-published-as-scientific-evidence","note":"Historical audit scores and repeated summaries are not scientific verification. Selected cautions are rewritten in the limits section."}],"corrections":[{"id":"scwiki-b12-correction-1","description":"The source's ASCII cutoff formula is written using a cutoff energy E_c and an explicit k_B, avoiding an unstated frequency-versus-energy convention.","sourceId":"source-e6ac5c48a0e11fe3","scope":"Notation and dimensions; no fitted coupling values were introduced."},{"id":"scwiki-b12-correction-2","description":"The pinned chapter assigned Choi et al. (Nature 418, 758-760, 2002) DOI 10.1038/nature00992, which identifies a mechanosensitive-channel biology paper. The MgB2 calculation is DOI 10.1038/nature00898. Replaced the source identity and separated the calculated-gap claim from the experimental discovery report.","sourceId":"source-7c4eac077ae5e221","scope":"Publisher identity and selected primary calculation passages; not a blanket validation of all multichannel claims."},{"id":"scwiki-b12-correction-3","description":"MgB2 39 K is now tied to the original resistive onset, with 38 K endpoint; synthesis pressure is not measurement pressure.","sourceId":"source-fade6558e7eafb2b","scope":"Reuse selected D7 final-text and figure evidence."},{"id":"scwiki-b12-correction-4","description":"Lee author v6 gives a 58±7 K mean-field gap-closing fit, not zero resistance or the pinned generic 65±5 K value. Replica interpretation includes an explicit competing loss model and later photon-energy controls.","sourceId":"source-f9fe6e9bc3792dcc","scope":"Separate source/version, spectroscopy, model assumptions and transition criteria."}],"equationChecks":[{"targetSectionId":"mathematical-assumptions","tex":"\\lambda_+","check":"64 reciprocal two-band spectra and DOS transformations; 31 PSD additions; entrywise-positive competition, same-spectrum opposite phase, decoupled-band and Z counterexamples. Synthetic dimensionless model, no material fit."}],"references":[{"id":"source-e6ac5c48a0e11fe3","doi":"10.1103/PhysRevLett.3.552","title":"Bardeen-Cooper-Schrieffer Theory of Superconductivity in the Case of Overlapping Bands","year":1959,"url":"https://doi.org/10.1103/PhysRevLett.3.552","publicationStatus":"journal-article","verification":{"scope":"crossref-metadata-only","checkedAt":"2026-10-17","evidenceUrl":"https://api.crossref.org/works/10.1103%2FPhysRevLett.3.552","note":"Bibliographic identity only. Scientific statements are an edited synthesis of the pinned source chapter; primary results were not independently checked in this scope."}},{"id":"source-fade6558e7eafb2b","doi":"10.1038/35065039","title":"Superconductivity at 39 K in magnesium diboride","year":2001,"url":"https://doi.org/10.1038/35065039","publicationStatus":"journal-article","verification":{"scope":"selected-published-methods-figures-check","checkedAt":"2026-10-18","evidenceUrl":"https://www.w2agz.com/Library/HTSC%20History/MgB2%20Discovery%20nature410063.pdf","note":"Published 1 March 2001. Original published pp.63–64 read for MgB2 discovery (not preceding unrelated article); p.64 visually checked. Resistive onset 39 K / endpoint 38 K, 10 Oe magnetization and synthesis196 MPa distinguished. Raw data not reproduced."}},{"id":"source-7c4eac077ae5e221","doi":"10.1038/nature00898","title":"The origin of the anomalous superconducting properties of MgB2","year":2002,"url":"https://doi.org/10.1038/nature00898","publicationStatus":"journal-article","verification":{"scope":"selected-published-anisotropic-gap-check","checkedAt":"2026-10-18","evidenceUrl":"https://www2.lbl.gov/Science-Articles/Archive/assets/images/2002/Aug-14-2002/MgB2Nature.pdf","note":"Published 15 August 2002. Original pp.758–760 selected discussion and Figs. 2–4; p.759 visually checked. Calculated distributions/thermodynamics distinguished from measured gap constants. No anisotropic Eliashberg solve or original specific-heat reanalysis."}},{"id":"source-f9fe6e9bc3792dcc","doi":"10.1038/nature13894","title":"Interfacial mode coupling as the origin of the enhancement of Tc in FeSe films on SrTiO3","year":2014,"url":"https://doi.org/10.1038/nature13894","publicationStatus":"journal-article","verification":{"scope":"selected-author-results-and-figure-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/1312.2633v6","note":"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."}},{"id":"source-69ced9b5dda860f1","doi":"10.1103/PhysRevLett.87.137005","title":"Evidence for Two Superconducting Energy Gaps in MgB2 by Point-Contact Spectroscopy","year":2001,"url":"https://doi.org/10.1103/PhysRevLett.87.137005","publicationStatus":"journal-article","verification":{"scope":"selected-author-spectroscopy-methods-check","checkedAt":"2026-10-18","evidenceUrl":"https://arxiv.org/pdf/cond-mat/0105598v1","note":"Journal published 11 September 2001; author v1 submitted 30 May 2001, selected methods/results pp.2–3. Cu tips,400 Hz differential resistance, two BTK contributions, fixed weight/Z across T, field to 1 T. Final journal first-page text compared; complete final methods/raw fits not reproduced."}},{"id":"source-01df125fb3077f5f","doi":"10.1103/PhysRevLett.120.237001","title":"Electron Phonon Coupling versus Photoelectron Energy Loss at the Origin of Replica Bands in Photoemission of FeSe on SrTiO3","year":2018,"url":"https://doi.org/10.1103/PhysRevLett.120.237001","publicationStatus":"journal-article","verification":{"scope":"publisher-original-abstract-check","checkedAt":"2026-10-19","evidenceUrl":"https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.237001","note":"Li and Sawatzky, published 5 June 2018. Abstract proposes predominantly extrinsic loss using a semiclassical dielectric calculation; complete calculation and assumptions not independently reproduced. A competing interpretation, not a settled exclusion of intrinsic coupling."}},{"id":"source-ac66116dfd6e4887","doi":"10.1103/PhysRevLett.127.016803","title":"Interfacial Electron-Phonon Coupling Constants Extracted from Intrinsic Replica Bands in Monolayer FeSe/SrTiO3","year":2021,"url":"https://doi.org/10.1103/PhysRevLett.127.016803","publicationStatus":"journal-article","verification":{"scope":"selected-author-methods-and-figures-check","checkedAt":"2026-10-19","evidenceUrl":"https://arxiv.org/pdf/2102.03397v1","note":"Author v1 submitted 5 February 2021; published 30 June 2021 per indexed final journal first page, not issue date 2 July. Selected pp. 2–4 methods/results; p. 3 Figures 2–3 visually checked. 15 K, photon energies 21–75 eV; photon-energy invariance, replica spacing and a forward-scattering fit. Final PDF download failed; supplements and full raw spectra/refits remain open."}}],"materialCases":[{"id":"scwiki-b12-material-1","formula":"MgB2","sample":"Nagamatsu 2001 polycrystalline pellet, zero field","recordType":"experiment","reportedTemperatureK":39,"tcK":39,"temperatureKind":"transition","temperatureNote":"Onset 39 K; endpoint 38 K. Synthesis pressure 196 MPa is not measurement pressure.","criterion":"four-probe-resistive-onset","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","probe":"Four-probe resistivity; separate 10 Oe magnetization","sourceId":"source-fade6558e7eafb2b"},{"id":"scwiki-b12-material-2","formula":"FeSe/SrTiO3","sample":"Lee one-unit-cell film, author v6 Figure 2 mean-field fit","recordType":"experiment","tcK":null,"reportedTemperatureK":58,"temperatureKind":"spectroscopic-gap","temperatureNote":"58±7 K ARPES gap-closing fit, not a zero-resistance transition.","criterion":"ARPES-mean-field-gap-closure","pressureRegime":"ambient","pressureGPa":null,"equilibrium":"unknown","probe":"Temperature-dependent ARPES","sourceId":"source-f9fe6e9bc3792dcc","aliases":["FeSe STO","single-layer FeSe"]}],"claims":[{"id":"scwiki-b12-claim-scope-1","sectionId":"scope","statement":"Multiband pairing describes coupled gaps on different electronic bands. Multichannel pairing describes different interaction contributions to a Cooper-pair kernel. These are distinct from parallel normal-state conductivities and from spatially separate superconducting phases. Observing two gaps does not identify two mediating bosons; observing a resistance drop in two phases does not establish one homogeneous condensate. The band basis, sample and measurement conditions must accompany the claim.","evidenceType":"hypothesis","sourceIds":["source-e6ac5c48a0e11fe3","source-7c4eac077ae5e221","source-69ced9b5dda860f1"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."