Operational support, semantic support, and quotient memory

Exact statement

For a demanded map on a finite product source, operational support records coordinates touched by a replay trace, semantic support records coordinates capable of changing the demanded answer, and quotient memory identifies sources with equal complete answers. These are distinct resources.

StatusDefined self-containedly with exact comparison maps

External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

A completed trace, the coordinates that matter to any future, and the compressed future behavior need not have the same size. Treating them separately prevents trace complexity from being mistaken for semantic memory or update cost.

Definitions

Operational support is implementation-relative and records source coordinates used by stable replay certificates.
Semantic support is the unique least coordinate set on which the demanded map depends.
Quotient memory is the equality partition induced by the complete demanded answer.

Proof or evidence

The accompanying theorem proves the exact order among the layers and supplies families with arbitrarily large gaps.

Three memory layers →

Verification notes

The distinctions were checked against adaptive replay slices, continuation response rows, parity, coordinate selectors, and deliberately over-querying programs.

Limitations

The definition assumes a finite product source for the coordinate-support theorem.
It does not yet measure stationary update, allocation, addressing, or transport cost.
No novelty claim is made for standard function-support or quotient concepts.

Open work

Define stationary transport cost for updating and naming quotient classes as the cut advances.