Same-Window Public Optical Branch-Budget Gate in IGDB for CHC-CBL

The CBL optical branch-budget reading used here is restricted to the public IGDB glazing-product surface. The retained quantities are the spectral triplet

(\Tsol,\Rf,\Rb)

on one IGDB release, one product identity, one wavelength grid, and one optical measurement convention. The derived optical absorptance branches are

\Af(\lambda)=1-\Tsol(\lambda)-\Rf(\lambda),
\qquad
\Ab(\lambda)=1-\Tsol(\lambda)-\Rb(\lambda).

The corresponding closure residuals are

\resf(\lambda)=\left|1-\Tsol(\lambda)-\Rf(\lambda)-\Af(\lambda)\right|,\notag

\resb(\lambda)=\left|1-\Tsol(\lambda)-\Rb(\lambda)-\Ab(\lambda)\right|.

The formulas in reference and reference are branch-budget identities under the declared IGDB optical convention. They are not a full CBL branch-tomography model. In particular, the gate does not identify externalized, ledger-retained, and sink branches for a single device or detector under a shared calibration map.

The excluded readings are:

- same-instance full CBL branch tomography; - sealed calibration/covariance certificate; - direct detector-microdynamics closure; - Maxwell or QED replacement; - Planck-law replacement; - branch-fraction assignment outside the declared IGDB optical convention.

IGDB is maintained by Lawrence Berkeley National Laboratory as a public optical data collection for glazing products and is used by LBNL WINDOW and the NFRC rating ecosystem [citation]. The IGDB installation procedure states that the setup file installs a complete declared IGDB glazing database [citation]. IGDB submission guidance specifies solar optical measurements over the 300--2500 nm interval [citation]. Supporting IGDB documentation and inter-laboratory comparison reports describe transmittance and front/back reflectance in the 300--2500 nm optical region and front/back emissivity from thermal-infrared reflectance in the 5--25 micron region [citation].

The evaluated public source surface is center

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The selected table has the retained columns

(\texttt{GlazingID},\texttt{WavelengthIndex},\texttt{AngleIndex},\texttt{Wavelength}),

(\texttt{Angle},\texttt{T},\texttt{Rf},\texttt{Rb}).

The same-window rule requires T, Rf, and Rb to be read from the same IGDB release, same product record, same wavelength entry, and same measurement convention. The evaluated scoring uses the wavelength column converted to nanometers before applying the 300--2500 nm gate.

The gate is tied to the following public source surfaces and diagnostic summaries. center adjustboxmax width=

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The construction record is: the public IGDB v110.1 release is identified; the embedded declared IGDB glazing database object is identified and used; the same-window spectral table is selected; wavelengths are converted to nanometers before the 300--2500 nm gate; row-level closure residuals and auxiliary product-bound scores are computed; and the non-claim boundary is confirmed. The route is a declared public-data evaluation on the official IGDB release, not a same-sample calibration/covariance evaluation.

For each retained row, the branch-budget construction computes $\Af$TeX\Af and $\Ab$TeX\Ab by reference. A row passes the row-level branch-budget part of the gate when

\resf(\lambda)\le \tau_{\rm cl},
\qquad
\resb(\lambda)\le \tau_{\rm cl},

with

\tau_{\rm cl}=10^{-9}.

The strict bound part of the gate further requires

-\tau_{\rm b}\le \Af(\lambda)\le 1+\tau_{\rm b},
\qquad
-\tau_{\rm b}\le \Ab(\lambda)\le 1+\tau_{\rm b},

with

\tau_{\rm b}=10^{-9}.

A product-level strict pass requires all retained row entries for that product in the gate to satisfy both reference and reference.

The public IGDB v110.1 route states a same-window optical branch-budget gate. The diagnostic summary is center

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The final classification is

\boxed{\mathrm{CBL\text{-}RTA\text{-}SAME\text{-}WINDOW\text{-}PUBLIC\text{-}CHECK\text{-}SATISFIED}}.

The substatus is

\boxed{\mathrm{IGDB\text{-}V110\_1\text{-}ROW\text{-}CLOSURE\text{-}CHECK\text{-}SATISFIED}}.