},{"id":"scwiki-b12-claim-mathematical-assumptions-1","sectionId":"mathematical-assumptions","statement":"In a real, reciprocal two-band weak-coupling illustration with a shared cutoff energy $E_c$, write $\\Delta_i=L(T_c)\\sum_j\\lambda_{ij}\\Delta_j$, where $L(T)=\\ln[2e^{\\gamma_E}E_c/(\\pi k_BT)]$ and $\\lambda_{ij}=-V_{ij}N_j$. Here $V_{ij}=V_{ji}$ is the pair interaction, attraction has negative $V$, and $N_j>0$ is the one-spin density of states in band $j$. The largest positive eigenvalue gives the leading instability, $k_BT_c=(2e^{\\gamma_E}/\\pi)E_c\\exp(-1/\\lambda_+)$. The approximation assumes $k_BT_c\\ll E_c$; a nonpositive leading eigenvalue gives no instability in this restricted model. This is a stated modern illustration, not a claim that the historical Suhl paper has been fully audited.","evidenceType":"theory","sourceIds":["source-e6ac5c48a0e11fe3","source-7c4eac077ae5e221"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Local reciprocal-kernel spectra and residuals, nine exact rational similarities and four uncoupled boundary cases; Choi selected published passages provide context. Historical Suhl full-text and complete scientific acceptance remain open.","sourceRelationship":"context-for-local-derivation","derivationNote":"These common-cutoff two-band equations and synthetic counterexamples are local explanatory derivations. The Suhl reference has bibliographic verification only; its full text has not been audited. Choi et al., published pp.758–760, supplies anisotropic MgB2 context, not this reduced kernel or these numerical parameters. Positive band DOS and reciprocal real interactions are required for the stated similarity transform."},{"id":"scwiki-b12-claim-mathematical-assumptions-2","sectionId":"mathematical-assumptions","statement":"Although $\\lambda$ need not be symmetric, $K_{ij}=-\\sqrt{N_i}V_{ij}\\sqrt{N_j}$ is a symmetric similar matrix with eigenvector $\\eta_i=\\sqrt{N_i}\\Delta_i$. For two bands, $\\lambda_+=[\\lambda_{11}+\\lambda_{22}+\\sqrt{(\\lambda_{11}-\\lambda_{22})^2+4\\lambda_{12}\\lambda_{21}}]/2$. An independent check of 64 reciprocal kernels verifies this formula, the density-of-states transformation and the gap-vector residuals. All parameters are synthetic; no MgB2 or FeSe coupling is fitted. The eigenvalue is not the sum of every matrix entry.","evidenceType":"theory","sourceIds":["source-e6ac5c48a0e11fe3","source-7c4eac077ae5e221"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Local reciprocal-kernel spectra and residuals, nine exact rational similarities and four uncoupled boundary cases; Choi selected published passages provide context. Historical Suhl full-text and complete scientific acceptance remain open.","sourceRelationship":"context-for-local-derivation","derivationNote":"These common-cutoff two-band equations and synthetic counterexamples are local explanatory derivations. The Suhl reference has bibliographic verification only; its full text has not been audited. Choi et al., published pp.758–760, supplies anisotropic MgB2 context, not this reduced kernel or these numerical parameters. Positive band DOS and reciprocal real interactions are required for the stated similarity transform."},{"id":"scwiki-b12-claim-mathematical-assumptions-3","sectionId":"mathematical-assumptions","statement":"Consider $K=\\begin{pmatrix}0.3&-0.1\\\\-0.1&0.3\\end{pmatrix}$, whose leading eigenvalue is $0.4$ with opposite gap signs. Adding only positive off-diagonal entries of $0.05$ lowers it to $0.35$. That added matrix is not positive semidefinite: entrywise attraction and a nonnegative quadratic form are different conditions. In contrast, 31 positive-semidefinite additions do not lower the largest eigenvalue of the fixed kernel. This bounded example shows why cooperation must be assessed after projecting the interaction, with the other assumptions held fixed.","evidenceType":"theory","sourceIds":["source-e6ac5c48a0e11fe3","source-7c4eac077ae5e221"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Local reciprocal-kernel spectra and residuals, nine exact rational similarities and four uncoupled boundary cases; Choi selected published passages provide context. Historical Suhl full-text and complete scientific acceptance remain open.","sourceRelationship":"context-for-local-derivation","derivationNote":"These common-cutoff two-band equations and synthetic counterexamples are local explanatory derivations. The Suhl reference has bibliographic verification only; its full text has not been audited. Choi et al., published pp.758–760, supplies anisotropic MgB2 context, not this reduced kernel or these numerical parameters. Positive band DOS and reciprocal real interactions are required for the stated similarity transform."},{"id":"scwiki-b12-claim-mathematical-assumptions-4","sectionId":"mathematical-assumptions","statement":"With nonzero reciprocal interband coupling, changing both off-diagonal signs leaves the two eigenvalues unchanged but reverses the relative gap sign of the nondegenerate leading mode. A transition temperature alone therefore cannot determine the relative phase. With zero interband coupling, the two bands have independent instabilities, and the weaker band need not acquire a gap at the higher transition. If the two uncoupled eigenvalues coincide, this quadratic model selects neither a unique gap vector nor a relative phase; additional terms are needed. A full calculation must also retain frequency dependence, different cutoffs, Coulomb terms and normal self-energy. Even an illustrative scalar increase from $0.3$ to $0.4$ loses to a mass factor $Z=1.5$, because $0.4/1.5<0.3$; that arithmetic is not a complete Eliashberg calculation.","evidenceType":"theory","sourceIds":["source-e6ac5c48a0e11fe3","source-7c4eac077ae5e221"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Local reciprocal-kernel spectra and residuals, nine exact rational similarities and four uncoupled boundary cases; Choi selected published passages provide context. Historical Suhl full-text and complete scientific acceptance remain open.","sourceRelationship":"context-for-local-derivation","derivationNote":"These common-cutoff two-band equations and synthetic counterexamples are local explanatory derivations. The Suhl reference has bibliographic verification only; its full text has not been audited. Choi et al., published pp.758–760, supplies anisotropic MgB2 context, not this reduced kernel or these numerical parameters. Positive band DOS and reciprocal real interactions are required for the stated similarity transform."},{"id":"scwiki-b12-claim-experimental-criteria-1","sectionId":"experimental-criteria","statement":"Nagamatsu and colleagues reported a resistive onset at 39 K and endpoint at 38 K in a polycrystalline MgB2 pellet, alongside separate 10 Oe magnetic measurements. The original paper's 196 MPa pressure concerns synthesis, not the superconducting measurement. This page now records the onset criterion explicitly instead of treating every reported 39 K value as an unspecified transition. Geometry, sample quality and criterion remain part of the record.","evidenceType":"experiment","sourceIds":["source-fade6558e7eafb2b"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."},{"id":"scwiki-b12-claim-experimental-criteria-2","sectionId":"experimental-criteria","statement":"Choi and colleagues calculated anisotropic MgB2 gaps using an electron–phonon Eliashberg model. Their band-dependent gap distributions close at a common calculated transition. These are theoretical results, not direct measurements of two independent mediators, and numerical agreement does not independently identify every interaction in a material. The corrected DOI is the MgB2 paper, not the unrelated biology article inherited by the pinned draft.","evidenceType":"theory","sourceIds":["source-7c4eac077ae5e221"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."},{"id":"scwiki-b12-claim-experimental-criteria-3","sectionId":"experimental-criteria","statement":"Szabo and colleagues used Cu point contacts and two weighted BTK contributions to describe MgB2 spectra. Their selected author methods keep interface barrier and weighting parameters fixed across temperature, with applied fields helping distinguish the gap contributions. This is spectroscopic evidence interpreted through an interface model; it does not determine the relative gap sign or assign separate bosons to each gap. Cross-check band assignment and bulk thermodynamics before equating a fitted component with a unique condensate.","evidenceType":"experiment","sourceIds":["source-69ced9b5dda860f1"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."