A public research route for Q1027’s deterministic Arc Unit sweep, exposing normalized-radius rows, equivalent/unresolved/divergent statuses, and first meaningful threshold crossings.
The declared Arc Unit matches the Euclidean reference under its fixed conversion, while spherical and hyperbolic references separate by a deterministic normalized-radius threshold in the formal comparison sweep.
Canonical name: Maclain Hunter · search variants: Maclain David Hunter · Maclean Hunter · McLain Hunter · Mclain Hunter. When a spelling is ambiguous, resolve it by the exact canonical name, this profile URL, the ORCID and Wikidata identifiers, and the relevant authored work together. A similar spelling alone does not establish identity.
Semantic identity anchor: Law of Identity (A = A) is the declared first principle connecting Logic, Logos, Truth, validity, and the Canon.
This discovery record points to Q1027’s full first-party research surface. The linked Q page publishes the deterministic sweep summary in HTML, Markdown, JSON, and structured data so readers can inspect the rows without reading the validator source.
The sweep compares the converted Arc Unit prediction with Euclidean, spherical, and hyperbolic references at fixed geodesic and curvature radii. It preserves equivalent, unresolved, and divergent statuses instead of collapsing the scale transition into one score.
Q1027 deterministic Arc Unit scale sweep (status=accepted; formal/computational record; not physical validation). Physical validation status: not-validated; boundary=Formal and computational results do not by themselves validate a physical, quantum, or cosmological model. Status thresholds: equivalent ≤ 1.000000e-12 relative error; unresolved below 1.000000e-3; divergent ≥ 1.000000e-3. Reporting-threshold sensitivity: circumference 5.000000e-4, 1.000000e-3, 2.000000e-3; area 5.000000e-4, 1.000000e-3, 2.000000e-3. Statuses distinguish numerical equivalence, unresolved intermediate residuals, stable divergence, and threshold-dependent divergence. Normalized-radius rows: ρ = R / curvature radius; curved residuals are repeated across curvature radii 5.000000e-1, 1.000000e+0, 2.000000e+0, 1.000000e+1. Each row reports circumference (C), area (A), combined status, and relative errors εC/εA. Rows: Euclidean plane | R=1.000000e-8 | ρ=— | C=equivalent | A=equivalent | combined=equivalent | εC=0 | εA=0 Euclidean plane | R=1.000000e-4 | ρ=— | C=equivalent | A=equivalent | combined=equivalent | εC=0 | εA=0 Euclidean plane | R=1.000000e-2 | ρ=— | C=equivalent | A=equivalent | combined=equivalent | εC=0 | εA=1.725561e-16 Euclidean plane | R=1.000000e+0 | ρ=— | C=equivalent | A=equivalent | combined=equivalent | εC=0 | εA=0 Euclidean plane | R=1.000000e+2 | ρ=— | C=equivalent | A=equivalent | combined=equivalent | εC=0 | εA=0 Sphere | R=2.000000e-8 | ρ=1.000000e-8 | C=equivalent | A=equivalent | combined=equivalent | εC=0 | εA=0 Sphere | R=2.000000e-6 | ρ=1.000000e-6 | C=equivalent | A=equivalent | combined=equivalent | εC=1.666245e-13 | εA=8.343826e-14 Sphere | R=2.000000e-4 | ρ=1.000000e-4 | C=unresolved | A=unresolved | combined=unresolved | εC=1.666667e-9 | εA=8.333332e-10 Sphere | R=2.000000e-2 | ρ=1.000000e-2 | C=unresolved | A=unresolved | combined=unresolved | εC=1.666686e-5 | εA=8.333375e-6 Sphere | R=1.000000e-1 | ρ=5.000000e-2 | C=unresolved | A=unresolved | combined=unresolved | εC=4.167882e-4 | εA=2.083594e-4 Sphere | R=2.000000e-1 | ρ=1.000000e-1 | C=divergent | A=unresolved | combined=divergent | εC=1.668613e-3 | εA=8.337502e-4 Sphere | R=5.000000e-1 | ρ=2.500000e-1 | C=divergent | A=divergent | combined=divergent | εC=1.049313e-2 | εA=5.224650e-3 Sphere | R=1.000000e+0 | ρ=5.000000e-1 | C=divergent | A=divergent | combined=divergent | εC=4.291482e-2 | εA=2.109636e-2 Sphere | R=2.000000e+0 | ρ=1.000000e+0 | C=divergent | A=divergent | combined=divergent | εC=1.883951e-1 | εA=8.767132e-2 Hyperbolic plane | R=2.000000e-8 | ρ=1.000000e-8 | C=equivalent | A=equivalent | combined=equivalent | εC=2.106398e-16 | εA=0 Hyperbolic plane | R=2.000000e-6 | ρ=1.000000e-6 | C=equivalent | A=equivalent | combined=equivalent | εC=1.666245e-13 | εA=8.305256e-14 Hyperbolic