| ProductLayoutWidth | https://uor.foundation/foundation/LayoutInvariant | layoutRule: SITE_COUNT(A × B) = SITE_COUNT(A) + SITE_COUNT(B)
| PartitionProduct layout-width invariant: products introduce no bookkeeping of their own, so layout widths add. Cited by primitive_partition_product when the caller-supplied combined SITE_COUNT differs from the sum of operand SITE_COUNTs. |
| CartesianLayoutWidth | https://uor.foundation/foundation/LayoutInvariant | layoutRule: SITE_COUNT(A ⊠ B) = SITE_COUNT(A) + SITE_COUNT(B)
| CartesianPartitionProduct layout-width invariant: cartesian products introduce no bookkeeping either, so layout widths add the same way PartitionProduct does. The distinction between these two constructions lives at the nerve-topology level (χ multiplicative vs additive), not the layout level. |
| CoproductLayoutWidth | https://uor.foundation/foundation/LayoutInvariant | layoutRule: SITE_COUNT(A + B) = max(SITE_COUNT(A), SITE_COUNT(B)) + 1
| PartitionCoproduct layout-width invariant: coproducts add exactly one tag site beyond the widest operand's full layout. Uses SITE_COUNT (not siteBudget) so nested coproducts whose operands carry inherited bookkeeping do not collide their outer tag with an inner tag site. |
| CoproductTagEncoding | https://uor.foundation/foundation/LayoutInvariant | layoutRule: Affine { coefficients: [0,…,0, 1 at tag_site], bias: 0 (left) | −1 (right) }
| PartitionCoproduct canonical tag-pinner encoding: each variant's tag-pinning constraint is the canonical Affine form with all-zero coefficients except a single 1 at tag_site, with bias 0 for the left variant and bias −1 for the right. Semantically equivalent but non-normalized encodings (coefficient ≠ 1, or alternative biases, etc.) are rejected at mint time because content-addressing depends on the normalized byte pattern, not the semantic equivalence class. |