CHC-PFW Public Scalar, Covariance, Contour, and ROOT Support Gates for Precision-Observable Windows

The parent -PFW paper defines a declared precision-observable basket on one fixed admitted family. Its central question is not whether an unrestricted global fit can be performed, but whether the declared family admits a nonempty benchmark-window intersection without channel-by-channel retuning. The present validation paper asks a narrower public-data question: quote Can the declared CHC-PFW windows be tied to independently identified public covariance, contour, ROOT source, and scalar-source surfaces by support checks with explicit non-claim boundaries? quote The bounded public lane reported here satisfies this support condition.

This paper does not claim any of the following:

- a global precision-electroweak likelihood; - a global leptonic-flavor or oscillation fit; - an ATLAS profile-likelihood reproduction; - a Daya Bay spectral/covariance reconstruction; - a T2K internal likelihood reproduction; - a new world-average combination; - an empirical proof of .

The only admitted output is a reproducible public validation board for selected declared windows.

The public validation board has four lanes.

- Scalar-source reproduction. Published scalar values and one algebraic transform are checked against the declared CHC-PFW windows. - LEP/SLD covariance subblock. The public arXiv source of the LEP/SLD final $Z$TeXZ-resonance report is identified, and the line-shape covariance / correlation subblock with lepton universality is identified from the TeX table. - KamLAND contour membership. Public KamLAND $\Delta\chi^2$TeX\Delta\chi^2 map files are parsed, and the declared $\ttwelve$TeX\ttwelve window is tested against KamLAND-only and global public map surfaces. - T2K ROOT source support comparison. The public electronic ROOT source surface for the T2K oscillation-parameter measurement is identified and inspected for $\stwo$TeX\stwo-containing objects and contour-range membership.

The board is intentionally incomplete as a global fit. It is a public support witness for the declared windows only.

For reader reproducibility the board is recorded as a non-floating support summary rather than as a wide table:

- LEP/SLD covariance subblock: public arXiv source for the LEP/SLD final $Z$TeXZ-resonance report [citation]; covariance matrix symmetry / positive-semidefinite check and declared $m_Z,\Gamma_Z$TeXm_Z,\Gamma_Z interval inclusion pass. - KamLAND contour membership: public KamLAND $\Delta\chi^2$TeX\Delta\chi^2 map files [citation]; declared $\ttwelve$TeX\ttwelve window intersects the public 1$\sigma$TeX\sigma, 90%, and 2$\sigma$TeX\sigma surfaces. - T2K ROOT support comparison: public electronic ROOT source for T2K [citation]; public objects identified, object list inspected, and $\stwo$TeX\stwo contour-range membership supported on the declared public surface. - Scalar-source reproduction: ATLAS, LEP/SLD, Daya Bay, KamLAND, and T2K public scalar surfaces [citation]; declared scalar intervals and benchmark transforms pass.

Each lane is a public-source summary gate, not a replacement for the collaboration analyses.

The LEP/SLD final $Z$TeXZ-resonance combination provides public line-shape pseudo-observables and their correlations [citation]. The support summary identifies the public arXiv source document set and states the lepton-universality line-shape subblock from the source TeX table. The subblock uses

(\mZ,\GZ,\sigma^0_{\rm had},R_\ell,A^{0,\ell}_{\rm FB})
  =
  (91.1875,2.4952,41.540,20.767,0.0171),

with one-sigma uncertainties

(0.0021,0.0023,0.037,0.025,0.0010).

The identified correlation matrix is

\rho=

 1.000  -0.023  -0.045  0.033  0.055

 -0.023  1.000  -0.297  0.004  0.003

 -0.045  -0.297  1.000  0.183  0.006

 0.033  0.004  0.183  1.000  -0.056

 0.055  0.003  0.006  -0.056  1.000
.

The covariance matrix is then

C_{ij}=\rho_{ij}\sigma_i\sigma_j.

The gate checks symmetry, positive semidefiniteness, and inclusion of the parent-paper $\mZ$TeX\mZ and $\GZ$TeX\GZ central values in their declared intervals. The observed maximum symmetry error was $2.65\times10^{-23}$TeX2.65\times10^{-23}, and the numerical eigenvalues were positive:

(9.92\times10^{-7},\ 4.32\times10^{-6},\ 4.88\times10^{-6},\ 5.88\times10^{-4},\ 1.41\times10^{-3}).

The local label is therefore center PFW-LEP-SLD-PUBLIC-COVARIANCE-SUBBLOCK-CHECK-SATISFIED. center This is a public-table covariance subblock. It is not a LEP/SLD raw-data refit and not a full electroweak global likelihood.

The support summary identifies the public KamLAND $\Delta\chi^2$TeX\Delta\chi^2 map files and parses rows of the form

(\log_{10}\ttwelve,\log_{10}\Delta m^2,\Delta\chi^2).

