QTT-VP2: Figure-Derived Same-Fabrication-Family Partial Gates for MIM/FN Tunneling Windows

QTT-VP0 records public computational STM and analytic support-action benchmark records. QTT-VP1 records public literature-curve support-action benchmark records. QTT-VP2 is stricter: it requires an identity-bearing ledger tying at least two tunneling windows to the same surface, device, or fabrication/barrier family.

The present paper is therefore not a universal tunneling theory, not a quantum-electrodynamics replacement, and not a same-instance experimental validation. The result is limited to the declared VP2 route record and the successful partial result on the MIM/FN same-fabrication-family route.

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The Bertolini route is the strongest same-surface candidate because the published article treats STM topography and scanning field-emission microscopy contrast on the same surface region and gives current--voltage characteristics for W/WC or Fe/WC domains [citation]. Public probing recovered the Zenodo-linked analysis archive but not the raw same-surface matrices. The archive scripts reference source files with suffixes 003.sxm, 005.sxm, and 010.sxm; these remain absent from the public record.

The Lebedev case is a same-device candidate because the published work studies STM-induced light emission and I(V) behavior of single plasmonic nanoantennas and reports correlations between photon maps and derived current--voltage curves [citation]. At the declared public-source boundary, PubMed and Crossref metadata were recoverable, but no public object supplied a nanoantenna or device identifier tying STM observables, I(V), and light emission. The case therefore remains unevaluated.

The Ozyigit route is a same-fabrication-family candidate. The article studies Pt--Al$_2$TeX_2O$_3$TeX_3--Al quantum-tunneling MIM nanodiodes produced by AP-CVD and PEALD, with Al$_2$TeX_2O$_3$TeX_3 thicknesses 3/6/9 nm, and discusses conduction mechanisms including direct tunneling and high-bias Fowler--Nordheim behavior [citation]. The article, PDF, supplementary PDF, and full-size figure surfaces were acquired. The public figures support a lower figure-derived family gate, but not a raw/export source-data recovery.

The public record is identified by the QTT--VP2 figure-derived public-source evaluation record and by the declared figure-derived summaries and identity-window statements retained with the supplementary materials. The route type is a figure-derived public route. The displayed identity fields, window count, and limitations are read only from those declared scientific summaries.

The MIM/FN figure-derived ledger uses two windows:

- Figure 5, recorded as a responsivity-versus-resistance family window. - Figure 6, recorded as a conduction-mechanism/high-bias transformed-coordinate window.

Figure 4 is retained as Al$_2$TeX_2O$_3$TeX_3 barrier/process-family identity support only. It is not counted as a tunneling-current window.

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The identity-window validation result is: center 3pt

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The digitization method is intentionally conservative. The extracted values remain in the axes as plotted. Figure 5 is not re-linearized from hidden source data. Figure 6 is not inverted into raw current--voltage data; its transformed coordinates are retained as published. Consequently, the result is a figure-derived public partial gate only.

The Bertolini Tier-A route could be evaluated if the referenced SXM files, Figure 3 STM/SFEM matrices, Figure 4 $I_c(U)$TeXI_c(U) and $I_s(U)$TeXI_s(U) exports, W/WC or Fe/WC domain labels, coordinate registration, and scan/channel metadata were obtained.

The Lebedev Tier-B route could be evaluated if same nanoantenna/device identifiers, STM observables, I(V) curves, photon maps or spectra, and figure-to-device mapping were obtained.

The MIM/FN Tier-C-ready route requires author-provided raw/export MIM J--V or conductance curves, FN/high-bias raw or transformed fit-window data, shared fabrication/run/batch/barrier-family/material-stack/process/thickness metadata, source-file mapping, axis definitions, units, calibration notes, and uncertainty information. Without those data, the correct status remains .

