From Executable Standard-Model Structure to Cosmological H/He Plasma Response: Derivability, Constrained Function-Space Closure, and the Execution-Authority Boundary

This work presents GCFT-0672, a sealed derivability and execution-authority study connecting an executable ordinary-Standard-Model starting point to the construction of a cosmological hydrogen-helium plasma response over the domain 0≤z≤250 \le z \le 25. The central question is not whether the Standard Model permits an ionized H/He plasma, but how far one can proceed from executable particle, charge, current, and interaction semantics toward a source-complete cosmological thermochemical system before additional atomic, many-body, transport, radiation, statistical, and astrophysical authority must be introduced. The study separates several layers that are frequently compressed together in cosmological plasma modelling: elementary particle and current definitions; atomic and bound-state reduction; evaluated reaction and transport data; radiation and source histories; species-population closure; multiphase and covariance structure; interface-work terms; and numerical admission of versioned scientific data. Rather than treating implementation defaults or convenient public tables as if they followed uniquely from the underlying field theory, GCFT-0672 applies a fail-closed authority model in which every transition is classified according to whether it is structurally derivable, requires standard atomic or many-body completion, depends on evaluated data, requires standard-astrophysics conditioning, or would introduce genuinely new GCFT-specific dynamics. Starting from executable ordinary-Standard-Model semantics, the programme establishes a conserved charge-resolved six-species cosmological plasma representation containing electrons, HI, HII, HeI, HeII, and HeIII. Hydrogen-number, helium-number, and charge conservation define the admissible population manifold. The work shows explicitly that a total free-electron history does not uniquely determine the full six-species split and that a bulk baryon temperature does not automatically determine independent species temperatures. Population and thermal histories therefore require additional conditioning and transport authority rather than being silently promoted from underdetermined aggregate variables. The thermochemical system is organized as a source-complete operator structure linking species and radiation states to reaction, transport, charge, energy, and statistical background quantities, and ultimately to later response objects. The programme distinguishes background closure from response-kernel closure and preserves the requirement that later response quantities be derived from the same underlying functional structure rather than introduced as unrelated phenomenological laws. No numerical C1 or C2 system is constructed in this work; the purpose is to determine the exact conditions under which such construction would become scientifically authorized. A central result is the identification of the joint sufficient-statistic structure required for nonlinear cosmological thermochemistry. Homogeneous means are insufficient when reaction, heating, transport, interface-work, or other nonlinear operators act on correlated multiphase fields. The closure interface therefore requires joint conditional moments and measures involving radiation, species, temperature, source, and interface variables. This statistical closure is finite at the operator level in the sense that only the statistics entering the sealed thermochemical operators are required, but those quantities are not automatically supplied by a representative cosmological history or a homogeneous background model. The remaining standard-astrophysics freedom is formalized as a physically constrained function space CASTROC_{\mathrm{ASTRO}}, subject to endpoint, positivity, conservation, causality, finite-energy, and domain constraints. A frozen operator map TT sends these admissible histories into the thermochemical operator set. The analysis establishes active underdetermination: infinitely many admissible function perturbations exist, and at least some of them alter one or more thermochemical operators. At the same time, exact null directions also exist—functional variations that are invisible to every frozen operator. The execution-relevant space is therefore represented by the quotient CACTIVE=CASTRO/ker⁡(T)C_{\mathrm{ACTIVE}} = C_{\mathrm{ASTRO}} / \ker(T). This distinction prevents both overstatements: the remaining freedom is neither uniquely fixed nor arbitrary. It is physically constrained standard-astrophysics freedom, not a new GCFT field, coupling, action term, or residual dynamical degree of freedom. The programme isolates a minimal sufficient set of six execution-critical authority objects. These are: A01 — Joint conditional sufficient statistics: quantitative radiation/species/temperature/source covariances and conditional moments over the required high-redshift domain. A02 — Absorbed-electron spectrum function: a phase-conditioned mapping from radiation and absorber states to the spectrum of primary energetic electrons. A03 — Secondary-deposition table or function: version-frozen deposition fractions for heating, HI ionization, HeI ionization, HeII ionization, and excitation over the required electron-energy and ionization-state domain. A04 — Versioned H/He rate and multilevel-reduction package: a domain-complete, machine-readable reaction and multilevel authority set with explicit level and recombination semantics. A05 — Direct interface-work sufficient statistic: the quantitative joint geometry, velocity, pressure, stress, and flux information required to evaluate the interface-work term. A06 — Versioned pair-exchange function suite: complete momentum- and energy-transfer functions for the required charged-charged, charged-neutral, and neutral-neutral species pairs, including the relevant elastic, inelastic, and charge-exchange structure. These six objects are sufficient in the operational sense that, once all are supplied and admitted under the frozen execution schema, every operator-active thermochemical input becomes numerically defined. They are also necessary under the sealed dependency structure because removing any one leaves at least one execution-critical operator undefined. None of the six presently satisfies the full admission criteria simultaneously: immutable/version-frozen identity, complete relevant state-domain coverage, machine-readable representation, frozen interpolation semantics, uncertainty or documented accuracy information, reproducible provenance, and deterministic validation. The resulting no-go statement is deliberately narrow. Under the sealed GCFT-0672 authority model, the ordinary-Standard-Model cosmological H/He plasma is structurally derivable but not presently numerically executable over 0≤z≤250 \le z \le 25 because the minimal sufficient authority set is not simultaneously available as version-frozen, domain-complete, machine-readable, and reproducible input. This is a current authority and data-closure boundary, not a claim of fundamental physical impossibility, not evidence that the Standard Model fails to describe the relevant atomic or plasma physics, and not evidence that new GCFT dynamics are required. The residual closure freedom is entirely assigned to standard astrophysical conditioning, evaluated atomic and plasma data, radiation/source mapping, and boundary/interface statistics. The resulting residual GCFT functional degree-of-freedom count is zero, and the programme reports NEW_GCFT_DYNAMICS_REQUIRED = NO. In particular, the study does not introduce an additional GCFT field, portal term, coupling, source law, or free response mode to compensate for unavailable ordinary-physics authority. The study also evaluates the role of large cosmological simulation products as prospective closure authority. THESAN data products were examined during the authority-resolution programme, but full-snapshot acquisition was ultimately classified as optional conditioning rather than a necessary ingredient of the final structural result. The programme therefore concludes that large multi-terabyte acquisition is not presently required for GCFT-0672 closure. The sealed resource result is RAW_THESAN_NECESSITY = OPTIONAL_CONDITIONING, EXTERNAL_STORAGE_DEPENDENCY = NOT_REQUIRED, and SCIENTIFIC_PAYLOAD_ACQUIRED_BYTES = 0. The structural closure was achieved without acquiring large scientific payloads. GCFT-0672 comprises twenty-one sealed scientific stages that progressively separate Standard-Model structure, atomic derivability, population conditioning, multispecies thermal exchange, neutral collision authority, photoheating and radiation closure, high-redshift patchiness, statistical multiphase closure, function-space underdetermination, representative conditioning, and residual execution authority. The final programme classification is CLOSED_WITH_MIXED_EXECUTION_DEPENDENCY: the derivability map, thermochemical operator structure, sufficient-statistic interface, active-function-space theorem, null-direction quotient, and minimal execution-authority set are closed, while numerical thermochemical execution remains deferred. No thermochemical numerical execution is performed in this work. C1 is not constructed, C2 is not executed, portal dynamics are not run, nonzero-ϵ\epsilon calculations are not performed, no observational likelihood is evaluated, and no GCFT route is selected. These non-executions are deliberate fail-closed governance results rather than omitted successful calculations. Likewise, GCFT-0672 does not satisfy the numerical return condition required to reopen GCFT-0671; the predecessor remains closed pending future admission of the necessary plasma-execution authority. The release includes the academic manuscript, sealed claim hierarchy, claim-to-evidence traceability, execution-blocker matrices, return-condition definitions, publication tables, vector figures, reproducibility material, deterministic assembly records, and provenance for the ext