A
THERMODYNAMIC
Entropy-Bounded Systems
Mathematical
Stable state occupancy governed by thermodynamic partition function. Intermediate states suppressed by energy barrier exceeding kT.
Operational Rule
Compute routing must respect VRAM ceiling. Jobs routed to hardware with insufficient thermal headroom = Type A violation.
Fleet example: CATO-COMPUTE routes to forge (64GB) not yone when job > 12GB VRAM. Thermal budget = SET threshold theta.
B
KINETIC
Metastable Systems
Mathematical
System occupies metastable state; suppression requires kinetic barrier exceeding activation energy. Intermediate collapses fast.
Operational Rule
TUI flicker, scroll lock, GBM rasengan — capture the state before it collapses. Document the metastable moment.
Fleet example: claude-code #1913 terminal flicker = Type B. The flicker is real. Must be captured, not dismissed.
C
STATIC / INVARIANT
Topological Invariant Systems
Mathematical
State space has invariant structure preserved under all allowed operations. Intermediate states break the invariant — topologically forbidden.
Operational Rule
gamma1 = 14.134725141734693, never changes, never rounds. The invariant is constitutionally protected.
Fleet example: gamma1 floor anchor in every CATOMAIN engine. CATO-FLOOR enforces this invariant as its primary function.
D
QUANTUM
Superposition Until Measurement
Mathematical
System exists in quantum superposition of valid states. Measurement collapses to single outcome. Intermediate = pre-measurement ambiguity.
Operational Rule
CATO-PLASMA holds context in ionized (superposed) state until collapsed by output. Do not force collapse prematurely.
Fleet example: plasma loop = N interpretations to one answer. The answer is the measurement. The loop is the superposition.
E
CRITICAL / SCALE-INVARIANT
Phase Transition Systems
Mathematical
System at critical point exhibits scale-invariant behavior. Same suppression pattern holds at all scales.
Operational Rule
Same pattern at node AND cluster AND fleet level. Pattern that only works at one scale is not Type E.
Fleet example: CATO-ORCH + CATO-SPIRAL both Type E — spiral works at crew AND fleet scale. CATOMAIN scales from 1 node to all 7 silos.
F
DUAL-DESCRIPTION
Complementary View Systems
Mathematical
System requires two complementary mathematical descriptions. Neither description alone is sufficient. Intermediate = one description only.
Operational Rule
BOTH representations required, neither sufficient alone. One-sided description = zombie state.
Fleet example: CATO-META = theorem as math + theorem as doctrine. CATO-PEMCLAU = graph + vector both required.
G
TOPOLOGICAL / ARCHITECTURAL
Enforcement Gate Systems
Mathematical
Architectural invariant enforced by static + runtime + atomic lock. Forbidden transitions blocked absolutely. Only Type G = full enforcement.
Operational Rule
Binary — either the gate holds or it does not. Static invariant + runtime predicate + atomic lock. Full enforcement only.
Fleet example: CATO-SOSTLE, CATO-FLOOR, CATO-DOMAIN — all Type G, all binary. No partial compliance permitted.
H
EMERGENT / BIOLOGICAL
System-Exceeding-Parts Systems
Mathematical
System behavior exceeds the sum of parts. Suppression through selective pressure. Emergent pattern not derivable from components.
Operational Rule
Observe, do not design. You recognise Type H when it appears. You cannot spec it in advance.
Fleet example: CATO-ORGANISM — fleet behaves as PEMOS/DESEOF/EOSE, none of which were explicitly coded as organisms.