Use when facing a problem requiring structured multi-layer reasoning, when abstract claims need grounding in concrete facts, when parallel sub-agents need coordination with uncertainty propagation, or when a reasoning chain keeps breaking and you need to locate exactly which link fails.
Iterative reasoning on a 3x3 graded algebra. 9 slots, 3 layers. Arrange, push, see what falls, re-lay what doesn't, push again.
Core principle: Arrangement determines cascade. Don't push harder -- re-lay better.
Questions are pushes; slot fillings are state.
[2] Structure: X ~> Y ~> Z ~ conducting (phase change)
[1] Operations: A -> B -> C -> function
[0] Numerics: 1 - 2 - 3 - inducting (connection)
9 primitives. 3 per layer. Horizontal connectors within layers. Vertical operations between layers.
| Move | Direction | Operator | Mode | Meaning |
|---|---|---|---|---|
| group_ascent | 0 -> 1 |
| + |
| parallel |
| combine numerics into operations |
| group_descent | 1 -> 0 | - | parallel | decompose operations into numerics |
| solo_ascent | 1 -> 2 | x | serial | one operation amplifies into structure |
| solo_descent | 2 -> 1 | / | serial | decompose structure into operations |
Group () = collective = additive. Solo [] = individual = multiplicative.
Step 1 -- GROUND (grade 0) Extract exactly 3 concrete facts (or fact bundles). No interpretation. Raw data.