Temporal Agnosticism of the Core Algebra

Invariant Statement

The composition algebra of gds-framework is temporally agnostic. The flag is_temporal=True on a wiring asserts structural recurrence and nothing else. No time model is implied or required by the core. The canonical form h = f . g is an atemporal map. Time models are DSL-layer declarations.

Three-Layer Temporal Stack

Layer 0 — gds-framework (core)
  is_temporal=True encodes structural recurrence only:
  "a temporal boundary exists here."
  No commitment to what model of time governs that boundary.
  h = f . g is a single atemporal map application.
  The algebra is silent on discrete steps, continuous flow, and events.

Layer 1 — DSL (ExecutionContract)
  The DSL declares what "temporal boundary" means for its domain:
    discrete    — boundary is a discrete index step
    continuous  — boundary is a continuous-time interval
    event       — boundary is triggered by a discrete event
    atemporal   — boundary carries no time semantics (e.g., OGS iterated games)
  This is the DSL author's commitment, not the core's.

Layer 2 — Simulation (SolverInterface / runner)
  Required only to execute a specification.
  A solver or runner instantiates the time model concretely.
  The choice of solver (RK4, event queue, discrete stepper) is
  simulation-layer, not specification-layer.
  Specification and verification are fully valid without a solver.

Proof by Inspection of Composition Operators

None of the four composition operators introduce a time model. They operate on structural interfaces only.

StackComposition (>>) chains forward_out to forward_in by token overlap. No temporal concept is referenced. The validator checks token sets, not time indices.

ParallelComposition (|) concatenates interfaces. No validation is performed between left and right. Time is not mentioned.

FeedbackLoop (.feedback()) routes backward_out to backward_in within a single evaluation. The wiring direction is CONTRAVARIANT. No time model is assumed -- "within a single evaluation" means "before the current map application completes," not "within a discrete timestep."

TemporalLoop (.loop()) routes forward_out to forward_in across evaluations. The wiring direction must be COVARIANT. The is_temporal flag is set on the resulting WiringIR edges. This flag tells the acyclicity checker (G-006) to exclude those edges from the covariant DAG constraint. It carries no semantic content about what kind of time governs the recurrence -- it is a structural recurrence marker only.

The is_temporal flag exists so that G-006 can distinguish "this edge closes a recurrence" from "this edge creates an illegal cycle." That is its entire semantics at Layer 0.

The OGS Existence Proof

OGS (Open Game Specification) iterated games compile and verify correctly with temporal wirings but no time model. The canonical form degenerates to h = g with X = empty, f = empty. This is not a special case -- it is existence proof that the algebra is genuinely time-agnostic.

An OGS IteratedGame wraps a OneShot game with .loop() temporal wirings that carry strategy and payoff signals across rounds. The word "round" here is a game-theoretic concept, not a time concept. No discrete-time index, no continuous-time interval, and no event trigger is declared at the core level. The temporal wirings assert only: "there is structural recurrence here."

This demonstrates that the core algebra supports recurrence patterns that have nothing to do with physical time. The .loop() operator is about structural feedback topology, not about clocks.

ExecutionContract Time Model Table

time_domain	Meaning at DSL layer	Example DSL
discrete	Temporal boundary is a discrete index step	gds-stockflow, gds-control
continuous	Temporal boundary is a continuous-time interval	gds-continuous
event	Temporal boundary is triggered by an event	(future)
atemporal	Temporal boundary carries no time semantics	gds-games (OGS)

Vocabulary Guide

When writing documentation for the core framework (Layer 0), use temporally neutral language:

Avoid (core docs)	Prefer
"within a single timestep"	"within a single evaluation"
"across timesteps"	"across temporal boundaries"
"next step" / "next timestep"	"subsequent application" or "recurrence"
"time t" / "t+1" subscripts	"evaluation k" / "k+1" (or omit indices)
"trajectory x_0, x_1, ..."	"sequence of states under repeated application of h"
"iteration" (implying counting)	"recurrence" or "repeated application"

DSL-layer exception

DSL-layer docs (gds-stockflow, gds-control, gds-continuous, gds-games) may use time-specific language because they have declared a time model via their ExecutionContract. The vocabulary guide applies only to core framework documentation.