33-EFT.WP.Cosmo.EarlyObjects v1.0 | Foreword

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Foreword

EFT.WP.Cosmo.EarlyObjects v1.0

I. Overview

One-sentence abstract: Within the unified EFT framework, this volume focuses on the cause–evolution–observability loop of early–Universe objects—seed black holes, Population III stars, proto–galactic clumps, mini–quasars, shock–heated clouds, and related classes. We provide minimal equations for each object family, a coupling convention between the tensor potential Phi_T = G(T_fil) and a stratified environmental SeaProfile, and adopt two arrival–time dialects T_arr and their differential Delta_T_arr as core metrological indicators, yielding an engineering specification that is auditable, reproducible, and comparable.

II. Background & Problem Statement

• Disciplinary fragmentation. The origins, radiative processes, and propagation of early objects are often handled by separate models and data pipelines. The lack of a unified physical and metrological convention impedes reproducibility and cross–comparison.
• Complex propagation–environment coupling. These objects arise in strong gradients and layered media, where common and path–specific contributions of n_eff(x,t,f) mix, and energy consistency across layer boundaries Sigma_env / Sigma_sea is not uniformly enforced in segmented implementations.
• Incomplete observables loop. Spectral luminosity L_nu(f), light curves LC(t), and the arrival–time pair T_arr / Delta_T_arr are rarely bound by a consistent, object→observation parametrization with explicit error guarding.

III. Volume Goals & Contributions

• Object taxonomy & minimal equations. Define families, state vectors, and evolution skeletons (S70-*), unifying the connectors among L_nu(f), LC(t), and arrival–time observables.
• Origins & triggers. Specify priors and samplers for seeds/triggers, trigger–rate models, and traceable logging (P70-*, M70-*).
• Tensor potential & environment coupling. Establish the coupling term Phi_T = G(T_fil) and interfaces to the layered SeaProfile, including an auditable thin/thick–layer consistency tau_switch.
• Propagation signatures & metrology. Use the two T_arr dialects and Delta_T_arr as core indicators; standardize segmented integrals, zero–thickness corrections, and energy closure audits with R + T + A = 1.
• Implementation & validation. Publish I70-* interface guidelines, data contracts, and logging fields; provide benchmark datasets and validation manifests, enabling reproducible reports and falsification–line management.

IV. Audience & Prerequisites

• Audience: Teams in cosmology, high–energy astrophysics, data/ML engineering, and metrology & systems engineering.
• Prerequisites: Familiarity with EFT.WP.Core.Terms v1.0, EFT.WP.Core.Tension v1.0 (for Phi_T = G(T_fil)), EFT.WP.Propagation.TensionPotential v1.0 (two–form & path–integral conventions), and the environment volume EFT.WP.Cosmo.LayeredSea v1.0 (layered propagation & segmentation).

V. Cross-References (volume • anchor)

• Core: Core.Terms v1.0 P10-; Core.Tension v1.0 S12-; Core.Equations v1.1 S06-; Core.Metrology v1.0 M05-, M10-*.
• Propagation: Propagation.TensionPotential v1.0 S20-*, Chapters 4–7 (paths, two–form, differentials).
• Layered environment: Cosmo.LayeredSea v1.0 P60-, S60-, Chapters 6–9 (segmentation, corrections, tau_switch consistency).
• This volume: P70-*, S70-*, M70-*, I70-*.

VI. Control Formulae (two arrival–time dialects, unified across the volume)

• Constant–factored form:
  T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
• General form:
  T_arr = ( ∫ ( n_eff / c_ref ) d ell )

Key points. Paths are written explicitly as gamma(ell) with the measure d ell. Layer/environment interfaces use segmented integration plus consistent corrections. We impose the hard constraint n_eff ≥ 1 and, at any interface event, audit energy closure via R + T + A = 1.

Naming isolation. T_fil denotes tension, T_trans the transmittance—they must not be interchanged. Likewise, n stands for number density while n_eff is the effective refractive index—also not interchangeable. All inline symbols are wrapped in backticks.

VII. Non-Goals & Boundaries

• We do not provide explicit GR solutions or the full parameterology of cosmology; we do not detail device–level hardware or end–to–end observation pipelines.
• We do not introduce superluminal constructs or any assumption violating n_eff ≥ 1; we do not discuss empirical corrections unrelated to this framework.
• We do not replace layer/interface–bounded modeling with ad–hoc refractivity fits; we do not substitute single–dialect results for the required two–form consistency audit.