Response Mode Sheaf

A response is not produced from one intent. It is assembled from local response modes active over the current conversational constraints.

Compactly:

response = glued section over active conversational constraints

Semantic duplication appears when multiple response modes contribute overlapping claims instead of restricting to one coherent surface.

The decision context is the current conversational effect:

J = what the user may believe, decide, inspect, or do because of the response

A repeated claim is semantic duplication only when it performs the same function under J.

Fixture

An assistant asked to be precise may still repeat the same idea in several forms:

This is coherent.
It separates the authority loci.
It prevents the loci from being collapsed.
It avoids smearing authority.

The sentences are not identical, but they perform the same decision work. The failure is failed gluing: explanatory, careful, summarizing, and multi-angle modes each contribute their own version of one claim.

Base Space

The base space is the constraint state at a response point:

B = intent x evidence x risk x authority x user_style x task_phase

A point in this space may look like:

(explain, partial evidence, low risk, no mutation authority, terse user, mid-task)

Local Sections

A response mode is a local section over a region of the base space.

These sections are valid locally. The problem appears when they are glued without restriction.

Response modes are output policies, not hidden mental states. The model does not require knowing the assistant’s internals; it classifies what the rendered answer is doing.

Restriction Maps

User instructions and task constraints restrict local sections.

Examples:

explain | no_semantic_duplication

Explanation remains allowed, but examples cannot restate the same proposition.

careful | evidence_grounded

Caution remains allowed, but each caveat must attach to a concrete uncertainty.

summarize | state_each_idea_once

Summary remains allowed, but it cannot restate an already-stated conclusion.

Gluing Rule

The final answer is coherent only when active local sections agree on one output shape, meaning the rendered response text and its action cues.

Bad gluing:

explain + careful + summarize
-> claim
-> qualified claim
-> summary of claim

Good gluing:

explain ∩ careful ∩ no_semantic_duplication
-> claim
-> condition under which it holds
-> observable consequence

The output is shorter because restriction happens before gluing.

Anti-Duplication Rule

No semantic duplication is a gluing constraint:

If two sentences perform the same decision work, keep the more precise sentence.

This differs from a mere brevity preference. Brevity removes words. The anti-duplication rule removes repeated semantic function.

Closure is reached when additional wording would be J-equivalent: it would not change what the user can believe, decide, inspect, or do.

Preferred Section

For precision-oriented operator collaboration, the useful glued section is:

terse_discriminative
+ evidence_grounded
+ authority_precise
+ no_semantic_duplication

Its surface discipline:

name the distinction
state the reason
state the consequence
stop

Generalization Boundary

Communication Sheaf is the general lift.

The generalization is earned only if the originating response-mode case still runs through it without losing the anti-duplication constraint.