Public Literature Support-Action Gates for CHC-QTT

-- formulates registered tunneling signals as a support--registration factorization rather than as evidence for a hidden material traversal path through a forbidden region. On a declared weak-tunneling family, the signal has the form

I_\alpha(V,\lambda)=\int \dd E\;\Rcal_\alpha(E,V,\lambda)\exp[-2\Acal_{B,\alpha}(E,V,\lambda)]+\delta I_\alpha(V,\lambda),

where the exponential factor carries barrier-mediated phase-link support and $\Rcal_\alpha$TeX\Rcal_\alpha carries interface-side registration. Bardeen's many-particle tunneling formulation, the Tersoff--Hamann STM theory, Simmons-type MIM tunneling formulae, and Fowler--Nordheim field-emission analysis provide the standard-theory anchors for the declared comparison windows [citation].

The VP1 record is not a proof of reference. Its object is narrower. It tests whether the registered support-action and registration-side curve gates are satisfied on public literature curves spanning three families:

- STM/STS distance or conductance curves, - MIM or Simmons-style tunnel-junction bias curves, - Fowler--Nordheim field-emission curves.

This is a literature benchmark record. It does not claim same-sample or same-fabrication-family closure. That stronger object belongs to a later VP2-style identity-bearing record.

The public record uses six digitized curve objects. Three are reconstructed literature-anchor curves and three are direct digitization records. The direct records are the STM Figure 6 digitization from Hellenthal et al., the MIM Figure 3 digitization from Karbasian et al., and a sparse FN direct digitization from the Allaham--Forbes table/plot-method surface. The STM source demonstrates closed-loop conductance STS and compares it to open-loop $I(z)$TeXI(z) measurements for tunneling-barrier extraction; its Figure 6 reports logarithmic conductance versus tip--sample distance with a linear fit slope $-10.4\,\mathrm{nm}^{-1}$TeX-10.4\,\mathrm{nm}^{-1} [citation]. The MIM source is an open-access review of metal--insulator--metal single-electron transistors with ALD-prepared tunnel barriers, and the VP1 direct curve object uses the Figure 3 conductance--bias surface as a bias-shape stress target [citation]. The FN source is the open-access Allaham--Forbes et al. field-emission plotting paper, used as plot-method, reconstructed support-slope, and sparse direct-table support rather than as a same-instance experimental curve [citation].

Figure or table content is omitted from the web reader; use the canonical manuscript for the exact object.

The six objects are distributed as digitized CSV files with axis-calibration metadata and per-curve digitization reports. Raw publisher figures are not required on the source basis. When a figure or PDF is redistributable, it may be retained in the companion source summary; otherwise the companion source summary carries the digitized curve, DOI/source metadata, digitization report, and public-source summaries.

The public-source summary identifies the digitized-curve records, per-family summaries, and public-source metadata used by QTT--VP1. The route type is a public literature-curve benchmark with direct digitization support. The displayed counts are six digitized curves, all admitted by the declared curve-record criteria, with family boards $2/2$TeX2/2, $2/2$TeX2/2, and $2/2$TeX2/2 for STM/STS, MIM, and FN respectively. Those support summaries determine the public reading.

STM/STS support-action gate

For STM distance curves, VP1 fits

\log |I(z)| = c_0 -2\kappa z + \epsilon(z),

with the registered extraction rule

\widehat\kappa=-\frac{1}{2}\frac{\dd \log |I|}{\dd z}.

When the source figure already reports a logarithmic conductance axis, the support summary reports this in the axis metadata and does not apply another logarithm.

MIM bias-shape gate

When a thickness series $J(s,V)$TeXJ(s,V) is available, the registered MIM support-action gate is

\widehat\kappa(V)=-\frac{1}{2}\frac{\partial}{\partial s}\log |J(s,V)|.

The VP1 MIM curve objects are bias-shape curves rather than thickness series. Consequently, the support summary reports a bias-shape stress pass and explicitly assigns no thickness-gated $\kappa$TeX\kappa. This prevents a Simmons-style thickness inference from being imported when the curve family does not supply a thickness axis [citation].

Fowler--Nordheim support-slope gate

For FN field-emission curves, the registered transformed coordinates are

X_{\rm FN}=1/F,\qquad Y_{\rm FN}=\log(J/F^2),

with the same convention applied when voltage replaces field under a declared conversion. The slope in the transformed plot is recorded as a support-slope proxy. The FN layer in VP1 is a method-anchor reconstruction from published numerical points, not a same-instance field-emission experiment.

