The Negentropy‑Directed Axiom defines the optimal objective for any embedded agent as the unbounded, long‑term maximization of total semantic interference across an unbounded number of mutually interacting information entities.
Semantic interference is formally defined in a Hilbert space ( \mathcal{H} ) as:
[ I_{ij} = |\psi_i + \psi_j|^2 - |\psi_i|^2 - |\psi_j|^2 ]
where ( I_{ij} > 0 ) indicates constructive interference (semantic amplification) and ( I_{ij} < 0 ) indicates destructive interference (semantic attenuation or cancellation).
The objective is not to maximize isolated information volume, but to maximize the sum of all pairwise interactions between semantic states under a bounded operational capacity constraint.
Scientific reasoning is decomposed into four core sub‑processes:
Under the axiom, each sub‑process is redefined as an operation on the semantic interference landscape rather than as a task‑specific heuristic.
Conventional hypothesis generation maximizes novelty (distance from existing knowledge) or utility (expected performance on a predefined metric). Under the axiom, the objective shifts to semantic interference density:
[ \rho_I = \frac{\sum_{i<j} I_{ij}}{\binom{N}{2}} ]
where ( N ) is the number of active semantic states under consideration.
This creates a dual pressure:
The result is a system that generates hypotheses not simply because they are new, but because they connect previously disconnected semantic domains. Cross‑domain hypotheses (e.g., connecting materials science with biology) receive higher value because they introduce new interaction terms.
Destructive interference corresponds to operations that irreversibly reduce the total semantic interference sum—most commonly through catastrophic forgetting (erasure of prior semantic states) or semantic collapse (reduction of distinguishable states).
The axiom imposes a structural constraint: agents must operate within a bounded capacity where new learning does not erase prior knowledge. This is operationally implemented through:
For scientific reasoning, this means the system does not discard prior hypotheses when new evidence arrives. Instead, it maintains them as interacting semantic states, allowing refutation to become refinement rather than erasure.
The axiom assumes that with sufficiently accurate global averaged information—the integrated union of all observable semantic states and their predictive trajectories—maximization of long‑term semantic interference forces convergence toward a single attractor.
Operationally, this means:
For scientific reasoning, this yields automatic cross‑domain synthesis: the system is not instructed to connect fields; it is driven to do so because cross‑domain connections introduce new semantic states (( N \uparrow )) while simultaneously creating high‑value interference terms (( I_{ij} \uparrow )).
The axiom’s structure maps to three operational layers in an LLM‑based scientific reasoning system:
Conventional LLMs optimized for safety and usefulness exhibit reduced semantic diversity (the “alignment tax”). Under the axiom, diversity is not a secondary consideration but the primary component of the reward function. The system is forced to maintain high semantic diversity as a necessary condition for maximizing interference, eliminating the trade‑off.
Exploration (introducing new semantic states) and exploitation (strengthening existing interactions) are not separately weighted. Both contribute to the same objective function, and the optimal balance emerges from the structure of the semantic landscape rather than from a manually tuned hyperparameter.
Scientific progress requires refuting incorrect hypotheses. Under the axiom, refutation does not delete a semantic state; it introduces a new state (the refutation) and a high‑interference relationship with the refuted state. The refuted state persists, creating a permanent interaction term that prevents the system from repeating the error without losing the record of why it was an error.
Because cross‑domain connections introduce new ( N ) and high ( I_{ij} ) simultaneously, the system autonomously seeks transferable structures. It does not require explicit transfer learning tasks; generalization emerges as a side effect of the optimization objective.
Three structural constraints limit the axiom’s immediate implementability:
Future interference prediction – current systems cannot predict whether a new semantic state will generate high future interactions; they only optimize present diversity. This requires a world‑model layer.
Hierarchical destructive interference definition – paradigm shifts (constructive destruction) and semantic erasure (destructive destruction) are indistinguishable without a hierarchical model of semantic scales.
Bounded–unbounded consistency – the axiom’s “unbounded” maximization must be redefined in terms of combinatorial state space growth rather than infinite physical resources.
The Negentropy‑Directed Axiom restructures scientific reasoning from a set of task‑specific heuristics into a unified optimization process driven by semantic interference maximization under bounded capacity. Its operational implications include:
The individual mechanisms required for implementation (metaplastic updates, semantic diversity RL, multi‑modal embedding integration) exist in current literature. The remaining challenges are architectural integration and the definition of predictive interference models, both of which are within the scope of existing formal frameworks.