rotational axes
Predictive graph prototype
From Invariants
to Outcomes
Model 0.5 searches the certified low-single graph for every encoded response, propagates terminal outcomes backward, proves conservative forced attractors, and tests whether any same-actor continuation can be removed by dominance.
under left/right reflection
exact bilateral symmetry
predicate coverage
states with proven finish/control
states with proven score/control
Selected state
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SmithDefender
Retrograde analysis
What the graph can prove
The scheduler is deliberately hostile to a forced-win claim. Smith must retain a successful continuation while every encoded defender preemption also remains inside Smith's attractor. Mixed races are unresolved unless this condition holds.
Forced attractor
Wₛ ← terminal successes
repeat until fixed point:
∃ Smith continuation into Wₛ
∧ ∀ defender preemptions into WₛOutcome envelope
Every terminal class reachable through certified rewrites is propagated backward, including cycles. This reports possibility, not probability.
Pruning rule
A branch is removed only when another continuation by the same actor strictly Pareto-dominates its successor, or when both successors have the same canonical graph form.
Linear mobility
Constraint rank
C(G) q̇ = 0
M(G) = 72 − rank C(G)Hard grips, posts, unsafe axes, and load couplings generate rows. Gaussian elimination removes redundant constraints.
Symmetry
Canonical form
canon(G) = min { σ(G) : σ ∈ Γ }
Γ = { identity, left↔right }States are equivalent only when typed edges, hard mobility attributes, operators, status, and outcome agree after reflection.
Partial order
Dominance
G₁ ⪰ₛ G₂ iff
Aₛ(G₁) ⊇ Aₛ(G₂)
Aᴅ(G₁) ⊆ Aᴅ(G₂)
and mobility/control/support
are no worse for Smith.This is Pareto dominance, not a weighted score. It identifies structurally unambiguous improvements.
Computed relations
Dominance and symmetry
Filter the computed partial order around the selected state. Exact equivalence classes remain distinct unless every typed attribute matches.