Public Computational and Analytic Benchmark Gates for CHC-QTT Support-Registration Factorization

The CHC-QTT sector reads barrier-mediated tunneling signals through a support--registration factorization of the schematic form

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

Here $\exp[-2\Acal_B]$TeX\exp[-2\Acal_B] is the barrier-mediated phase-link support factor and $\Rcal$TeX\Rcal is the registration factor carrying interface, lead, density-of-states, bias-window, or readout availability. The present companion benchmark record does not attempt a same-instance experimental closure of reference. It supplies a first public benchmark with two declared components:

- a computational STM registration-feature test using public JARVIS-STM image data; - analytic support-action consistency gates for Fowler--Nordheim, rectangular-barrier, and Simmons-style families.

The result is therefore a computational/analytic benchmark certificate for the registered checks. It is not a measurement of a hidden traversal path, a QED replacement, a detector microdynamics model, or a tunneling-time theory.

The STM benchmark uses the JARVIS-STM computational database. Choudhary et al. introduced a systematic database of STM images calculated using density functional theory and the Tersoff--Hamann method for $716$TeX716 exfoliable two-dimensional materials, and made the generated computational STM images available through JARVIS-STM and Figshare [citation]. The Tersoff--Hamann formalism provides the STM theory anchor in which the tunneling current is connected to the surface local density of states at the tip position [citation]. The older Bardeen matrix-element formulation supplies the standard many-particle tunneling anchor [citation]. The Fowler--Nordheim, Simmons, and rectangular-barrier analytic gates are used only as support-action extractor consistency checks, with Fowler--Nordheim and Simmons serving as field-emission and MIM tunneling anchors [citation].

The public-source summary identifies two official source surfaces: center

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

center The public benchmark record identifies the official STM source surfaces and the declared feature tables used for the benchmark summaries. The computational STM objects are not treated as experimental STS current--voltage curves.

The public record identifies the computational image source, lattice-label metadata, declared feature-extraction route, and resulting feature summaries. Public source is retained in the companion source summary and is not part of the physical claim.

STM registration-feature gate

Let $I_+$TeXI_+ and $I_-$TeXI_- denote the positive- and negative-bias computational STM images associated with a declared material identifier. Images are normalized by

I_{\rm norm}=\frac{I-\min(I)}{\max(I)-\min(I)+\epsilon},
\qquad
\epsilon=10^{-12}.

For a paired positive/negative image on the common cropped shape, the pair-distance feature is

d_{+-}=\frac{\|I_{+,\rm norm}-I_{-,\rm norm}\|_2}{\sqrt{N}},

where $N$TeXN is the number of pixels in the common image domain. A high-frequency Fourier proxy is also computed using a fixed one-third Nyquist-radius cutoff. The final feature table is stored in float64. Flat-image cases are handled by explicit flags; no flat-image rows occur in the present evaluation.

Analytic support-action gates

The Fowler--Nordheim sanity gate uses

J(F)=C F^2\exp(-B/F).

The extractor regresses $\log(J/F^2)$TeX\log(J/F^2) against $1/F$TeX1/F; the recovered slope is $-B$TeX-B. The registered cases use $B\in\{6.83,8.25,9.75\}$TeXB\in\{6.83,8.25,9.75\}.

The rectangular-barrier gate compares finite positive values of the exact transmission coefficient

T_{\rm rect}(E)=
\left[
1+\frac{U_0^2\sinh^2(\kappa a)}{4E(U_0-E)}
\right]^{-1},
\qquad
\kappa=\frac{\sqrt{2m(U_0-E)}}{\hbar},

with its WKB envelope $\exp(-2\kappa a)$TeX\exp(-2\kappa a) on the declared parameter grid. The gate is a positivity and finite-value check, not a new tunneling law.

The Simmons-style thickness-decay gate uses the synthetic form

J(s,V)=C V\exp(-2\kappa s).

The extractor regresses $\log(J/V)$TeX\log(J/V) against thickness $s$TeXs and returns $\kappa=-\frac12\,\partial_s\log(J/V)$TeX\kappa=-\frac12\,\partial_s\log(J/V). The registered cases use $\kappa\in\{1.25,1.75,2.25\}$TeX\kappa\in\{1.25,1.75,2.25\}.

The JARVIS-STM public source set contains $716$TeX716 declared JIDs. All $716$TeX716 have positive- and negative-bias pairs. The deterministic feature extraction produces $716$TeX716 finite feature rows in $15$TeX15 completed feature groups. The analytic layer produces $9$TeX9 completed chunks: three Fowler--Nordheim cases, three rectangular-barrier cases, and three Simmons-style cases.

center

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

center

For the Fowler--Nordheim cases, the relative errors in $B$TeXB recovery are $2.08\times10^{-15}$TeX2.08\times10^{-15}, $6.46\times10^{-16}$TeX6.46\times10^{-16}, and $1.28\times10^{-15}$TeX1.28\times10^{-15}. For the Simmons-style cases, the relative errors in $\kappa$TeX\kappa recovery are $2.49\times10^{-15}$TeX2.49\times10^{-15}, $1.14\times10^{-15}$TeX1.14\times10^{-15}, and $9.87\times10^{-16}$TeX9.87\times10^{-16}. Rectangular-barrier exact and WKB values are finite and positive on all declared cases. The declared construction summary records $15$TeX15 feature groups and $9$TeX9 analytic chunks, and the merge-consistency check returns declared chunk presence, non-overlap, non-gap, source-identity match, and no NaN/inf conditions.

The declared classification rule returns

\boxed{\mathrm{QTT\mbox{-}VP0\mbox{-}COMPUTATIONAL\mbox{-}GATES\mbox{-}SATISFIED}} .

The classification means that the public computational STM acquisition, pair reconstruction, deterministic registration-feature extraction, and analytic support-action checks are satisfied on the declared benchmark records.

remark: Non-claim boundary. The result does not close same-instance experimental STM/MIM/Fowler--Nordheim validation. It does not identify a separated detector microdynamics, does not replace QED, does not infer a hidden path through the barrier, and does not decide tunneling-time questions. Experimental literature benchmarks and same-sample cross-window closure remain separate verification stages.

CHC-QTT-VP0 supplies a reproducible computational/analytic benchmark for the CHC-QTT support--registration reading of tunneling signals. The computational STM component confirms that the registered JARVIS-STM acquisition, pairing, and registration-feature extraction gates close on all $716$TeX716 declared JIDs. The analytic component confirms that the Fowler--Nordheim, rectangular-barrier, and Simmons-style support-action extractors recover their registered consistency-check targets. The declared computational and analytic gates therefore establish $\mathrm{QTT\mbox{-}VP0\mbox{-}COMPUTATIONAL\mbox{-}GATES\mbox{-}SATISFIED}$TeX\mathrm{QTT\mbox{-}VP0\mbox{-}COMPUTATIONAL\mbox{-}GATES\mbox{-}SATISFIED} at the declared computational/analytic level. It remains a benchmark result, not an empirical same-instance tunneling validation.

The companion source summary summarizes the public source, processed feature tables, analytic benchmark tables, protocol-compliance checks, merge-consistency checks, declared computational procedures, and result summaries for the declared computational/analytic VP0 gates. Raw computational STM public sources remain attributable to the official JARVIS-STM/Figshare sources. The record is a bounded computational/analytic companion source summary only; it is not same-instance experimental STM/MIM/Fowler--Nordheim validation and not an empirical tunneling-time claim.

Funding and competing interests..

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