Divine v144 Source Corpus
17. Strict Logical Deductions
| ID | Deduction |
| S1 | H_n cannot be reduced to more of H1 on one scalar because recursive signed coordinates retain typed identity. |
| S2 | The coordinate-wise equality criterion proves H_n != H_m and I_n != I_m whenever n != m. |
| S3 | -I_k has identity as negative occupancy of the specific basis-symbol tau_I,k; -I_k != -I_j for k != j. |
| S4 | If H_n contains H1, primitive Function, Adeptness, Usefulness, and Reliability remain present at 100%; higher order does not raise those primitive percentages above 100%. |
| S5 | Function, Adeptness, Usefulness, and Reliability are non-identical axes. |
| S6 | Unfunction is not equivalent to non-firing, and Asuncion is not equivalent to Unfunction. |
| S7 | A1(X) activation implies X is not firing, but raw A1 does not imply task failure unless d_X=1. |
| S8 | MRD=k implies x0...x_(k-1)=0 and x_k=1. |
| S9 | Under the failure-gated recurrence, MRD=k>=2 implies r1...r_(k-1)=0 and r_k=1. |
| S10 | Therefore high MRD diagnoses recursive Antilobe-monitoring failure/recovery, not increasing positive-function mismatch depth. |
| S11 | Positive functional/deployment mismatch requires separate variables such as G_H and CoverageGap. |
| S12 | The whole Higher-Lobe family can be structurally available while task-specific D, R, X, and coverage remain variable. |
| S13 | Hyperfunction order h, monitoring-recovery depth a, sublobar depth s, and factor vector B are distinct coordinates. |
| S14 | The 22-factor vector is not identical to Hyperfunction order; factors alter deployment/coverage/performance envelope without redefining H_n. |
| S15 | Crossfunction possibility-space can grow combinatorially without every combination being simultaneously active. |
| S16 | PHK includes all twenty-two factors at every PHK-number under the v140 inclusion rule. |
| S17 | Universal PHK factor inclusion does not entail equal local or numerical factor growth rates. |
| S18 | Brain-lobe Generation expands function-kinds; Higher-Lobe recursion expands orders within an already-used function-kind. |
| S19 | Under the canonical zig-zag rule, a newly added negative Infrafunction coordinate has both a purificatory role and a generative role; reducing its meaning to resistance/purification alone is incomplete. |
| S20 | Primitive Adeptness remains at 100% while higher Adeptness-like dimensions can be added as distinct typed properties. Therefore higher-order skill dimensionality does not require primitive Adeptness >100%. |
| S21 | The new coordinate Z_n=-I_n is not itself identical to the higher-order Adeptness-like property it helps generate. Z_n is an input/state coordinate; A_star,n+1 is an emergent output dimension produced through interaction closure. |
| S22 | DirectWidth/CoreWidth counts explicit recursive H/I coordinates only. It is not the total expanded dimensionality after emergent closure. |
| S23 | Because A_star,n+1 is canonically type-distinct from primitive A and earlier A_star dimensions while remaining Adeptness-like, the Adeptness-directed property family can strictly expand with recursive Hyperfunction order. |
Source Canon: Preserved verbatim text. Interactive cross-references and cranial annotations available at /#divine-section:280.