FSDU Solver Mode Atlas

Status: CANDIDATE_SOLVER_BASIS

Claim boundary: this is a solver-mode atlas for the FAMM Scar Differential Update surface. It is not a claim that every algorithm has been implemented, benchmarked, or proven equivalent. It defines how traversal algorithms enter the adaptive mixture as bounded projection modes.

Theory anchor:

2-Search-Space/FAMM/docs/FSDU_theory.md

Lean anchor:

2-Search-Space/FAMM/FAMM_FSDU.lean

Core Fixture Modes

The current finite Lean fixture uses nine modes:

Mode	Geometry	Use	Scar risk
A*	cost plus goal curvature	admissible heuristic route	stale heuristic
Dijkstra	isotropic cost relaxation	weighted graph baseline	expensive wavefront
Greedy Best-First	goal attractor collapse	fast scout	false attractor
BFS	expanding wavefront	unweighted reachability	frontier blow-up
DFS	tunneling strand	narrow/deep passage	dead-end depth
Bidirectional BFS	two-front closure	known start and goal	midpoint mismatch
Weighted A*	inflated heuristic	speed-biased route	suboptimality debt
Recursive Backtrack	constructive DFS with rollback	local exhaustive structure	oscillation
Wall Follower	boundary contour trace	embodied/local wall navigation	loop/island trap

Extended Atlas

Additional modes can be lowered into the finite basis until they earn their own formal field.

Family	Examples	Initial lowering
bounded-memory heuristic	IDA, RBFS, SMA	A* + DFS
bounded-width heuristic	Beam Search, Fringe Search	Greedy + Weighted A*
incremental replanning	LPA, D, D* Lite, ARA*	A* + scar repair sidecar
line-of-sight	Theta, Lazy Theta, Any-angle A*	A* + ray shortcut sidecar
grid acceleration	Jump Point Search, HPA*	A* + cached symmetry sidecar
weighted relaxation	Bellman-Ford, Johnson, Floyd-Warshall	Dijkstra + baseline map
continuous sampling	RRT, RRT, PRM, BIT	DFS + random scout sidecar
local embodied	Bug algorithms, potential fields	Wall Follower + Greedy
stochastic/metaheuristic	ant colony, simulated annealing, tabu, genetic	Greedy + FAMM exploration
game/tree search	MCTS, minimax, alpha-beta	DFS + receipt branching
retrieval graph	HNSW, ANN walks, learned heuristics	Greedy + Dijkstra

Admission Rule

Each new mode needs:

selection law Q_m(v)
weight-increase alert
weight-decrease alert
scar type it tends to create
receipt shape for committed segments
negative control or failure case

If those are missing, the mode remains an atlas note rather than a formal field.

FSDU Control Law

X_t = (M_a, M_b, S_a, S_b, Theta)
DeltaS_t = S_a - S_b
commit allowed iff ||DeltaS_t|| <= epsilon

The solver atlas only changes Theta. It does not change the commitment rule.

Keeper Distinction

Classic pathfinding asks:

which algorithm finds the best path on this graph?

FSDU asks:

which mixture keeps speculative and committed scars bounded
while the graph itself may be changing?

That is the important expansion. The algorithm name is not the truth source. The replay receipt and bounded scar differential are.

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