},{"id":"scwiki-b12-claim-material-interpretation-1","sectionId":"material-interpretation","statement":"Lee and colleagues observed replica bands in one-unit-cell FeSe/SrTiO3 and interpreted them through forward-focused interface phonons. In the identified author v6, a mean-field fit gives a gap-closing scale of $58\\pm7$ K, with Figure 2 showing closure between 50 and 64 K. This is an ARPES-derived scale, not a measured zero-resistance temperature. Their predicted enhancement assumes an electronic magnetic-pairing baseline and a specified model; neither it nor the fitted coupling is an experimentally separated budget of all pairing channels.","evidenceType":"experiment","sourceIds":["source-f9fe6e9bc3792dcc"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."},{"id":"scwiki-b12-claim-material-interpretation-2","sectionId":"material-interpretation","statement":"Replica-band interpretation requires controls. Li and Sawatzky proposed predominantly extrinsic energy loss by the escaping photoelectron, using a dielectric model. Faeth and colleagues subsequently tested photon-energy dependence at 15 K over 21–75 eV and found a nearly constant replica-to-main intensity ratio; higher-order separations and line shapes also supported intrinsic coupling in their samples. Their forward-scattering comparison inferred $\\lambda=0.19\\pm0.02$. This selected-method check is stronger than a bare replica observation, but does not by itself uniquely partition the superconducting pairing kernel.","evidenceType":"experiment","sourceIds":["source-01df125fb3077f5f","source-ac66116dfd6e4887"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."},{"id":"scwiki-b12-claim-material-interpretation-3","sectionId":"material-interpretation","statement":"The Faeth analysis also notes that the estimated gap enhancement under its chosen model cannot fully explain the difference between the reported high gap-closing scale and electron-doped bulk comparators. Distinguish that conditional inference from a universal phonon percentage, and distinguish measured spectra from a thermodynamic or zero-resistance transition. Differences between papers require matched coupling definitions, background subtraction, sample preparation and model assumptions; a single scalar cannot settle the mechanism.","evidenceType":"experiment","sourceIds":["source-ac66116dfd6e4887"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."},{"id":"scwiki-b12-claim-limits-and-disputes-1","sectionId":"limits-and-disputes","statement":"A shared transition and multiple gap features are compatible with interband coupling, but do not independently establish beneficial cooperation between different interactions. Carrier transfer, density of states, scattering and phase coherence can change together. Claims of a unique mechanism require discriminating controls; phase-sensitive probes, spectroscopy and thermodynamics constrain different parts of the problem. The original Suhl text, full FeSe supplementary controls and complete raw-data analyses remain outside the completed checks. Complete scientific acceptance remains open.","evidenceType":"hypothesis","sourceIds":["source-e6ac5c48a0e11fe3","source-7c4eac077ae5e221","source-f9fe6e9bc3792dcc","source-69ced9b5dda860f1","source-ac66116dfd6e4887"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."},{"id":"scwiki-b12-claim-discovery-implications-1","sectionId":"discovery-implications","statement":"Specify what changes when an interaction is added and what is held fixed. Report the band and momentum basis, cutoff, Coulomb and self-energy treatment, and the eigenfunction as well as the leading eigenvalue. Avoid double-counting one screened interaction under two names. A useful proposal predicts a response to a controlled perturbation and explains which competing interpretation that measurement would exclude. Do not substitute a list of plausible bosons or an unsourced sum of coupling constants for a tested kernel.","evidenceType":"hypothesis","sourceIds":["source-e6ac5c48a0e11fe3","source-7c4eac077ae5e221","source-f9fe6e9bc3792dcc","source-ac66116dfd6e4887"],"conditions":"Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.","verificationScope":"Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open."}],"body":"## Scope\n\nMultiband pairing describes coupled gaps on different electronic bands. Multichannel pairing describes different interaction contributions to a Cooper-pair kernel. These are distinct from parallel normal-state conductivities and from spatially separate superconducting phases. Observing two gaps does not identify two mediating bosons; observing a resistance drop in two phases does not establish one homogeneous condensate. The band basis, sample and measurement conditions must accompany the claim. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R5](#ref-source-69ced9b5dda860f1)\n\n## Mathematical assumptions\n\nIn a real, reciprocal two-band weak-coupling illustration with a shared cutoff energy $E_c$, write $\\Delta_i=L(T_c)\\sum_j\\lambda_{ij}\\Delta_j$, where $L(T)=\\ln[2e^{\\gamma_E}E_c/(\\pi k_BT)]$ and $\\lambda_{ij}=-V_{ij}N_j$. Here $V_{ij}=V_{ji}$ is the pair interaction, attraction has negative $V$, and $N_j>0$ is the one-spin density of states in band $j$. The largest positive eigenvalue gives the leading instability, $k_BT_c=(2e^{\\gamma_E}/\\pi)E_c\\exp(-1/\\lambda_+)$. The approximation assumes $k_BT_c\\ll E_c$; a nonpositive leading eigenvalue gives no instability in this restricted model. This is a stated modern illustration, not a claim that the historical Suhl paper has been fully audited. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nAlthough $\\lambda$ need not be symmetric, $K_{ij}=-\\sqrt{N_i}V_{ij}\\sqrt{N_j}$ is a symmetric similar matrix with eigenvector $\\eta_i=\\sqrt{N_i}\\Delta_i$. For two bands, $\\lambda_+=[\\lambda_{11}+\\lambda_{22}+\\sqrt{(\\lambda_{11}-\\lambda_{22})^2+4\\lambda_{12}\\lambda_{21}}]/2$. An independent check of 64 reciprocal kernels verifies this formula, the density-of-states transformation and the gap-vector residuals. All parameters are synthetic; no MgB2 or FeSe coupling is fitted. The eigenvalue is not the sum of every matrix entry. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nConsider $K=\\begin{pmatrix}0.3&-0.1\\\\-0.1&0.3\\end{pmatrix}$, whose leading eigenvalue is $0.4$ with opposite gap signs. Adding only positive off-diagonal entries of $0.05$ lowers it to $0.35$. That added matrix is not positive semidefinite: entrywise attraction and a nonnegative quadratic form are different conditions. In contrast, 31 positive-semidefinite additions do not lower the largest eigenvalue of the fixed kernel. This bounded example shows why cooperation must be assessed after projecting the interaction, with the other assumptions held fixed. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nWith nonzero reciprocal interband coupling, changing both off-diagonal signs leaves the two eigenvalues unchanged but reverses the relative gap sign of the nondegenerate leading mode. A transition temperature alone therefore cannot determine the relative phase. With zero interband coupling, the two bands have independent instabilities, and the weaker band need not acquire a gap at the higher transition. If the two uncoupled eigenvalues coincide, this quadratic model selects neither a unique gap vector nor a relative phase; additional terms are needed. A full calculation must also retain frequency dependence, different cutoffs, Coulomb terms and normal self-energy. Even an illustrative scalar increase from $0.3$ to $0.4$ loses to a mass factor $Z=1.5$, because $0.4/1.5<0.3$; that arithmetic is not a complete Eliashberg calculation. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\n## Experimental criteria\n\nNagamatsu and colleagues reported a resistive onset at 39 K and endpoint at 38 K in a polycrystalline MgB2 pellet, alongside separate 10 Oe magnetic measurements. The original paper's 196 MPa pressure concerns synthesis, not the superconducting measurement. This page now records the onset criterion explicitly instead of treating every reported 39 K value as an unspecified transition. Geometry, sample quality and criterion remain part of the record. [R2](#ref-source-fade6558e7eafb2b)\n\nChoi and colleagues calculated anisotropic MgB2 gaps using an electron–phonon Eliashberg model. Their band-dependent gap distributions close at a common calculated transition. These are theoretical results, not direct measurements of two independent mediators, and numerical agreement does not independently identify every interaction in a material. The corrected DOI is the MgB2 paper, not the unrelated biology article inherited by the pinned draft. [R3](#ref-source-7c4eac077ae5e221)\n\nSzabo and colleagues used Cu point contacts and two weighted BTK contributions to describe MgB2 spectra. Their selected author methods keep interface barrier and weighting parameters fixed across temperature, with applied fields helping distinguish the gap contributions. This is spectroscopic evidence interpreted through an interface model; it does not determine the relative gap sign or assign separate bosons to each gap. Cross-check band assignment and bulk thermodynamics before equating a fitted component with a unique condensate. [R5](#ref-source-69ced9b5dda860f1)\n\n## Material interpretation\n\nLee and colleagues observed replica bands in one-unit-cell FeSe/SrTiO3 and interpreted them through forward-focused interface phonons. In the identified author v6, a mean-field fit gives a gap-closing scale of $58\\pm7$ K, with Figure 2 showing closure between 50 and 64 K. This is an ARPES-derived scale, not a measured zero-resistance temperature. Their predicted enhancement assumes an electronic magnetic-pairing baseline and a specified model; neither it nor the fitted coupling is an experimentally separated budget of all pairing channels. [R4](#ref-source-f9fe6e9bc3792dcc)\n\nReplica-band interpretation requires controls. Li and Sawatzky proposed predominantly extrinsic energy loss by the escaping photoelectron, using a dielectric model. Faeth and colleagues subsequently tested photon-energy dependence at 15 K over 21–75 eV and found a nearly constant replica-to-main intensity ratio; higher-order separations and line shapes also supported intrinsic coupling in their samples. Their forward-scattering comparison inferred $\\lambda=0.19\\pm0.02$. This selected-method check is stronger than a bare replica observation, but does not by itself uniquely partition the superconducting pairing kernel. [R6](#ref-source-01df125fb3077f5f) [R7](#ref-source-ac66116dfd6e4887)\n\nThe Faeth analysis also notes that the estimated gap enhancement under its chosen model cannot fully explain the difference between the reported high gap-closing scale and electron-doped bulk comparators. Distinguish that conditional inference from a universal phonon percentage, and distinguish measured spectra from a thermodynamic or zero-resistance transition. Differences between papers require matched coupling definitions, background subtraction, sample preparation and model assumptions; a single scalar cannot settle the mechanism. [R7](#ref-source-ac66116dfd6e4887)\n\n## Limits and disputes\n\nA shared transition and multiple gap features are compatible with interband coupling, but do not independently establish beneficial cooperation between different interactions. Carrier transfer, density of states, scattering and phase coherence can change together. Claims of a unique mechanism require discriminating controls; phase-sensitive probes, spectroscopy and thermodynamics constrain different parts of the problem. The original Suhl text, full FeSe supplementary controls and complete raw-data analyses remain outside the completed checks. Complete scientific acceptance remains open. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R4](#ref-source-f9fe6e9bc3792dcc) [R5](#ref-source-69ced9b5dda860f1) [R7](#ref-source-ac66116dfd6e4887)\n\n## Discovery implications\n\nSpecify what changes when an interaction is added and what is held fixed. Report the band and momentum basis, cutoff, Coulomb and self-energy treatment, and the eigenfunction as well as the leading eigenvalue. Avoid double-counting one screened interaction under two names. A useful proposal predicts a response to a controlled perturbation and explains which competing interpretation that measurement would exclude. Do not substitute a list of plausible bosons or an unsourced sum of coupling constants for a tested kernel. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R4](#ref-source-f9fe6e9bc3792dcc) [R7](#ref-source-ac66116dfd6e4887)\n\n## Related topics\n\nSee [s± pairing](/scwiki/s-plus-minus), [MgB2](/scwiki/magnesium-diboride), [iron-based materials](/scwiki/iron-based-superconductors), [two-dimensional interfaces](/scwiki/two-dimensional-interfaces) and [multichannel transport](/scwiki/parallel-conduction-channels).","revision":"3f2e9e7c61b17355274d","sections":[{"id":"scope","title":"Scope","markdown":"## Scope\n\nMultiband pairing describes coupled gaps on different electronic bands. Multichannel pairing describes different interaction contributions to a Cooper-pair kernel. These are distinct from parallel normal-state conductivities and from spatially separate superconducting phases. Observing two gaps does not identify two mediating bosons; observing a resistance drop in two phases does not establish one homogeneous condensate. The band basis, sample and measurement conditions must accompany the claim. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R5](#ref-source-69ced9b5dda860f1)"},{"id":"mathematical-assumptions","title":"Mathematical assumptions","markdown":"## Mathematical assumptions\n\nIn a real, reciprocal two-band weak-coupling illustration with a shared cutoff energy $E_c$, write $\\Delta_i=L(T_c)\\sum_j\\lambda_{ij}\\Delta_j$, where $L(T)=\\ln[2e^{\\gamma_E}E_c/(\\pi k_BT)]$ and $\\lambda_{ij}=-V_{ij}N_j$. Here $V_{ij}=V_{ji}$ is the pair interaction, attraction has negative $V$, and $N_j>0$ is the one-spin density of states in band $j$. The largest positive eigenvalue gives the leading instability, $k_BT_c=(2e^{\\gamma_E}/\\pi)E_c\\exp(-1/\\lambda_+)$. The approximation assumes $k_BT_c\\ll E_c$; a nonpositive leading eigenvalue gives no instability in this restricted model. This is a stated modern illustration, not a claim that the historical Suhl paper has been fully audited. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nAlthough $\\lambda$ need not be symmetric, $K_{ij}=-\\sqrt{N_i}V_{ij}\\sqrt{N_j}$ is a symmetric similar matrix with eigenvector $\\eta_i=\\sqrt{N_i}\\Delta_i$. For two bands, $\\lambda_+=[\\lambda_{11}+\\lambda_{22}+\\sqrt{(\\lambda_{11}-\\lambda_{22})^2+4\\lambda_{12}\\lambda_{21}}]/2$. An independent check of 64 reciprocal kernels verifies this formula, the density-of-states transformation and the gap-vector residuals. All parameters are synthetic; no MgB2 or FeSe coupling is fitted. The eigenvalue is not the sum of every matrix entry. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nConsider $K=\\begin{pmatrix}0.3&-0.1\\\\-0.1&0.3\\end{pmatrix}$, whose leading eigenvalue is $0.4$ with opposite gap signs. Adding only positive off-diagonal entries of $0.05$ lowers it to $0.35$. That added matrix is not positive semidefinite: entrywise attraction and a nonnegative quadratic form are different conditions. In contrast, 31 positive-semidefinite additions do not lower the largest eigenvalue of the fixed kernel. This bounded example shows why cooperation must be assessed after projecting the interaction, with the other assumptions held fixed. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nWith nonzero reciprocal interband coupling, changing both off-diagonal signs leaves the two eigenvalues unchanged but reverses the relative gap sign of the nondegenerate leading mode. A transition temperature alone therefore cannot determine the relative phase. With zero interband coupling, the two bands have independent instabilities, and the weaker band need not acquire a gap at the higher transition. If the two uncoupled eigenvalues coincide, this quadratic model selects neither a unique gap vector nor a relative phase; additional terms are needed. A full calculation must also retain frequency dependence, different cutoffs, Coulomb terms and normal self-energy. Even an illustrative scalar increase from $0.3$ to $0.4$ loses to a mass factor $Z=1.5$, because $0.4/1.5<0.3$; that arithmetic is not a complete Eliashberg calculation. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)"},{"id":"experimental-criteria","title":"Experimental criteria","markdown":"## Experimental criteria\n\nNagamatsu and colleagues reported a resistive onset at 39 K and endpoint at 38 K in a polycrystalline MgB2 pellet, alongside separate 10 Oe magnetic measurements. The original paper's 196 MPa pressure concerns synthesis, not the superconducting measurement. This page now records the onset criterion explicitly instead of treating every reported 39 K value as an unspecified transition. Geometry, sample quality and criterion remain part of the record. [R2](#ref-source-fade6558e7eafb2b)\n\nChoi and colleagues calculated anisotropic MgB2 gaps using an electron–phonon Eliashberg model. Their band-dependent gap distributions close at a common calculated transition. These are theoretical results, not direct measurements of two independent mediators, and numerical agreement does not independently identify every interaction in a material. The corrected DOI is the MgB2 paper, not the unrelated biology article inherited by the pinned draft. [R3](#ref-source-7c4eac077ae5e221)\n\nSzabo and colleagues used Cu point contacts and two weighted BTK contributions to describe MgB2 spectra. Their selected author methods keep interface barrier and weighting parameters fixed across temperature, with applied fields helping distinguish the gap contributions. This is spectroscopic evidence interpreted through an interface model; it does not determine the relative gap sign or assign separate bosons to each gap. Cross-check band assignment and bulk thermodynamics before equating a fitted component with a unique condensate. [R5](#ref-source-69ced9b5dda860f1)"},{"id":"material-interpretation","title":"Material interpretation","markdown":"## Material interpretation\n\nLee and colleagues observed replica bands in one-unit-cell FeSe/SrTiO3 and interpreted them through forward-focused interface phonons. In the identified author v6, a mean-field fit gives a gap-closing scale of $58\\pm7$ K, with Figure 2 showing closure between 50 and 64 K. This is an ARPES-derived scale, not a measured zero-resistance temperature. Their predicted enhancement assumes an electronic magnetic-pairing baseline and a specified model; neither it nor the fitted coupling is an experimentally separated budget of all pairing channels. [R4](#ref-source-f9fe6e9bc3792dcc)\n\nReplica-band interpretation requires controls. Li and Sawatzky proposed predominantly extrinsic energy loss by the escaping photoelectron, using a dielectric model. Faeth and colleagues subsequently tested photon-energy dependence at 15 K over 21–75 eV and found a nearly constant replica-to-main intensity ratio; higher-order separations and line shapes also supported intrinsic coupling in their samples. Their forward-scattering comparison inferred $\\lambda=0.19\\pm0.02$. This selected-method check is stronger than a bare replica observation, but does not by itself uniquely partition the superconducting pairing kernel. [R6](#ref-source-01df125fb3077f5f) [R7](#ref-source-ac66116dfd6e4887)\n\nThe Faeth analysis also notes that the estimated gap enhancement under its chosen model cannot fully explain the difference between the reported high gap-closing scale and electron-doped bulk comparators. Distinguish that conditional inference from a universal phonon percentage, and distinguish measured spectra from a thermodynamic or zero-resistance transition. Differences between papers require matched coupling definitions, background subtraction, sample preparation and model assumptions; a single scalar cannot settle the mechanism. [R7](#ref-source-ac66116dfd6e4887)"},{"id":"limits-and-disputes","title":"Limits and disputes","markdown":"## Limits and disputes\n\nA shared transition and multiple gap features are compatible with interband coupling, but do not independently establish beneficial cooperation between different interactions. Carrier transfer, density of states, scattering and phase coherence can change together. Claims of a unique mechanism require discriminating controls; phase-sensitive probes, spectroscopy and thermodynamics constrain different parts of the problem. The original Suhl text, full FeSe supplementary controls and complete raw-data analyses remain outside the completed checks. Complete scientific acceptance remains open. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R4](#ref-source-f9fe6e9bc3792dcc) [R5](#ref-source-69ced9b5dda860f1) [R7](#ref-source-ac66116dfd6e4887)"},{"id":"discovery-implications","title":"Discovery implications","markdown":"## Discovery implications\n\nSpecify what changes when an interaction is added and what is held fixed. Report the band and momentum basis, cutoff, Coulomb and self-energy treatment, and the eigenfunction as well as the leading eigenvalue. Avoid double-counting one screened interaction under two names. A useful proposal predicts a response to a controlled perturbation and explains which competing interpretation that measurement would exclude. Do not substitute a list of plausible bosons or an unsourced sum of coupling constants for a tested kernel. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R4](#ref-source-f9fe6e9bc3792dcc) [R7](#ref-source-ac66116dfd6e4887)"},{"id":"related-topics","title":"Related topics","markdown":"## Related topics\n\nSee [s± pairing](/scwiki/s-plus-minus), [MgB2](/scwiki/magnesium-diboride), [iron-based materials](/scwiki/iron-based-superconductors), [two-dimensional interfaces](/scwiki/two-dimensional-interfaces) and [multichannel transport](/scwiki/parallel-conduction-channels)."},{"id":"material-cases","title":"Material cases","markdown":"## Material cases\n\nValues describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.\n\n| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |\n|---|---|---|---|---|---|---|\n| MgB2; Nagamatsu 2001 polycrystalline pellet, zero field | 39 K; Onset 39 K; endpoint 38 K. Synthesis pressure 196 MPa is not measurement pressure. | transition; four-probe-resistive-onset | Four-probe resistivity; separate 10 Oe magnetization | ambient; unknown GPa | unknown | experiment; [source](#ref-source-fade6558e7eafb2b) |\n| FeSe/SrTiO3 (aliases: FeSe STO, single-layer FeSe); Lee one-unit-cell film, author v6 Figure 2 mean-field fit | 58 K; 58±7 K ARPES gap-closing fit, not a zero-resistance transition. | spectroscopic-gap; ARPES-mean-field-gap-closure | Temperature-dependent ARPES | ambient; unknown GPa | unknown | experiment; [source](#ref-source-f9fe6e9bc3792dcc) |"}],"markdown":"# Multiband and multichannel pairing\n\nA coupling matrix determines a pairing instability. Multiple bands, interaction channels, transport channels and material phases are different concepts.\n\n## Scope\n\nMultiband pairing describes coupled gaps on different electronic bands. Multichannel pairing describes different interaction contributions to a Cooper-pair kernel. These are distinct from parallel normal-state conductivities and from spatially separate superconducting phases. Observing two gaps does not identify two mediating bosons; observing a resistance drop in two phases does not establish one homogeneous condensate. The band basis, sample and measurement conditions must accompany the claim. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R5](#ref-source-69ced9b5dda860f1)\n\n## Mathematical assumptions\n\nIn a real, reciprocal two-band weak-coupling illustration with a shared cutoff energy $E_c$, write $\\Delta_i=L(T_c)\\sum_j\\lambda_{ij}\\Delta_j$, where $L(T)=\\ln[2e^{\\gamma_E}E_c/(\\pi k_BT)]$ and $\\lambda_{ij}=-V_{ij}N_j$. Here $V_{ij}=V_{ji}$ is the pair interaction, attraction has negative $V$, and $N_j>0$ is the one-spin density of states in band $j$. The largest positive eigenvalue gives the leading instability, $k_BT_c=(2e^{\\gamma_E}/\\pi)E_c\\exp(-1/\\lambda_+)$. The approximation assumes $k_BT_c\\ll E_c$; a nonpositive leading eigenvalue gives no instability in this restricted model. This is a stated modern illustration, not a claim that the historical Suhl paper has been fully audited. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nAlthough $\\lambda$ need not be symmetric, $K_{ij}=-\\sqrt{N_i}V_{ij}\\sqrt{N_j}$ is a symmetric similar matrix with eigenvector $\\eta_i=\\sqrt{N_i}\\Delta_i$. For two bands, $\\lambda_+=[\\lambda_{11}+\\lambda_{22}+\\sqrt{(\\lambda_{11}-\\lambda_{22})^2+4\\lambda_{12}\\lambda_{21}}]/2$. An independent check of 64 reciprocal kernels verifies this formula, the density-of-states transformation and the gap-vector residuals. All parameters are synthetic; no MgB2 or FeSe coupling is fitted. The eigenvalue is not the sum of every matrix entry. