{
  "schema_version": 1,
  "purpose": "Source and inspection record for research-book Chapters 26-28. Theory and proposed verification specifications; no production compressible solver qualification.",
  "inspection_dates_utc": ["2026-10-13", "2026-10-14"],
  "inspection_method": "Public web retrieval of publisher/author/NASA records, parsed HTML and one parsed primary-paper PDF. Inspection scopes below identify what was actually consulted; opening a record does not imply full-paper inspection.",
  "material_use": {
    "activity": "Original explanatory synthesis and independently stated mathematical fixture specifications, with links and source attribution.",
    "copied_source_code": false,
    "copied_figures": false,
    "redistributed_papers": false,
    "new_solver_dependencies": [],
    "gpl_code_or_dependencies_incorporated": false,
    "license_claim": "Citation and mathematical discussion only. No blanket redistribution permission is inferred from online availability or from a project's software license.",
    "reference_scope": "The separate original Python lab and Lean contracts have their own source and qualification records. These chapters distinguish those executed bounded references from the proposed V0-V5 ladder."
  },
  "sources": [
    {
      "id": "C01",
      "title": "Navier-Stokes Equations",
      "author_or_owner": "NASA Glenn Research Center",
      "kind": "primary_institutional_educational_documentation",
      "url": "https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html",
      "inspection_scope": "Page discussion of continuity, three momentum equations, total energy, dependent fields and constitutive closure. Linked figures were not copied.",
      "supports": ["Coupled conservative mass, momentum and energy system"],
      "chapters": [26],
      "limits": "Overview rather than a numerical-method proof; displayed chapter equations are independently stated with explicit notation."
    },
    {
      "id": "C02",
      "title": "Equations, tables, and charts for compressible flow",
      "author_or_owner": "National Advisory Committee for Aeronautics",
      "year": 1953,
      "report": "NACA-TR-1135",
      "kind": "primary_report_metadata",
      "url": "https://ntrs.nasa.gov/citations/19930091059",
      "inspection_scope": "NTRS abstract, report identity, publication date, public distribution and government-work notice. Full report tables/figures were not inspected or incorporated.",
      "supports": ["Original report's declared perfect/imperfect-gas scope", "Source identity for NASA shock relations"],
      "chapters": [26, 28],
      "limits": "Normal and oblique relations were checked against the separate NASA pages C03/C04; metadata alone does not establish every report derivation."
    },
    {
      "id": "C03",
      "title": "Normal Shock Wave Equations",
      "author_or_owner": "NASA Glenn Research Center",
      "kind": "primary_institutional_educational_documentation",
      "url": "https://www.grc.nasa.gov/www/k-12/airplane/normal.html",
      "inspection_scope": "Page assumptions, conservation basis, pressure/density/Mach relations, entropy increase and stagnation-pressure loss.",
      "supports": ["Calorically perfect normal shock relations", "Shock entropy interpretation"],
      "chapters": [26],
      "limits": "One-dimensional inviscid adiabatic shock; no molecular shock thickness or viscous heating qualification."
    },
    {
      "id": "C04",
      "title": "Oblique Shock Waves",
      "author_or_owner": "NASA Glenn Research Center",
      "kind": "primary_institutional_educational_documentation",
      "url": "https://www.grc.nasa.gov/www/k-12/airplane/oblique.html",
      "inspection_scope": "Turning-angle equation, normal/tangential decomposition, post-shock property ratios and weak/strong attached-shock branches. Applet and images were not used.",
      "supports": ["V4 analytical reference and attachment/branch limitations"],
      "chapters": [28],
      "limits": "Perfect-gas inviscid attached shock; not a viscous shock-boundary-layer or detached-shock reference."
    },
    {
      "id": "C05",
      "title": "Stiffened gas approximation and GRP resolution for fluid flows of real materials",
      "authors": ["Yue Wang", "Jiequan Li"],
      "year": 2021,
      "kind": "primary_research_paper",
      "url": "https://arxiv.org/html/2108.13780",
      "identity_url": "https://arxiv.org/abs/2108.13780",
      "inspection_scope": "HTML sections 1-3: Gibbs relation, general EOS, local stiffened-gas convention, sound speed, Rankine-Hugoniot relations, rarefaction/shock functions and pressure matching. Source code and figures were not incorporated.",
      "supports": ["EOS thermodynamic derivative", "Stiffened-gas pressure and acoustic speed", "Ideal-gas limit of Riemann pressure matching"],
      "chapters": [26, 28],
      "limits": "Their local EOS approximation/GRP scheme is not implemented here. A pressure law alone does not supply a calibrated material model."
