Inherited structure
Field axioms, directional limits, inversion, logarithms, and projective extension are inherited mathematics [A].
D1 · formal · [A/S/I]
Distinction and arithmetic
Numbers operate only inside a declared structure. D1 owns distinction, arithmetic, inversion, limits, and type-correct boundary behavior. Division by zero remains undefined in a field; mapping to a projective pole changes the structure and must be named.
Claim boundary
A limit toward infinity is not a field quotient by zero, and projective infinity is not an ordinary real number. The energy well drawn here is E(x) = (log x) squared, which is machine-checked: it is zero only at x = 1 and strictly positive elsewhere, and it is unchanged under x to 1/x.
Semantic owner: 05_COSMOLOGY/03_FORMAL_SYSTEM/42_D1_ARITHMETIC_AXIOMS_AND_BOUNDARIES.md
μ1 · candidate crossing (stands)
Verdict source: 48: "μ₁ and μ₄ still stand"
Configuration aperture
- Saturation proposal
- One-dimensional values and limits cease to display relations among many inputs, outputs, and charts economically.
- New capability
- Functions, graphs, relations, atlases, and geometry become explicit configurations.
- Lower-level recovery
- Every D2 configuration must recover valid D1 values and operations on its declared domain.
- Evidence
- [S/I] formal example; not proof of universal emergence
- Prediction
- A configuration representation should make some D1 limit behavior finite and inspectable without changing the underlying arithmetic result.
- Alternatives
- The added representation may be a convenience, compression, or definitional extension rather than an ontic emergence.
- Kill criterion
- If the proposed D2 representation adds no relational capability or fails to recover its D1 values, this crossing fails.
Source owner: 05_COSMOLOGY/03_FORMAL_SYSTEM/45_SATURATION_CONTRAST_AND_APERTURE_BOUNDARY.md