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nConsider $K=\\begin{pmatrix}0.3&-0.1\\\\-0.1&0.3\\end{pmatrix}$, whose leading eigenvalue is $0.4$ with opposite gap signs. Adding only positive off-diagonal entries of $0.05$ lowers it to $0.35$. That added matrix is not positive semidefinite: entrywise attraction and a nonnegative quadratic form are different conditions. In contrast, 31 positive-semidefinite additions do not lower the largest eigenvalue of the fixed kernel. This bounded example shows why cooperation must be assessed after projecting the interaction, with the other assumptions held fixed. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\nWith nonzero reciprocal interband coupling, changing both off-diagonal signs leaves the two eigenvalues unchanged but reverses the relative gap sign of the nondegenerate leading mode. A transition temperature alone therefore cannot determine the relative phase. With zero interband coupling, the two bands have independent instabilities, and the weaker band need not acquire a gap at the higher transition. If the two uncoupled eigenvalues coincide, this quadratic model selects neither a unique gap vector nor a relative phase; additional terms are needed. A full calculation must also retain frequency dependence, different cutoffs, Coulomb terms and normal self-energy. Even an illustrative scalar increase from $0.3$ to $0.4$ loses to a mass factor $Z=1.5$, because $0.4/1.5<0.3$; that arithmetic is not a complete Eliashberg calculation. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221)\n\n## Experimental criteria\n\nNagamatsu and colleagues reported a resistive onset at 39 K and endpoint at 38 K in a polycrystalline MgB2 pellet, alongside separate 10 Oe magnetic measurements. The original paper's 196 MPa pressure concerns synthesis, not the superconducting measurement. This page now records the onset criterion explicitly instead of treating every reported 39 K value as an unspecified transition. Geometry, sample quality and criterion remain part of the record. [R2](#ref-source-fade6558e7eafb2b)\n\nChoi and colleagues calculated anisotropic MgB2 gaps using an electron–phonon Eliashberg model. Their band-dependent gap distributions close at a common calculated transition. These are theoretical results, not direct measurements of two independent mediators, and numerical agreement does not independently identify every interaction in a material. The corrected DOI is the MgB2 paper, not the unrelated biology article inherited by the pinned draft. [R3](#ref-source-7c4eac077ae5e221)\n\nSzabo and colleagues used Cu point contacts and two weighted BTK contributions to describe MgB2 spectra. Their selected author methods keep interface barrier and weighting parameters fixed across temperature, with applied fields helping distinguish the gap contributions. This is spectroscopic evidence interpreted through an interface model; it does not determine the relative gap sign or assign separate bosons to each gap. Cross-check band assignment and bulk thermodynamics before equating a fitted component with a unique condensate. [R5](#ref-source-69ced9b5dda860f1)\n\n## Material interpretation\n\nLee and colleagues observed replica bands in one-unit-cell FeSe/SrTiO3 and interpreted them through forward-focused interface phonons. In the identified author v6, a mean-field fit gives a gap-closing scale of $58\\pm7$ K, with Figure 2 showing closure between 50 and 64 K. This is an ARPES-derived scale, not a measured zero-resistance temperature. Their predicted enhancement assumes an electronic magnetic-pairing baseline and a specified model; neither it nor the fitted coupling is an experimentally separated budget of all pairing channels. [R4](#ref-source-f9fe6e9bc3792dcc)\n\nReplica-band interpretation requires controls. Li and Sawatzky proposed predominantly extrinsic energy loss by the escaping photoelectron, using a dielectric model. Faeth and colleagues subsequently tested photon-energy dependence at 15 K over 21–75 eV and found a nearly constant replica-to-main intensity ratio; higher-order separations and line shapes also supported intrinsic coupling in their samples. Their forward-scattering comparison inferred $\\lambda=0.19\\pm0.02$. This selected-method check is stronger than a bare replica observation, but does not by itself uniquely partition the superconducting pairing kernel. [R6](#ref-source-01df125fb3077f5f) [R7](#ref-source-ac66116dfd6e4887)\n\nThe Faeth analysis also notes that the estimated gap enhancement under its chosen model cannot fully explain the difference between the reported high gap-closing scale and electron-doped bulk comparators. Distinguish that conditional inference from a universal phonon percentage, and distinguish measured spectra from a thermodynamic or zero-resistance transition. Differences between papers require matched coupling definitions, background subtraction, sample preparation and model assumptions; a single scalar cannot settle the mechanism. [R7](#ref-source-ac66116dfd6e4887)\n\n## Limits and disputes\n\nA shared transition and multiple gap features are compatible with interband coupling, but do not independently establish beneficial cooperation between different interactions. Carrier transfer, density of states, scattering and phase coherence can change together. Claims of a unique mechanism require discriminating controls; phase-sensitive probes, spectroscopy and thermodynamics constrain different parts of the problem. The original Suhl text, full FeSe supplementary controls and complete raw-data analyses remain outside the completed checks. Complete scientific acceptance remains open. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R4](#ref-source-f9fe6e9bc3792dcc) [R5](#ref-source-69ced9b5dda860f1) [R7](#ref-source-ac66116dfd6e4887)\n\n## Discovery implications\n\nSpecify what changes when an interaction is added and what is held fixed. Report the band and momentum basis, cutoff, Coulomb and self-energy treatment, and the eigenfunction as well as the leading eigenvalue. Avoid double-counting one screened interaction under two names. A useful proposal predicts a response to a controlled perturbation and explains which competing interpretation that measurement would exclude. Do not substitute a list of plausible bosons or an unsourced sum of coupling constants for a tested kernel. [R1](#ref-source-e6ac5c48a0e11fe3) [R3](#ref-source-7c4eac077ae5e221) [R4](#ref-source-f9fe6e9bc3792dcc) [R7](#ref-source-ac66116dfd6e4887)\n\n## Related topics\n\nSee [s± pairing](/scwiki/s-plus-minus), [MgB2](/scwiki/magnesium-diboride), [iron-based materials](/scwiki/iron-based-superconductors), [two-dimensional interfaces](/scwiki/two-dimensional-interfaces) and [multichannel transport](/scwiki/parallel-conduction-channels).\n\n## Material cases\n\nValues describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.\n\n| Material and sample | Reported temperature | Criterion | Probe | Pressure | State | Evidence |\n|---|---|---|---|---|---|---|\n| MgB2; Nagamatsu 2001 polycrystalline pellet, zero field | 39 K; Onset 39 K; endpoint 38 K. Synthesis pressure 196 MPa is not measurement pressure. | transition; four-probe-resistive-onset | Four-probe resistivity; separate 10 Oe magnetization | ambient; unknown GPa | unknown | experiment; [source](#ref-source-fade6558e7eafb2b) |\n| FeSe/SrTiO3 (aliases: FeSe STO, single-layer FeSe); Lee one-unit-cell film, author v6 Figure 2 mean-field fit | 58 K; 58±7 K ARPES gap-closing fit, not a zero-resistance transition. | spectroscopic-gap; ARPES-mean-field-gap-closure | Temperature-dependent ARPES | ambient; unknown GPa | unknown | experiment; [source](#ref-source-f9fe6e9bc3792dcc) |\n\n## Sources\n\n### Ref source-e6ac5c48a0e11fe3\n\n[R1] Bardeen-Cooper-Schrieffer Theory of Superconductivity in the Case of Overlapping Bands (1959). [DOI 10.1103/PhysRevLett.3.552](https://doi.org/10.1103/PhysRevLett.3.552). Publication: journal-article. Check: crossref-metadata-only. Checked: 2026-10-17. Bibliographic identity only. Scientific statements are an edited synthesis of the pinned source chapter; primary results were not independently checked in this scope.\n### Ref source-fade6558e7eafb2b\n\n[R2] Superconductivity at 39 K in magnesium diboride (2001). [DOI 10.1038/35065039](https://doi.org/10.1038/35065039). Publication: journal-article. Check: selected-published-methods-figures-check. Checked: 2026-10-18. Published 1 March 2001. Original published pp.63–64 read for MgB2 discovery (not preceding unrelated article); p.64 visually checked. Resistive onset 39 K / endpoint 38 K, 10 Oe magnetization and synthesis196 MPa distinguished. Raw data not reproduced.