This substatus is deliberately row-level. The auxiliary strict product-bound score reports 6,775 strict candidate-pass products and 55 strict non-pass products among the 6,830 retained products. The non-pass products are strict-bound non-pass cases, not closure non-pass cases: the retained rows satisfy the declared closure condition, while the strict product-bound criterion is not universal. The retained rows satisfy the branch-budget identity after $\Af$TeX\Af and $\Ab$TeX\Ab are computed by reference, while some derived absorptance values fall just outside the declared strict bound tolerance.

Representative strict-pass product records include: center adjustboxmax width=

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CBL-VP0 classified the EKHI radiative-property branch as $R/T/A$TeXR/T/A-partial because a same-window reflectance--transmittance--absorptance triple was not present on that analysis. The IGDB gate supplies a public same-window optical triplet for a glazing-product release and therefore supports CBL-RTA-SAME-WINDOW-PUBLIC-CHECK-SATISFIED under the IGDB convention. This is a same-window optical branch-budget result only. It does not alter the status of same-instance full CBL branch tomography, which remains unavailable without a shared sample/interface manifest, calibration map, and covariance or interval object.

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is a public IGDB v110.1 same-window optical branch-budget result, with

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

as the stable row-level substatus. & Do not read this as same-instance full CBL branch tomography, universal product-bound closure, sealed calibration/covariance certification, detector microdynamics closure, Maxwell/QED replacement, Planck-law replacement, or empirical branch-fraction closure outside the IGDB optical convention. tabular center

The classification in reference must be rejected or re-evaluated if any of the following occurs:

- the IGDB v110.1 installer or declared IGDB glazing database public source is inconsistent with the declared public-source summary; - declared spectral-data table is not recovered from the same declared database; - T, Rf, and Rb are not read from the same product and same wavelength convention; - the wavelength conversion to nanometers is not applied before the 300--2500 nm gate; - row-level closure residuals exceed $\tau_{\rm cl}=10^{-9}$TeX\tau_{\rm cl}=10^{-9}; - the result is described as same-instance full branch tomography, sealed calibration/covariance closure, detector microdynamics closure, Maxwell/QED replacement, or Planck-law replacement.

The same-window optical budget must close as an instrument, not merely as a fitted sum of intensities. Absorption or no-return described by a positive sink $K$TeXK is completed by event operators $L_a$TeXL_a with $K=\sum_aL_a^\dagger L_a$TeXK=\sum_aL_a^\dagger L_a; the corresponding jump probabilities, including any unresolved loss channel, must exhaust the no-event trace decrease. This condition is independent of the chosen optical normalization.

If one relaxation coordinate is invoked for transient branch conversion, its completely monotone response must also have Hankel rank one and satisfy $\mu_0\mu_2-\mu_1^2=0$TeX\mu_0\mu_2-\mu_1^2=0. The analysis therefore tests probability closure, memory order, and cross-branch parameter sharing separately. Retuning an efficiency or time constant for each branch defines a different, rank-enlarged model.

The closure test for the same-window optical closure 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 optical and carrier branch observables on the identical window. Let $a$TeXa range over the independent constitutive inputs comprising optical response, carrier response, memory state, and instrument calibration.

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 both modalities share one interface parameter vector, while memory order and probability closure are tested separately.

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 agreement on different windows cannot establish a common interface mechanism. Failure of that condition therefore rejects the proposed microscopic closure before parameter estimation can be counted as evidence for it.

CBL--VP1 verifies extraction of the IGDB transmittance and reflectance columns on a common wavelength grid. The reported row closure follows identically from defining $A=1-T-R$TeXA=1-T-R and therefore is a software arithmetic check, not validation of a physical branching model. Independent absorptance or calorimetric measurements and uncertainty covariance would be required for an empirical test.

The companion source summary associated with this gate summarizes source attribution, public-source availability, table identification, row-closure results, and auxiliary product-score results. Source IGDB records remain attributable to Lawrence Berkeley National Laboratory and should be obtained under the applicable public-source terms.

Funding and competing interests..

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