Invariants

Invariants are immutable laws

They don’t persuade, They don’t motivate, They don’t care who believes them They simply define what can and cannot occur, and what happens when thresholds are crossed. Systems that align behaviour to invariants can degrade gracefully. Systems that align behaviour to narrative tend to overshoot, then collapse.and they come in three types

• Universal invariants
  Examples include the speed of light, spacetime, gravity, and the laws of physics.
• Domain-agnostic invariants
  These apply across many domains, for example:
  
  
  • systemic_autophagy
    This invariant applies when a system’s extractive or optimisation efficiency is sufficient enough to eliminate the agent population or substrate it depends on for continued existence unless the current behaviour changes. System viability is proportional to agent presence; when agents are driven to extinction, the system’s own viability collapses. This invariant captures terminal self-destruction caused by unbounded efficiency, not external shock or scarcity.
  • constraint_governed_state_transition
    If a system’s state variables change, the subsequent state is determined by prior state and governing constraints. Environmental or energetic changes propagate as lawful state transitions across all substrates, producing predictable changes in system properties once thresholds are crossed.
  • transdomain_debt_pathogen
    Applies when symbolic or nominal constraints (e.g. debt, performance targets, abstract obligations) induce measurable degradation in biological, psychological, or ecological substrates.
  • harm_benefit_polarity
    Applies when evaluating the effect of any interaction, condition, policy, or intervention on a system under load. An effect is classified by its polarity: beneficial when it increases corrective, repair, or adaptive capacity relative to imposed load; harmful when it decreases such capacity; neutral when it produces no persistent change. System health is the accumulated result of these polarity effects over time. Apparent stability produced by continual harm–benefit cancellation without surplus corrective capacity constitutes pathological equilibrium rather than viability.
• Domain-specific invariants
  These apply only within a single domain. They have polarity and thresholds, but do not generalise across substrates. Their role is to define when execution is meaningful within that domain only.
  
  
  • Aerobic–anaerobic threshold breach (physiology):
    When oxygen demand exceeds delivery in muscle tissue, metabolism shifts to anaerobic pathways, increasing fatigue and reducing sustainable output.
  • Synaptic pruning window closure (neurodevelopment):
    Neural structures must be reinforced or pruned within specific developmental windows. Missed windows produce irreversible functional deficits.
  • Wing loading exceedance (aerodynamics):
    If mass per wing area exceeds a critical threshold, lift cannot counteract gravity at feasible speeds, resulting in stall or inability to take off.
  • Renal filtration saturation (biology):
    When toxin load exceeds kidney filtration capacity, waste accumulates systemically, producing organ failure.
  • Cache line thrashing (computer architecture):
    When memory access patterns exceed cache coherence capacity, performance collapses non-linearly due to repeated eviction and reload.
  • Photosynthetic light saturation (plant biology):
    Beyond a certain photon flux, photosynthetic efficiency declines due to photoinhibition and cellular damage.