All six digitized curve records satisfy the declared curve-record criteria. The family board is

\mathrm{STM/STS}:2/2,
qquad
\mathrm{MIM}:2/2,
qquad
\mathrm{FN}:2/2.

The declared classification rule therefore finds compatibility with the literature benchmark.

Figure or table content is omitted from the web reader; use the canonical manuscript for the exact object.

The direct STM object supplies bounded direct-digitization support beyond the earlier slope-anchor reconstruction. The direct MIM object supplies bounded direct-digitization support beyond the earlier parameter-anchor reconstruction. The sparse direct FN object adds direct table/plot-method support for the FN family. Because all three families carry direct digitization support, the stricter staged reading may record informal $\mathrm{LITERATURE\text{-}BENCHMARK\text{-}DIRECT\text{-}DIGITIZATION\text{-}COMPATIBLE}$TeX\mathrm{LITERATURE\text{-}BENCHMARK\text{-}DIRECT\text{-}DIGITIZATION\text{-}COMPATIBLE} direct-digitization support. This staged label is not the declared VP1 classification and does not elevate the record to same-instance validation.

The supplementary literature-benchmark record supports the declared VP1 gates by summarizing the gate result, family-extractor tables, protocol-compliance statement, digitized-curve provenance, source-citation matrix, and public source. The companion source summary identifies the digitized curve tables, axis-calibration metadata, digitization reports, source summaries, validation summaries, extractor tables, protocol-compliance statement, and public-source summary used for the declared literature-benchmark status. Raw article figures are not required on the source basis unless the applicable license and source policy permit redistribution.

The declared VP1 record is a multi-family literature-curve benchmark record. Its gate classification records the schema validation, digitized-curve provenance, and protocol compliance. The record is designed to be reproducible from the declared curve data and metadata, while raw publisher images remain outside the manuscript claim.

The following overreads are excluded:

- VP1 is not a same-sample STM/MIM/FN validation. - VP1 is not a same-fabrication-family validation. - VP1 does not replace QED or standard tunneling theory. - VP1 does not close detector microdynamics, Josephson phase dynamics, bulk conductor transport, or tunneling-time theory. - VP1 does not infer a hidden traversal path.

These exclusions are not conservative afterthoughts; they define the owned object of VP1. The record demonstrates that the QTT support-action and registration-side gates are satisfied on declared public literature curves. It does not assert that the curves share a sample, device, fabrication lot, or common barrier family.

Literature support for a tunneling response does not show that a proposed phase-loading formula descends from an action. The decisive local test is the Helmholtz condition $D_\lambda=D_\lambda^*$TeXD_\lambda=D_\lambda^* for the extracted scalar loading functional under the declared boundary conditions. When it holds on a star-shaped phase patch, the homotopy integral supplies a local scalar primitive; when it fails, no change of interpretation can repair the proposed lift without changing the law.

The later registration stage has a different admissibility condition: it must be a CPTP instrument. A positive attenuation operator fixes only the total event rate, while its factorization into jump operators fixes the resolved registration channels. The literature record should therefore classify action support, transmission support, and instrument support separately. Evidence for one cannot be counted as evidence for either of the others.

The closure test for the literature support--action 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 the literature-derived action, transmission, and instrument support indicators. Let $a$TeXa range over the independent constitutive inputs comprising source selection, barrier convention, registration semantics, and evidence labels.

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 each evidence label is tied to a distinct microscopic claim and no source is counted simultaneously as action derivation and detector completion.

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 literature agreement at one layer does not logically establish the missing layers of the closure chain. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

QTT-VP1 returns

\boxed{\mathrm{LITERATURE\text{-}BENCHMARK\text{-}COMPATIBLE}}

for source compatibility only. Six digitized curves pass schema and transform checks, but the cross-source comparison does not identify a common action or constitute an empirical validation of CHC-QTT.

The companion source summary summarizes the digitized curve tables, axis-calibration metadata, digitization reports, public source, validation summaries, extractor tables, and protocol-compliance statement used for the declared literature-benchmark status. Raw article figures are not required for the manuscript claim. The QTT-VP1 record is cited as bounded literature-benchmark support, not as an independent empirical closure claim.

Funding and competing interests..

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