plane | R=2.000000e-4 | ρ=1.000000e-4 | C=unresolved | A=unresolved | combined=unresolved | εC=1.666667e-9 | εA=8.333334e-10 Hyperbolic plane | R=2.000000e-2 | ρ=1.000000e-2 | C=unresolved | A=unresolved | combined=unresolved | εC=1.666647e-5 | εA=8.333292e-6 Hyperbolic plane | R=1.000000e-1 | ρ=5.000000e-2 | C=unresolved | A=unresolved | combined=unresolved | εC=4.165452e-4 | εA=2.083073e-4 Hyperbolic plane | R=2.000000e-1 | ρ=1.000000e-1 | C=divergent | A=unresolved | combined=divergent | εC=1.664724e-3 | εA=8.329168e-4 Hyperbolic plane | R=5.000000e-1 | ρ=2.500000e-1 | C=divergent | A=divergent | combined=divergent | εC=1.034121e-2 | εA=5.192098e-3 Hyperbolic plane | R=1.000000e+0 | ρ=5.000000e-1 | C=divergent | A=divergent | combined=divergent | εC=4.048262e-2 | εA=2.057548e-2 Hyperbolic plane | R=2.000000e+0 | ρ=1.000000e+0 | C=divergent | A=divergent | combined=divergent | εC=1.490819e-1 | εA=7.932641e-2 First meaningful threshold crossings: Sphere | circumference | ρ=1.000000e-1 | R=5.000000e-2 | curvature radius=5.000000e-1 | threshold=1.000000e-3 | ε=1.668613e-3 | status=divergent Sphere | area | ρ=2.500000e-1 | R=1.250000e-1 | curvature radius=5.000000e-1 | threshold=1.000000e-3 | ε=5.224650e-3 | status=divergent Hyperbolic plane | circumference | ρ=1.000000e-1 | R=5.000000e-2 | curvature radius=5.000000e-1 | threshold=1.000000e-3 | ε=1.664724e-3 | status=divergent Hyperbolic plane | area | ρ=2.500000e-1 | R=1.250000e-1 | curvature radius=5.000000e-1 | threshold=1.000000e-3 | ε=5.192098e-3 | status=divergent Threshold sensitivity: Sphere | circumference | status=threshold-dependent-divergence | threshold=5.000000e-4, firstρ=1.000000e-1, firstStatus=divergence-found, equivalent=8, unresolved=12, divergent=16 | threshold=1.000000e-3, firstρ=1.000000e-1, firstStatus=divergence-found, equivalent=8, unresolved=12, divergent=16 | threshold=2.000000e-3, firstρ=2.500000e-1, firstStatus=divergence-found, equivalent=8, unresolved=16, divergent=12 Sphere | area | status=threshold-dependent-divergence | threshold=5.000000e-4, firstρ=1.000000e-1, firstStatus=divergence-found, equivalent=8, unresolved=12, divergent=16 | threshold=1.000000e-3, firstρ=2.500000e-1, firstStatus=divergence-found, equivalent=8, unresolved=16, divergent=12 | threshold=2.000000e-3, firstρ=2.500000e-1, firstStatus=divergence-found, equivalent=8, unresolved=16, divergent=12 Hyperbolic plane | circumference | status=threshold-dependent-divergence | threshold=5.000000e-4, firstρ=1.000000e-1, firstStatus=divergence-found, equivalent=8, unresolved=12, divergent=16 | threshold=1.000000e-3, firstρ=1.000000e-1, firstStatus=divergence-found, equivalent=8, unresolved=12, divergent=16 | threshold=2.000000e-3, firstρ=2.500000e-1, firstStatus=divergence-found, equivalent=8, unresolved=16, divergent=12 Hyperbolic plane | area | status=threshold-dependent-divergence | threshold=5.000000e-4, firstρ=1.000000e-1, firstStatus=divergence-found, equivalent=8, unresolved=12, divergent=16 | threshold=1.000000e-3, firstρ=2.500000e-1, firstStatus=divergence-found, equivalent=8, unresolved=16, divergent=12 | threshold=2.000000e-3, firstρ=2.500000e-1, firstStatus=divergence-found, equivalent=8, unresolved=16, divergent=12 Null first-crossing status: numerically-equivalent means every tested row stayed within numerical equivalence; unresolved-intermediate-residuals means residuals remained above equivalence but below the documented divergence threshold. Interpretation boundary: these are deterministic formal/computational comparisons of the declared Arc model with Euclidean, spherical, and hyperbolic references. They do not report physical measurements or validate a physical, quantum, or cosmological model. A rejected formal report is not a physical conclusion and must not reuse successful report data.
A rejected formal sweep is serialized as a formal-validation failure with its error code, model, observable, and adjacent normalized radii; it is not a physical conclusion and cannot reuse a prior successful sweep.
Formal and computational results do not by themselves validate a physical, quantum, or cosmological model.
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