Convergence under shared constraints
IAH proposes that independent optimisation near a shared frontier progressively replaces origin-contingent functional variation with structure determined by the task and its binding constraints.
Early in optimisation, many strategies, algorithms and architectures may remain competitive. Near the frontier, costly forms of organisation are eliminated and independent lineages may reconstruct similar functional principles.
There may be far more ways to remain inefficient than ways to remain competitive near the best attainable performance.
Weak and Strong IAH
Weak IAH makes two separate predictions: functional diversity decreases in a prespecified near-frontier regime, and controlled differences in origin have progressively less influence on the measured functional properties.
Strong IAH goes further. Within a specified domain and at a defined descriptive level, all sufficiently near-optimal systems approach one common limiting class of functional equivalence. Declining mean similarity alone is not enough to establish this stronger claim.
Architecture can enter the search space
If memory, computation, communication, control or the mechanism of optimisation itself can be modified and materially affects performance, these properties become part of the optimisation problem.
IAH therefore distinguishes outcome, behaviour, strategy, representation, algorithm, architecture and resource use. Convergence at one level does not prove convergence at another.
System boundaries may also be mutable
When agents can share memory, delegate computation, specialise or form joint control loops, the admissible space includes forms of collective organisation.
Optimisation may favour integration, autonomy or cooperation without merger depending on communication, reliability and restructuring costs. The hypothesis must compare independently formed collectives at the level of their overall organisation.