For the declared CHC-PFW solar-angle window

\ttwelve\in[0.49,0.66],

we test whether the public map contains points inside the declared window below standard two-parameter contour thresholds. The KamLAND-only map has its public minimum at

\log_{10}\ttwelve=-0.26,
  \qquad
  \log_{10}\Delta m^2=-4.12,
  \qquad
  \Delta\chi^2=0,

which corresponds to $\ttwelve\simeq0.5495$TeX\ttwelve\simeq0.5495. This lies inside the declared window. The KamLAND+solar global public map has a minimum slightly below the lower declared edge, but the best point inside the declared window occurs at

\log_{10}\ttwelve=-0.30,
  \qquad
  \log_{10}\Delta m^2=-4.12,
  \qquad
  \Delta\chi^2=0.3,

which also passes the 1$\sigma$TeX\sigma, 90%, and 2$\sigma$TeX\sigma public contour thresholds used by the gate. The local label is center PFW-KAMLAND-PUBLIC-CHI2-CONTOUR-MEMBERSHIP-SATISFIED. center This is a public contour-membership check, not a new KamLAND or solar-neutrino oscillation fit.

The T2K collaboration provides public electronic contour information for the oscillation-parameter measurements reported in Ref. [citation]. The companion source summary identifies the public Bayesian and frequentist contour surfaces and records the public-source basis for the declared $\sin^2\theta_{23}$TeX\sin^2\theta_{23} window. The manuscript uses the following public contour classes:

- Bayesian ROOT-format posterior object; - Frequentist ROOT-format contour object.

The public source presents one-dimensional posterior / $\Delta\chi^2$TeX\Delta\chi^2 objects and two-dimensional contour graphs for oscillation parameters. The gate verifies that $\stwo$TeX\stwo-containing objects are present and extracts the $\stwo$TeX\stwo-$\Delta m^2$TeX\Delta m^2 frequentist normal-hierarchy contour ranges with reactor constraint. The declared CHC-PFW window

\stwo\in[0.529,0.593]

intersects the extracted contour ranges, and the extracted best-fit marker lies inside the declared interval. The local label is center PFW-T2K-ZENODO-ROOT-CONTOUR-EXTRACTION-SATISFIED. center This is a public ROOT source surface and contour-range extraction. It is not a T2K internal likelihood reproduction and not a global oscillation analysis.

The scalar-source lane retained from the VP1 support summary checks direct scalar intervals and one algebraic transform. The checked rows include

\mW=80.3665\pm0.0159\ \mathrm{GeV},

  \mZ=91.1875\pm0.0021\ \mathrm{GeV},

  \seff=0.23153\pm0.00016,

  \GZ=2.4952\pm0.0023\ \mathrm{GeV},

  \Gl=83.984\pm0.086\ \mathrm{MeV}.

For Daya Bay, the public scalar value is transformed by

\sin^2\theta_{13}
  =\frac{1-\sqrt{1-\sin^2(2\theta_{13})}}{2},

which maps $\sin^2(2\theta_{13})=0.0856\pm0.0029$TeX\sin^2(2\theta_{13})=0.0856\pm0.0029 to a one-sigma range approximately

\sin^2\theta_{13}\in[0.021121,0.022637],

inside the declared CHC-PFW interval. The retained scalar-source label is center PFW-VP1-PUBLIC-SCALAR-SOURCE-READBACK-SATISFIED. center

The combined public source basis has two declared VP1-local support-lane labels: center PFW-VP1-PUBLIC-SCALAR-AND-CONTOUR-SUPPORT-SATISFIED center for the manuscript-level scalar/contour lane, and center PFW-VP1-PUBLIC-COVARIANCE-CONTOUR-ROOT-SUPPORT-SATISFIED center for the deeper covariance/contour/ROOT support comparison. The public manuscript sequence remains CHC-PFW-VP1. The scalar/contour comparison and the deeper covariance/contour comparison are reported as distinct bounded support comparisons, not as separate parent-paper claims. Companion source summaries summarize the public input surfaces, scalar/covariance/contour comparisons, diagnostic summaries, and public-source conditions for those lanes. These classifications remain local to the declared support comparisons and do not promote the parent paper to a global fit claim.

The CHC-PFW parent paper defines a fixed admitted precision-observable window problem. This companion validates that the declared windows can be attached to public source bases: a public LEP/SLD covariance subblock, public KamLAND $\Delta\chi^2$TeX\Delta\chi^2 maps, a public T2K ROOT source, and scalar-source reproduction gates. The result materially strengthens the public source basis of CHC-PFW because it moves beyond a declared interval witness into covariance, contour, and public-source summary.

The result remains deliberately bounded. It does not construct a global electroweak / collider / flavor likelihood, does not reconstruct unpublished covariance matrices, and does not claim a new precision-data anomaly. Its value is sharper and narrower: it shows how the parent paper's declared PFW windows can be represented as bounded public companion lanes, and it identifies the point at which a stronger claim would require collaboration-level likelihoods or a new audited global-fit analysis.

The companion source summaries record the public scalar-source, covariance-subblock, contour-membership, and public contour-source support comparisons used in this companion paper, including declared source boundaries, diagnostic summaries, and the VP1-local support-lane labels. Primary public inputs should be consulted at the cited public sources. These materials are bounded public support summaries only; they are not a global electroweak, collider, or flavor likelihood and not an unpublished covariance reconstruction.

Funding and competing interests..

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