CMB-VP0: Primary-Sector Linked-Ruler Public Gates in CHC

The CMB paper declares a restricted primary-sector object: a last-accessibility width envelope, a fixed-kernel acoustic-angle comparison, a linked-ruler relation between the recombination ruler and the drag-era ruler, and an external later-transfer consistency layer. The present companion note implements those declared gates on public source surfaces. It does not infer a new background expansion, does not re-run a full CMB likelihood, and does not construct a complete polarization or lensing transfer theory.

The public result is intentionally named a primary diagnostic partial. The word ``partial'' marks that the companion record evaluates the declared public surfaces and declared algebraic gates without attempting a full CMB parameter fit.

The companion record uses public source surfaces from Planck PR4/NPIPE, ACT DR6, and DESI DR2. Planck PR4 is the public NPIPE reprocessing of LFI and HFI data using a common pipeline, with public full-sky maps, half-ring maps, low-resolution maps, effective beams, and single-channel maps [citation]. The Planck 2018 parameter paper supplies the acoustic-angle benchmark comparison used here, reporting the angular acoustic scale at high precision [citation]. ACT DR6.02 provides maps, beams, passbands, NILC products, PSPIPE products, likelihood-related material, and public MCMC chains [citation]. DESI DR2 provides cosmology chains, posterior maximization products, and BAO supplementary data products, including a Zenodo archive for reproducing numerical results in the DR2 BAO paper [citation].

The evidence record identifies the required public surfaces and their public-source basis. It also identifies the DESI DR2 BAO and ACT DR6 LCDM source surfaces through cited public references and companion statements. Large public inputs are represented in the manuscript only by source name, diagnostic role, and provenance statement.

center

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

center

The ledger is a public-source basis board. It is not a claim that the companion record performs a full CMB parameter inference. Public-source summaries are used only to identify source surfaces and result summaries.

The companion record follows five bounded steps.

- Public-source materialization: read the Planck PR4/NPIPE, ACT DR6.02, DESI DR2 release, and DESI DR2 BAO supplementary surfaces named in reference. - Public-source check: record the declared public-source basis and large-source resource status where applicable. - Gate computation: evaluate the width, acoustic-angle, linked-ruler, and later-transfer diagnostic rules from the declared gate configuration. - Classification assignment: assign only the four declared sub-gate labels and the combined CMB-VP0-PRIMARY-DIAGNOSTIC-PARTIAL classification. - Non-claim confirmation: verify that the result remains a restricted primary-sector diagnostic and does not become a likelihood closure, Boltzmann replacement, drag-transfer inference, late-transfer theorem, or DE/LBD/DM closure.

G2: width gate For a representative peak window, retained oscillatory fraction one half, acoustic peak scale $\ell_{\rm peak}=2500$TeX\ell_{\rm peak}=2500, and $\bar c\in[0.45,0.47]$TeX\bar c\in[0.45,0.47], the companion record evaluates the temperature-sector width envelope. The comparison is

\theta_* = 0.010411,\qquad
\sigma_*/r_* \in [0.0962492636,0.1005270086].

This lies within the declared expected range $[0.096,0.100]$TeX[0.096,0.100] under tolerance $0.005$TeX0.005. The assigned label is

\mathrm{CMB\text{-}WIDTH\text{-}GATE\text{-}SATISFIED}.

G3: acoustic-angle gate The acoustic-angle gate uses the benchmark comparison

100\theta_* = 1.0411,\qquad \sigma(100\theta_*)=0.0003,

with $\alpha_*=0.0499$TeX\alpha_*=0.0499 and declared $|\epsH|\le 0.012$TeX|\epsH|\le 0.012. The assigned label is

\mathrm{CMB\text{-}ACOUSTIC\text{-}ANGLE\text{-}GATE\text{-}SATISFIED}.

This is a declared benchmark comparison, not a full CMB likelihood evaluation.

G4: linked-ruler gate The linked-ruler gate evaluates the fixed-kernel relation between the recombination ruler and the drag-era ruler. The companion record uses

\alpha_*=0.0499,
\qquad
\alpha_{\rm d}=0.0951,
\qquad
|\epsH|\le 0.012,

and returns

|\delta\ln(r_{\rm d}/r_*)|\le 2.712\times10^{-4},

against a declared expected bound $2.7\times10^{-4}$TeX2.7\times10^{-4}. The assigned label is

\mathrm{CMB\text{-}LINKED\text{-}RULER\text{-}GATE\text{-}SATISFIED}.

This is not a complete drag-transfer inference.

G5: later-transfer diagnostic The later-transfer gate verifies the presence of declared external consistency surfaces. The companion record lists Planck PR4 and ACT DR6 landing surfaces as required-present surfaces, and lists ACT lensing derived products and the ACT DR6 chain readme as optional later-transfer source bases. The assigned label is

\mathrm{CMB\text{-}LATER\text{-}TRANSFER\text{-}DIAGNOSTIC\text{-}CHECK\text{-}SATISFIED}.

This is a source-basis diagnostic. It is not a late-transfer theorem.

center

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

center

The combined classification is

\boxed{\mathrm{CMB\text{-}VP0\text{-}PRIMARY\text{-}DIAGNOSTIC\text{-}PARTIAL}}.

center

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

center

Failure of any declared sub-gate would have excluded the corresponding primary-sector family on the declared window. Passage of the present gates means only that the declared restricted primary-sector diagnostics survive the public-source comparison.

The public-source summary is reproducible from the declared source surfaces and diagnostic summaries stated above. The principal diagnostic-summary groups are: center

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

center The companion source summary identifies the public Planck PR4/NPIPE, ACT DR6, and DESI DR2 source surfaces, the declared diagnostic summaries, and the public-source boundary notes used for the width, acoustic-angle, linked-ruler, and later-transfer gates. The scientific classification is read only from those declared public-source summaries and result summaries.

CMB-VP0 supplies the public companion diagnostic record for the CMB primary-sector gate structure. Planck PR4/NPIPE, ACT DR6, and DESI DR2 products supply the external source surfaces; the companion record evaluates the width, acoustic-angle, linked-ruler, and later-transfer diagnostic gates; and all four declared gates return pass labels under the declared restrictions. The declared companion diagnostic reading is CMB-VP0-PRIMARY-DIAGNOSTIC-PARTIAL. It is a bounded companion diagnostic result, not a full cosmological parameter fit.

Data and code availability..

This companion manuscript uses public cosmic-microwave-background data products, reference quantities, and cited public references and companion statements as described in the text. 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.