The bounded reading for this paper is: quote QTT-VP2 reaches a Tier-C figure-derived partial result for the MIM/FN same-fabrication-family case. Tier-A same-surface and Tier-B same-device cases remain unevaluated because identity-bearing source data are absent. The result does not recover raw source data, validate the same device or instance, close QED or detector dynamics, or resolve tunneling-time questions. quote

The same-fabrication-family tests become overidentifying only when one frozen parameter vector predicts all selected Fowler--Nordheim slopes, barrier responses, and registration fractions. If the resulting observable vector has dimension $m$TeXm and its common sensitivity matrix has rank $r<m$TeXr<m, every vector in the left null space supplies a first-order equality $w^{\mathsf T}\delta y=0$TeXw^{\mathsf T}\delta y=0. These relations are invariant under nonsingular re-expression of the reported observables.

Figure-derived partial support does not license device-wise retuning. Adding a separate barrier or registration coefficient for each plotted output can raise the response rank to $m$TeXm, in which case the model image is locally open and no compatibility equation remains. The present partial analysis should therefore report both the frozen parameter count and sensitivity rank; otherwise agreement cannot distinguish a shared branch law from an observable-saturated fit.

The closure test for the figure-derived tunneling gates is applied to a dimensionless observable vector $y\in\mathbb R^m$TeXy\in\mathbb R^m formed from fixed reference scales and the declared basket of same-family curves, ratios, slopes, and partial-gate residuals. Let $a$TeXa range over the independent constitutive inputs comprising figure digitization, barrier proxy, registration correction, and group normalization.

proposition: Functional saturation, finite closure, and sector admissibility. Suppose the unrestricted prediction map $F:a\mapsto y$TeXF:a\mapsto y is continuously differentiable on a Banach space of constitutive inputs. If $D_aF$TeXD_aF is surjective and has a bounded right inverse at the calibration point, the unrestricted family is locally open in observable space and supplies no nonzero local equality restriction on $y$TeXy. Suppose instead that a single microscopic closure replaces $a$TeXa by finite parameters $\theta\in\mathbb R^p$TeX\theta\in\mathbb R^p, with profiled nuisance coordinates $\eta\in\mathbb R^q$TeX\eta\in\mathbb R^q. If

J=D_\eta F_{\rm cl}D_\theta F_{\rm cl},
 \qquad \operatorname{rank}J=r<m,

then there are $m-r$TeXm-r independent first-order restrictions

w^{\mathsf T}\delta y=0,
 \qquad w\in\ker J^{\mathsf T}.

If the rank is constant locally, these restrictions are tangent to a compatibility manifold of codimension $m-r$TeXm-r. For this sector, the finite closure is admissible only if one frozen lower-rank response map is used for every digitized group and evaluated on an unused contrast.

proof. Split surjectivity gives a bounded right inverse $R$TeXR with $D_aF\,R=I_m$TeXD_aF\,R=I_m. The Banach-space submersion theorem then makes $F$TeXF locally onto a neighborhood of the calibrated observable vector. Any smooth equality holding throughout that image must therefore vanish on an open set and contributes no model-specific local restriction. Under finite closure, the attainable first-order variations are exactly the column space of $J$TeXJ. Its orthogonal complement is $\ker J^{\mathsf T}$TeX\ker J^{\mathsf T}, whose dimension is $m-r$TeXm-r by rank--nullity, which proves reference. The constant-rank theorem supplies the stated local manifold. The sector condition is necessary because group-specific normalizations can otherwise reproduce each figure without constraining a shared mechanism. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

QTT-VP2 identifies two figure-derived windows from a shared fabrication family. This is insufficient to identify a common barrier action because the registration factor remains unconstrained and the raw/export data are unavailable. The partial label records source availability only.

If Bertolini, Lebedev, or Ozyigit source-data exports arrive later, they should be assessed in a separate source-data follow-up record, not retroactively read into the present figure-derived partial status.

Data and code availability..

This companion manuscript uses public literature, figure-derived, or reference inputs as described in the text. No proprietary observational data are introduced. Cited public references and companion statements, where provided, are identified by the companion source summaries cited in the text.

Funding and competing interests..

No external funding was received for this work. The author declares no competing interests.