    },
    {
      "id": "C06",
      "title": "Shock compression-based equation of state for perfluorohexane",
      "authors": ["Anunay Prasanna", "Guillaume T. Bokman", "Samuele Fiorini", "Armand Sieber", "Bratislav Lukic", "Daniel Foster", "Outi Supponen"],
      "kind": "primary_experimental_research_paper",
      "url": "https://arxiv.org/html/2503.21306",
      "identity": "arXiv:2503.21306v2, observed HTML version banner 15 Aug 2025",
      "inspection_scope": "HTML introduction, stated 100-400 MPa shock-compression regime, EOS fitting methodology, material identity and discussion of calibration/uncertainty. No experimental images, tabulated fit or simulation implementation incorporated.",
      "supports": ["Need for material-specific liquid EOS calibration and validity range"],
      "chapters": [26],
      "limits": "Perfluorohexane study; no parameters transferred to water or Rheon, and no biomedical prediction is made. The page also displays a manuscript date differing from the arXiv version banner; identity is retained rather than inferring publication chronology."
    },
    {
      "id": "C07",
      "title": "On the Geometric Conservation Law for the Non Linear Frequency Domain and Time-Spectral Methods",
      "authors": ["Marc Benoit", "Siva Nadarajah"],
      "year": 2018,
      "kind": "primary_research_paper",
      "url": "https://arxiv.org/html/1804.03731",
      "identity_url": "https://arxiv.org/abs/1804.03731v1",
      "related_publisher_doi": "https://doi.org/10.1016/j.cma.2019.04.002",
      "inspection_scope": "HTML section 2.1 ALE conservative state/flux and sections 3-4 integrated face velocities, volume change and freestream-preservation protocol; arXiv identity/authors inspected.",
      "supports": ["ALE moving-face flux subtraction", "Geometric conservation law", "Need for consistent swept-face integration"],
      "chapters": [26, 28],
      "limits": "Structured hexahedral frequency-domain/time-spectral study. Chapter wall-work expressions are independently derived from its ALE balance; no claim transfers its method to arbitrary cut-cell topology."
    },
    {
      "id": "C08",
      "title": "Optimized geometrical metrics satisfying free-stream preservation",
      "authors": ["Irving Reyna Nolasco", "Lisandro Dalcin", "David C. Del Rey Fernandez", "Stefano Zampini", "Matteo Parsani"],
      "year": 2019,
      "kind": "primary_research_paper",
      "url": "https://arxiv.org/html/1911.03682",
      "identity_url": "https://arxiv.org/abs/1911.03682v2",
      "inspection_scope": "HTML metric/GCL discussion, sections 3-4 viscous/entropy discretization, section 5.1 analytical isentropic vortex and convergence-study structure. Numerical tables and figures were not copied.",
      "supports": ["Geometry and freestream compatibility", "Viscous/entropy term compatibility", "Smooth analytical vortex verification"],
      "chapters": [26, 27, 28],
      "limits": "Smooth mapped-element metric study; not evidence for Rheon polyhedral clipping, geometry assembly or an entropy-stable production method. Chapter V3 is a separately specified standard vortex fixture."
    },
    {
      "id": "C09",
      "title": "Outflow Positivity Limiting for Hyperbolic Conservation Laws. Part I: Framework and Recipe",
      "authors": ["Evan Alexander Johnson", "James A. Rossmanith"],
      "year": 2012,
      "kind": "primary_research_paper",
      "url": "https://arxiv.org/pdf/1212.4695",
      "identity_url": "https://arxiv.org/abs/1212.4695v1",
      "inspection_scope": "Parsed 32-page PDF, especially introduction assumptions, finite-volume balance, convex positive-state framework, reconstructed-node limiting and outflow/CFL conditions. No figures or implementation copied.",
      "supports": ["Conservation and positivity are separate conditions", "Average-preserving convex scaling", "Flux/quadrature/CFL/stage requirements"],
      "chapters": [27],
      "limits": "Does not furnish a positivity theorem for the separately implemented LLF lab, arbitrary EOS, moving cut cells or newly chosen quadrature."