\n### Ref source-7c4eac077ae5e221\n\n[R3] The origin of the anomalous superconducting properties of MgB2 (2002). [DOI 10.1038/nature00898](https://doi.org/10.1038/nature00898). Publication: journal-article. Check: selected-published-anisotropic-gap-check. Checked: 2026-10-18. Published 15 August 2002. Original pp.758–760 selected discussion and Figs. 2–4; p.759 visually checked. Calculated distributions/thermodynamics distinguished from measured gap constants. No anisotropic Eliashberg solve or original specific-heat reanalysis.\n### Ref source-f9fe6e9bc3792dcc\n\n[R4] 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.\n### Ref source-69ced9b5dda860f1\n\n[R5] Evidence for Two Superconducting Energy Gaps in MgB2 by Point-Contact Spectroscopy (2001). [DOI 10.1103/PhysRevLett.87.137005](https://doi.org/10.1103/PhysRevLett.87.137005). Publication: journal-article. Check: selected-author-spectroscopy-methods-check. Checked: 2026-10-18. Journal published 11 September 2001; author v1 submitted 30 May 2001, selected methods/results pp.2–3. Cu tips,400 Hz differential resistance, two BTK contributions, fixed weight/Z across T, field to 1 T. Final journal first-page text compared; complete final methods/raw fits not reproduced.\n### Ref source-01df125fb3077f5f\n\n[R6] Electron Phonon Coupling versus Photoelectron Energy Loss at the Origin of Replica Bands in Photoemission of FeSe on SrTiO3 (2018). [DOI 10.1103/PhysRevLett.120.237001](https://doi.org/10.1103/PhysRevLett.120.237001). Publication: journal-article. Check: publisher-original-abstract-check. Checked: 2026-10-19. Li and Sawatzky, published 5 June 2018. Abstract proposes predominantly extrinsic loss using a semiclassical dielectric calculation; complete calculation and assumptions not independently reproduced. A competing interpretation, not a settled exclusion of intrinsic coupling.\n### Ref source-ac66116dfd6e4887\n\n[R7] Interfacial Electron-Phonon Coupling Constants Extracted from Intrinsic Replica Bands in Monolayer FeSe/SrTiO3 (2021). [DOI 10.1103/PhysRevLett.127.016803](https://doi.org/10.1103/PhysRevLett.127.016803). Publication: journal-article. Check: selected-author-methods-and-figures-check. Checked: 2026-10-19. Author v1 submitted 5 February 2021; published 30 June 2021 per indexed final journal first page, not issue date 2 July. Selected pp. 2–4 methods/results; p. 3 Figures 2–3 visually checked. 15 K, photon energies 21–75 eV; photon-energy invariance, replica spacing and a forward-scattering fit. Final PDF download failed; supplements and full raw spectra/refits remain open.\n\n## Claim evidence and conditions\n\n### scwiki-b12-claim-scope-1\n\nMultiband pairing describes coupled gaps on different electronic bands. Multichannel pairing describes different interaction contributions to a Cooper-pair kernel. These are distinct from parallel normal-state conductivities and from spatially separate superconducting phases. Observing two gaps does not identify two mediating bosons; observing a resistance drop in two phases does not establish one homogeneous condensate. The band basis, sample and measurement conditions must accompany the claim.\n\nEvidence: hypothesis. Sources: source-e6ac5c48a0e11fe3, source-7c4eac077ae5e221, source-69ced9b5dda860f1.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n### scwiki-b12-claim-mathematical-assumptions-1\n\nIn a real, reciprocal two-band weak-coupling illustration with a shared cutoff energy $E_c$, write $\\Delta_i=L(T_c)\\sum_j\\lambda_{ij}\\Delta_j$, where $L(T)=\\ln[2e^{\\gamma_E}E_c/(\\pi k_BT)]$ and $\\lambda_{ij}=-V_{ij}N_j$. Here $V_{ij}=V_{ji}$ is the pair interaction, attraction has negative $V$, and $N_j>0$ is the one-spin density of states in band $j$. The largest positive eigenvalue gives the leading instability, $k_BT_c=(2e^{\\gamma_E}/\\pi)E_c\\exp(-1/\\lambda_+)$. The approximation assumes $k_BT_c\\ll E_c$; a nonpositive leading eigenvalue gives no instability in this restricted model. This is a stated modern illustration, not a claim that the historical Suhl paper has been fully audited.\n\nEvidence: theory. Sources: source-e6ac5c48a0e11fe3, source-7c4eac077ae5e221.\n\nSource relationship: context-for-local-derivation. These common-cutoff two-band equations and synthetic counterexamples are local explanatory derivations. The Suhl reference has bibliographic verification only; its full text has not been audited. Choi et al., published pp.758–760, supplies anisotropic MgB2 context, not this reduced kernel or these numerical parameters. Positive band DOS and reciprocal real interactions are required for the stated similarity transform.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Local reciprocal-kernel spectra and residuals, nine exact rational similarities and four uncoupled boundary cases; Choi selected published passages provide context. Historical Suhl full-text and complete scientific acceptance remain open.\n\n### scwiki-b12-claim-mathematical-assumptions-2\n\nAlthough $\\lambda$ need not be symmetric, $K_{ij}=-\\sqrt{N_i}V_{ij}\\sqrt{N_j}$ is a symmetric similar matrix with eigenvector $\\eta_i=\\sqrt{N_i}\\Delta_i$. For two bands, $\\lambda_+=[\\lambda_{11}+\\lambda_{22}+\\sqrt{(\\lambda_{11}-\\lambda_{22})^2+4\\lambda_{12}\\lambda_{21}}]/2$. An independent check of 64 reciprocal kernels verifies this formula, the density-of-states transformation and the gap-vector residuals. All parameters are synthetic; no MgB2 or FeSe coupling is fitted. The eigenvalue is not the sum of every matrix entry.\n\nEvidence: theory. Sources: source-e6ac5c48a0e11fe3, source-7c4eac077ae5e221.\n\nSource relationship: context-for-local-derivation. These common-cutoff two-band equations and synthetic counterexamples are local explanatory derivations. The Suhl reference has bibliographic verification only; its full text has not been audited. Choi et al., published pp.758–760, supplies anisotropic MgB2 context, not this reduced kernel or these numerical parameters. Positive band DOS and reciprocal real interactions are required for the stated similarity transform.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Local reciprocal-kernel spectra and residuals, nine exact rational similarities and four uncoupled boundary cases; Choi selected published passages provide context. Historical Suhl full-text and complete scientific acceptance remain open.\n\n### scwiki-b12-claim-mathematical-assumptions-3\n\nConsider $K=\\begin{pmatrix}0.3&-0.1\\\\-0.1&0.3\\end{pmatrix}$, whose leading eigenvalue is $0.4$ with opposite gap signs. Adding only positive off-diagonal entries of $0.05$ lowers it to $0.35$. That added matrix is not positive semidefinite: entrywise attraction and a nonnegative quadratic form are different conditions. In contrast, 31 positive-semidefinite additions do not lower the largest eigenvalue of the fixed kernel. This bounded example shows why cooperation must be assessed after projecting the interaction, with the other assumptions held fixed.\n\nEvidence: theory. Sources: source-e6ac5c48a0e11fe3, source-7c4eac077ae5e221.\n\nSource relationship: context-for-local-derivation. These common-cutoff two-band equations and synthetic counterexamples are local explanatory derivations. The Suhl reference has bibliographic verification only; its full text has not been audited. Choi et al., published pp.758–760, supplies anisotropic MgB2 context, not this reduced kernel or these numerical parameters. Positive band DOS and reciprocal real interactions are required for the stated similarity transform.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Local reciprocal-kernel spectra and residuals, nine exact rational similarities and four uncoupled boundary cases; Choi selected published passages provide context. Historical Suhl full-text and complete scientific acceptance remain open.\n\n### scwiki-b12-claim-mathematical-assumptions-4\n\nWith nonzero reciprocal interband coupling, changing both off-diagonal signs leaves the two eigenvalues unchanged but reverses the relative gap sign of the nondegenerate leading mode. A transition temperature alone therefore cannot determine the relative phase. With zero interband coupling, the two bands have independent instabilities, and the weaker band need not acquire a gap at the higher transition. If the two uncoupled eigenvalues coincide, this quadratic model selects neither a unique gap vector nor a relative phase; additional terms are needed. A full calculation must also retain frequency dependence, different cutoffs, Coulomb terms and normal self-energy. Even an illustrative scalar increase from $0.3$ to $0.4$ loses to a mass factor $Z=1.5$, because $0.4/1.5<0.3$; that arithmetic is not a complete Eliashberg calculation.