R113 → R179

Methodological consolidation, qualification governance, controlled review and final integrity approval

Development from R113 to the file-level confirmed R179-L15 active master through mathematical, computational, scientific-review, research-extension, visual-governance, production-integrity and revision-identity governance.

Principal developments

• The representation hierarchy was extended to include mixed discrete–continuous heat–temperature configurations, while preserving discrete, piecewise-isothermal and continuous formulations as representations of the same governing Clausius equality.
• Configuration-dependent closed-form solutions, Riemann partition and sample-point notation, scalar and coupled numerical formulations, and the distinction between exact discrete structures and discretized continuous trajectories were made explicit.
• Solver convergence was separated from equality closure, First-Law closure, domain and constitutive admissibility, cycle-architecture qualification and final benchmark qualification. A converged numerical solution is therefore not automatically a qualified thermodynamic benchmark.
• Residual, constraint, dataset and unresolved-variable terminology was consolidated. Zero Carnot or Clausius residual now establishes equality closure only and does not by itself establish reversibility, uniqueness, feasibility or a complete cycle architecture.
• The cycle-classification and qualification hierarchy was strengthened through coordinated Figure 1a/1b routing and clearer separation of performance formulas, reversible-cycle equalities and complete process-specific benchmark construction.
• Reviewer and evidence governance was expanded to distinguish correctness, completeness, novelty, reproducibility, pedagogical or engineering usefulness and validation status. Contextual literature, bounded textbook evidence and representative assessments were kept separate from independent validation.
• Existing solid-state and distributed thermo-fluid research extensions were reorganized under tighter claim boundaries. Solid-body tidal dissipation was added, while the qualified thermoelastic heat-conduction pathway was formalized visually in Figure 23.
• The Publisher’s Pitch, Abstract, Executive Summary, Contents and education/publication hierarchy were reorganized. Figure provenance, source attribution, authorship, Unified Energy B.V. rights and controlled-review circulation were aligned across the document.
• R178 completed the final document-integrity gate by verifying 81 formula labels, 26 figures, 8 tables, 350 mathematical objects and 34 media assets, together with bookmarks, internal references, Word mechanics and Acrobat-compatible PDF structure. One obsolete section reference was corrected without scientific or numerical change and without renumbering.
• R179 added an explicit reader-facing distinction between controlled R content revisions and L layout and production editions, without changing the scientific meaning, equations, numerical values, claims, qualification boundaries or source basis.