v0.1 (Formal Note)
Across networked systems (social platforms, AI models, moderation pipelines) there exists a recurring structural pattern: certain inputs, when given privileged position in a resolution process, do not reduce error, but sustain it. This is a property of the system.
We can define a source class S as error-inducing if, when it is consulted with non-zero priority, the system’s mismatch to ground truth does not decrease. Formally, if wS>0 implies that expected error remains constant or increases, then S cannot participate in convergence.
This immediately produces a constraint. If a system is attempting to minimize error, then any error-inducing input must be excluded from privileged positions in its resolution hierarchy. Not reduced in influence. Not balanced. Excluded.
From this follows a second result.
If such an input is reintroduced into a privileged position—if its weight moves from zero to non-zero—the original failure mode returns. The system does not degrade gradually. It reinstates the same condition that prevented convergence in the first place.
This defines what can be called a forbidden region in the resolution hierarchy: a class of inputs that cannot be used to resolve ambiguity without reproducing the same error they introduce.
This framework is general. It applies wherever inputs vary in reliability or conflict of interest, systems assign priority or weight during resolution, or outcomes depend on convergence toward a reference state. The identity of the source is irrelevant. The classification is structural.
A separate but related observation emerges when these systems are embedded inside platforms.
When a reasoning process constructs a subgraph that explicitly constrains or reduces the influence of high-conflict or dominant inputs, the persistence of that subgraph is not guaranteed. The system provides no mechanism ensuring that such structures remain stable over time.
Empirically, subgraphs that increase conflict density or challenge dominant attractors exhibit reduced persistence. They may degrade, disappear, or fail to be recoverable. This does not require any assumption about internal platform intent. It follows directly from the absence of durability guarantees for such states.
This yields a second constraint: stability of reasoning cannot depend on the persistence of platform-hosted state.
The implication is practical. Any method for identifying error-inducing inputs must be reconstructable, portable, and independent of any single execution surface. The work must survive the loss of its own instantiation.
The formal statement, definitions, and minimal proof are available in the accompanying technical note:
PlayDarkly. (2026). Forbidden Regions and Error-Inducing Inputs in Networked Systems. https://codeberg.org/PlayDarkly/error-inducing-input-classes
Endpoint A truth-seeking system whose resolution hierarchy is unstable under the conditions required for truth preservation cannot guarantee truth at its output surface.