    },
    {
      "id": "C10",
      "title": "A Cure for numerical shock instability in HLLC Riemann solver using antidiffusion control",
      "authors": ["Simon Sangeeth", "J. C. Mandal"],
      "year": 2018,
      "kind": "primary_research_paper",
      "url": "https://arxiv.org/html/1803.04954",
      "identity_url": "https://arxiv.org/abs/1803.04954",
      "inspection_scope": "HTML sections 4.1-4.2 HLL/HLLE/HLLC construction and sections 5-7 shock-instability analysis/antidiffusion control; abstract/author identity checked. Figures and algorithms not incorporated.",
      "supports": ["HLL and HLLC wave structures", "Contact/shear resolution versus multidimensional shock instability"],
      "chapters": [27],
      "limits": "Their original contribution is instability analysis and control; foundational solver derivations are discussed within the paper. No HLLC-ADC implementation or universal shock-stability guarantee is claimed."
    },
    {
      "id": "C11",
      "title": "All speed scheme for the low mach number limit of the Isentropic Euler equation",
      "authors": ["Pierre Degond", "Min Tang"],
      "year": 2009,
      "kind": "primary_research_paper_abstract",
      "url": "https://arxiv.org/abs/0908.1929",
      "identity_url": "https://arxiv.org/abs/0908.1929v1",
      "inspection_scope": "Author record and abstract: first-order LLF framework, semi-implicit stiff/nonstiff split, low-Mach difficulties and intended incompressible limit.",
      "supports": ["LLF-based method exists with an additional all-speed semi-implicit treatment"],
      "chapters": [27],
      "limits": "Full paper was not inspected. This citation is limited to the stated method scope, not a theorem for the explicit total-energy LLF flux."
    },
    {
      "id": "C12",
      "title": "A Weakly Asymptotic Preserving Low Mach Number Scheme for the Euler Equations of Gas Dynamics",
      "authors": ["Sebastian Noelle", "Georgij Binev", "K. R. Arun", "Maria Lukacova-Medvidova", "Claus-Dieter Munz"],
      "year": 2014,
      "kind": "primary_research_paper",
      "url": "https://arxiv.org/html/1412.1606",
      "identity_url": "https://arxiv.org/abs/1412.1606",
      "inspection_scope": "HTML introduction and sections 3-6 discussion of physical/pseudo-time, stiff acoustic scale, implicit-explicit treatment, asymptotic consistency and stabilization-induced limitations.",
      "supports": ["Low-Mach stiffness", "CFL independence does not establish asymptotic stability or uniform accuracy"],
      "chapters": [27],
      "limits": "The chapter does not implement their scheme or claim an all-speed result."
    },
    {
      "id": "C13",
      "title": "Wind-US User's Guide - Boundary Conditions",
      "author_or_owner": "NASA Glenn Research Center / NPARC Alliance",
      "kind": "primary_implementation_documentation",
      "url": "https://www.grc.nasa.gov/www/winddocs/user/bc.html",
      "inspection_scope": "Inviscid/viscous/moving-wall descriptions and flow-interface freestream/outflow characteristic treatment, including constant-pressure reflection limitation.",
      "supports": ["Incoming-characteristic boundary data", "Distinct slip/no-slip/thermal conditions", "Outlet reflection caveat"],
      "chapters": [28],
      "limits": "Wind-US implementation details do not define Rheon BCs. Generic characteristic counts and wall fluxes are independently derived."
    },
    {
      "id": "C14",
      "title": "Wind-US User's Guide - Keyword Reference, TURBULENCE",
      "author_or_owner": "NASA Glenn Research Center / NPARC Alliance",
      "kind": "primary_implementation_documentation",
      "url": "https://www.grc.nasa.gov/www/winddocs/user/keywords/turbulence.html",
      "inspection_scope": "Separate laminar, RANS, LES and hybrid choices, model-variant/coefficient options, compressibility and transition modelling limitations.",
      "supports": ["Turbulence closure is separate from Euler/NS equations", "Closure variant and parameter documentation"],
      "chapters": [28],
      "limits": "No closure is incorporated and no NASA recommendation is adopted as a universal Rheon default. Wall-resolution discussion is a stated research requirement."
    },
    {
      "id": "C15",
      "title": "Verification Assessment",
      "author_or_owner": "NASA Glenn Research Center / NPARC Alliance",
      "kind": "primary_institutional_method_documentation",
      "url": "https://www.grc.nasa.gov/www/wind/valid/tutorial/verassess.html",
      "inspection_scope": "Code versus calculation verification and error-assessment discussion.",
      "supports": ["Verification ladder and claim/evidence separation"],
      "chapters": [28],
      "limits": "General assessment guidance; no fixed universal error thresholds adopted."