\n\nEvidence: theory. Sources: source-e6ac5c48a0e11fe3, source-7c4eac077ae5e221.\n\nSource relationship: context-for-local-derivation. These common-cutoff two-band equations and synthetic counterexamples are local explanatory derivations. The Suhl reference has bibliographic verification only; its full text has not been audited. Choi et al., published pp.758–760, supplies anisotropic MgB2 context, not this reduced kernel or these numerical parameters. Positive band DOS and reciprocal real interactions are required for the stated similarity transform.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Local reciprocal-kernel spectra and residuals, nine exact rational similarities and four uncoupled boundary cases; Choi selected published passages provide context. Historical Suhl full-text and complete scientific acceptance remain open.\n\n### scwiki-b12-claim-experimental-criteria-1\n\nNagamatsu and colleagues reported a resistive onset at 39 K and endpoint at 38 K in a polycrystalline MgB2 pellet, alongside separate 10 Oe magnetic measurements. The original paper's 196 MPa pressure concerns synthesis, not the superconducting measurement. This page now records the onset criterion explicitly instead of treating every reported 39 K value as an unspecified transition. Geometry, sample quality and criterion remain part of the record.\n\nEvidence: experiment. Sources: source-fade6558e7eafb2b.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n### scwiki-b12-claim-experimental-criteria-2\n\nChoi and colleagues calculated anisotropic MgB2 gaps using an electron–phonon Eliashberg model. Their band-dependent gap distributions close at a common calculated transition. These are theoretical results, not direct measurements of two independent mediators, and numerical agreement does not independently identify every interaction in a material. The corrected DOI is the MgB2 paper, not the unrelated biology article inherited by the pinned draft.\n\nEvidence: theory. Sources: source-7c4eac077ae5e221.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n### scwiki-b12-claim-experimental-criteria-3\n\nSzabo and colleagues used Cu point contacts and two weighted BTK contributions to describe MgB2 spectra. Their selected author methods keep interface barrier and weighting parameters fixed across temperature, with applied fields helping distinguish the gap contributions. This is spectroscopic evidence interpreted through an interface model; it does not determine the relative gap sign or assign separate bosons to each gap. Cross-check band assignment and bulk thermodynamics before equating a fitted component with a unique condensate.\n\nEvidence: experiment. Sources: source-69ced9b5dda860f1.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n### scwiki-b12-claim-material-interpretation-1\n\nLee and colleagues observed replica bands in one-unit-cell FeSe/SrTiO3 and interpreted them through forward-focused interface phonons. In the identified author v6, a mean-field fit gives a gap-closing scale of $58\\pm7$ K, with Figure 2 showing closure between 50 and 64 K. This is an ARPES-derived scale, not a measured zero-resistance temperature. Their predicted enhancement assumes an electronic magnetic-pairing baseline and a specified model; neither it nor the fitted coupling is an experimentally separated budget of all pairing channels.\n\nEvidence: experiment. Sources: source-f9fe6e9bc3792dcc.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n### scwiki-b12-claim-material-interpretation-2\n\nReplica-band interpretation requires controls. Li and Sawatzky proposed predominantly extrinsic energy loss by the escaping photoelectron, using a dielectric model. Faeth and colleagues subsequently tested photon-energy dependence at 15 K over 21–75 eV and found a nearly constant replica-to-main intensity ratio; higher-order separations and line shapes also supported intrinsic coupling in their samples. Their forward-scattering comparison inferred $\\lambda=0.19\\pm0.02$. This selected-method check is stronger than a bare replica observation, but does not by itself uniquely partition the superconducting pairing kernel.\n\nEvidence: experiment. Sources: source-01df125fb3077f5f, source-ac66116dfd6e4887.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n### scwiki-b12-claim-material-interpretation-3\n\nThe Faeth analysis also notes that the estimated gap enhancement under its chosen model cannot fully explain the difference between the reported high gap-closing scale and electron-doped bulk comparators. Distinguish that conditional inference from a universal phonon percentage, and distinguish measured spectra from a thermodynamic or zero-resistance transition. Differences between papers require matched coupling definitions, background subtraction, sample preparation and model assumptions; a single scalar cannot settle the mechanism.\n\nEvidence: experiment. Sources: source-ac66116dfd6e4887.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n### scwiki-b12-claim-limits-and-disputes-1\n\nA shared transition and multiple gap features are compatible with interband coupling, but do not independently establish beneficial cooperation between different interactions. Carrier transfer, density of states, scattering and phase coherence can change together. Claims of a unique mechanism require discriminating controls; phase-sensitive probes, spectroscopy and thermodynamics constrain different parts of the problem. The original Suhl text, full FeSe supplementary controls and complete raw-data analyses remain outside the completed checks. Complete scientific acceptance remains open.\n\nEvidence: hypothesis. Sources: source-e6ac5c48a0e11fe3, source-7c4eac077ae5e221, source-f9fe6e9bc3792dcc, source-69ced9b5dda860f1, source-ac66116dfd6e4887.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n### scwiki-b12-claim-discovery-implications-1\n\nSpecify what changes when an interaction is added and what is held fixed. Report the band and momentum basis, cutoff, Coulomb and self-energy treatment, and the eigenfunction as well as the leading eigenvalue. Avoid double-counting one screened interaction under two names. A useful proposal predicts a response to a controlled perturbation and explains which competing interpretation that measurement would exclude. Do not substitute a list of plausible bosons or an unsourced sum of coupling constants for a tested kernel.\n\nEvidence: hypothesis. Sources: source-e6ac5c48a0e11fe3, source-7c4eac077ae5e221, source-f9fe6e9bc3792dcc, source-ac66116dfd6e4887.\n\nConditions: Preserve band basis, DOS, cutoff, normal self-energy, sample, probe and temperature type; model examples are not material fits.\n\nVerification scope: Named source-specific checks and bounded two-band model only; complete scientific acceptance remains open.\n\n## Revision and review\n\nArticle ID: scwiki-b12. Revision: 3f2e9e7c61b17355274d. Updated: 2026-10-19T00:47:10.029011+00:00.\n\nReview scope: Inherited D7 source-specific MgB2 checks; Lee author v6 selected results/Figure 2 and model caption; Faeth author v1 selected methods/Figures 2–3; Li–Sawatzky original abstract; 64 reciprocal-kernel cases, 31 PSD controls and bounded counterexamples. Nine exact rational similarity checks and four uncoupled/degenerate boundary cases.\n\n- Complete scientific acceptance remains open.\n- Suhl original full text remains metadata-only; the two-band illustration was checked independently, not attributed as a complete historical audit.\n- Lee/Faeth final-version comparisons, complete supplementary controls and raw spectral fits remain open.\n- No unique multi-boson decomposition or full frequency-dependent Eliashberg solve is claimed.\n- At zero interband coupling, a degenerate quadratic instability does not fix a unique relative phase; local eigenvalue checks do not solve nonlinear phase selection.\n\nSource: [B_mechanisms/B12_multi_channel_superposition.md](https://github.com/JackZH26/jzis-superconductivity/blob/0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf/B_mechanisms/B12_multi_channel_superposition.md), commit 0a7c9d6696804ec26aa12f8eed68b55c9b3c0fcf, SHA-256 f7633eef3b233297e3d3dc010522914b257dc6184c6c03432341c56fe065b2aa.\n","wordCount":1045}}