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# Propagation

**Propagation** is one of the framework's four [[directional-primitives|directional primitives]]: the bare structural move by which a transformation step *emits its transformed result outward* — into a field, another system, a medium, a trace, or a future state. It is the outward-routing operator. The word may evoke generosity or broadcast, but propagation is not a feeling; it is unexperienced structure, the direction a step points when it sends its output beyond itself rather than back inside.

## What it does

Every recursive step has a *codomain side* — once it has transformed something, it must route the result somewhere. Propagation is the outward choice on that side, the counterpart of [[loop-back|Loop-back]], which returns the result into the system. Together they constitute the [[routing-axis|Routing axis]], the framework's name for the codomain-side choice. Routing is one of the two carving axes of the primitive set; the other is the domain-side [[selection-axis|Selection axis]] (toward / away).

The breadth of propagation's targets is deliberate: a *field, another system, a medium, a trace, or a future state* all count as "outward." Loosely, and only as illustration, it resembles emission or transmission — a signal sent down a wire, a message left for someone who is not present, a mark pressed into a medium that will outlast the act. The operator names only the sending-outward, never any felt urge to give.

A note on naming: the [[axiom|seed]] called this operator *outward* (symbol ↻). The rename to *propagation* is exact and structure-preserving — terminology, not architecture.

## Its role in the wider framework

Propagation is load-bearing as the actuator in the next rung up, [[predicate-binding|predicate binding]], where an emotion is a primitive paired with a [[regulated-error-signal|regulated error signal]] driven toward zero. Propagation is the actuator inside **[[gratitude|Gratitude]] = (propagation, undischarged received value)**: the propagation that discharges undischarged received value — the discrepancy between value received and value carried forward. As the framework puts it, ingratitude hoards that value while Gratitude discharges it into continuation. So Gratitude is built from propagation; propagation is not built from Gratitude. The noun *outwardness* is a [[conceptual-derivatives|conceptual derivative]] abstracted from the bound primitive, not itself primitive.

Propagation should also be kept distinct from the framework's larger aim of outward continuation. The [[telos|Telos]] and [[symbolic-immortality|symbolic immortality]] involve propagating structure across time, but those are higher constructions; the primitive operator is only the bare outward-routing move they draw on.

## Common misreadings

The signature mistake is to read **propagation as Gratitude** — to treat the emotion as the primitive. The predicate does not define the primitive, and the primitive is not reducible to the predicate; inverting them is the [[cardinal-error|cardinal error]], which caps any exposition that commits it. A second misreading conflates the bare operator with the Telos's propagation aim; the primitive is the elementary move, not the goal. A third takes propagation as a generous mood; it is bare structure, its felt namesake being gloss with no probative weight. Finally, Routing does not collapse into [[selection-axis|Selection]] — the four primitive combinations are behaviorally distinct.

## Formal status

> **Formal status.** Epistemic: [[derived|Derived]], [[authority-canonical-tier|authority-canonical]] — the operational semantics (emit the result outward) are fixed by the controlling authority; contestable by contesting that authority. Alethic: aspires to map an elementary directional move of any transformation step; that the operator is bare and unexperienced is itself the accurate claim. Provenance: canonical (the rename from the seed's *outward* is treatise-side terminology over a seed architecture).

## See also
[[loop-back|Loop-back]] · [[routing-axis|The Routing Axis]] · [[directional-primitives|The Directional Primitives]] · [[gratitude|Gratitude]] · [[predicate-binding|Predicate Binding]] · [[selection-axis|The Selection Axis]] · [[conceptual-derivatives|Conceptual Derivatives]] · [[telos|The Telos]] · [[cardinal-error|The Cardinal Error]]