    },
    {
      "id": "C16",
      "title": "Validation Assessment",
      "author_or_owner": "NASA Glenn Research Center / NPARC Alliance",
      "kind": "primary_institutional_method_documentation",
      "url": "https://www.grc.nasa.gov/www/wind/valid/tutorial/valassess.html",
      "inspection_scope": "Iterative convergence, solution consistency, grid convergence and physical comparison requirements.",
      "supports": ["Physical validation requires independent real-world comparisons", "Convergence and conservation assessment"],
      "chapters": [28],
      "limits": "Proposed analytical cases are not presented as experimental physical validation."
    },
    {
      "id": "C17",
      "title": "Laminar Flat Plate: Study #1",
      "author_or_owner": "John W. Slater / NASA Glenn Research Center / NPARC Alliance",
      "kind": "primary_numerical_validation_archive_description",
      "url": "https://www.grc.nasa.gov/www/wind/valid/fplam/fplam01/fplam01.html",
      "inspection_scope": "Case introduction, grid 51x37, Mach/pressure/temperature/length/Reynolds conditions, boundary assignment, laminar mode, steady strategy and Blasius comparison. Archive programs, raw data and plots were not downloaded or incorporated.",
      "supports": ["V5 reproduction seed and approximation limits"],
      "chapters": [28],
      "limits": "Low-Mach incompressible-approximation comparison; no high-Mach thermal or turbulence qualification. V5 proposes independent reference solution and fresh refinement."
    },
    {
      "id": "C18",
      "title": "Approximate solvers for the Euler equations",
      "authors": ["David I. Ketcheson", "Randall J. LeVeque", "Mauricio J. del Razo"],
      "kind": "author_educational_exposition_secondary_to_Roe_and_Einfeldt",
      "url": "https://www.clawpack.org/riemann_book/html/Euler_approximate.html",
      "inspection_scope": "Roe flux-difference/eigenstructure explanation, transonic-rarefaction entropy fix and negative-density counterexample, HLLE comparison. Embedded source code was neither adapted nor incorporated.",
      "supports": ["Illustrative Roe rarefaction and positivity failure modes"],
      "chapters": [27],
      "limits": "This is author-written mathematical exposition, not Roe's original research paper. Its one-interface examples do not qualify a complete numerical scheme."
    },
    {
      "id": "C19",
      "title": "On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes",
      "authors": ["Xiangxiong Zhang", "Chi-Wang Shu"],
      "year": 2010,
      "journal": "Journal of Computational Physics 229, 8918-8934",
      "kind": "primary_author_bibliographic_record",
      "url": "https://www.dam.brown.edu/people/shu/pub.html",
      "inspection_scope": "Author's publication list entry 216 establishes title, authors, venue/year/pages. Publisher full text was not accessible through the attempted link.",
      "supports": ["Identity of the original Euler positivity publication"],
      "chapters": [27],
      "limits": "No uninspected theorem is attributed to this record; inspected primary framework C09 supplies the technical discussion."
    },
    {
      "id": "C20",
      "title": "On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws",
      "authors": ["Amiram Harten", "Peter D. Lax", "Bram van Leer"],
      "year": 1983,
      "journal": "SIAM Review 25(1), 35-61",
      "kind": "primary_publisher_metadata_and_abstract",
      "url": "https://epubs.siam.org/doi/10.1137/1025002",
      "doi": "https://doi.org/10.1137/1025002",
      "inspection_scope": "Publisher authors/title/issue/abstract and bibliography identifying Roe's original 1981 paper; full text requires access and was not inspected.",
      "supports": ["Foundational HLL source identity and approximate-Riemann-method context"],
      "chapters": [27],
      "limits": "Included as further primary reading. Explicit HLL/HLLC formulas in Chapter 27 are independently stated and checked against inspected C10."
    }
  ],
  "retrieval_notes": [
    "Several broad search queries returned poor nontechnical matches; none of those results were used as technical evidence.",
    "NTRS API shell retrieval was unavailable (network tunnel 403); the official NTRS report page was successfully inspected with the web tool.",
    "Direct DOI retrieval of Roe 1981, Sod 1978, Poinsot-Lele 1992 and Toro-Spruce-Speares 1994 was unavailable; no full-text inspection of those papers is claimed.",
    "NASA Turbulence Modeling Resource's historical flatplate URL redirected to a general NASA page; it is not used as a flat-plate oracle. The separate NASA Glenn laminar study C17 was successfully inspected.",
    "No remaining access failure blocks this original chapter synthesis. Further detailed implementation work should inspect the exact theorem and primary-paper assumptions for its selected method."
  ]
}