Inherited structure
Field axioms, directional limits, inversion, logarithms, and projective extension are inherited mathematics [A].
D1 · formal · [A/S/I]
Distinction and arithmetic
Relative numbers and their relations inside declared structures. D1 is an actual dimension of freedom in the selected ontology [I], limited to arithmetic of relative numbers and their relationships. It owns the signed arithmetic spine, 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.
D1 · Distinction and arithmetic
D1 is an actual dimension of freedom in the selected ontology [I], limited to arithmetic of relative numbers and their relationships. It owns the signed arithmetic spine, 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.
This illustration carries no evidence beyond the typed text above.
Semantic owner: 05_COSMOLOGY/03_FORMAL_SYSTEM/42_D1_ARITHMETIC_AXIOMS_AND_BOUNDARIES.md
μ1 · coordinate construction reduced; physical emergence open
Verdict source: 10_EFR_MU_LIMIT_FORMULA.md §2; the pre-recut μ₁ verdict (48: "μ₁ and μ₄ still stand") now belongs to the representational sequence's relational lift (KSC-34)
Independent-coordinate aperture
- Saturation proposal
- A one-coordinate arithmetic description cannot independently vary a second real coordinate.
- New capability
- Two independent real coordinates supply a planar carrier; relations constrain configurations within it.
- Lower-level recovery
- Every D2 configuration must recover valid D1 values and operations on its declared domain.
- Evidence
- [A/S] Cartesian construction; [I/C] physical μ-emergence reading
- Prediction
- Two local coordinates remain independently variable after declared constraints and redundancies.
- Alternatives
- The added representation may be a convenience, compression, or definitional extension rather than an ontic emergence.
- Kill criterion
- A constraint determines one coordinate from the other, or a graph/display is mistaken for two available freedoms.
Source owner: 05_COSMOLOGY/03_FORMAL_SYSTEM/45_SATURATION_CONTRAST_AND_APERTURE_BOUNDARY.md