Mapping DEF to Spacetime

This page outlines how spacetime-based physical descriptions can be understood as a specific regime-level realization of the Dimensional Emergence Framework (DEF).

The purpose of this mapping is interpretative, not reductive.
DEF does not derive spacetime; it specifies the structural conditions under which spacetime descriptions become admissible.

Structural role of spacetime in DEF

In DEF, spacetime is not treated as a fundamental primitive.

Instead, spacetime is understood as a regime-dependent representation that emerges when:

structural relations admit metric interpretation,
ordering relations are stabilized,
and exchange–dynamics coupling becomes externally coordinatizable.

Spacetime is therefore a descriptive layer, not an ontological ground.

Dimensional correspondence

DEF introduces two emergent dimensions:

Existence (E) — structural and relational persistence
Happening (H) — transformation and interaction

In spacetime-based physics, these are commonly expressed as:

spatial extension and configuration,
temporal ordering and dynamical evolution.

The correspondence is structural, not identical:

Existence does not equal space.
Happening does not equal time.

Rather, spacetime arises when Existence–Happening coupling is represented using geometric and temporal coordinates.

Operative modes and spacetime notions

The four operative modes of DEF map onto familiar spacetime concepts as follows:

Structure (S)
↔ invariant relations, fields, or conserved configurations
Space / Room (R)
↔ spatial extension, topology, metric relations
Dynamics (D)
↔ equations of motion, temporal change, evolution operators
Exchange (X̂)
↔ interaction, coupling, information or energy transfer

This mapping is contextual:
the same DEF mode may correspond to different spacetime constructs in different physical theories.

Kernel self-reference and perceptual interpretation

The DEF kernel admits seven self-referential relations.
These self-references do not need to be fully accessible within a given regime.

A useful interpretative distinction is:

3 + 3 + 1 self-references at the kernel level
3 + 1 self-references at the perceptual level

Kernel-level structure (3 + 3 + 1)

At the kernel level, self-reference decomposes into:

Three Existence-side self-references
- Structure referring to Structure
- Space referring to Space
- Space anchoring Structure
Three Happening-side self-references
- Dynamics referring to Dynamics
- Exchange referring to Exchange
- Exchange anchoring Dynamics
One trans-dimensional self-reference
- (Structure · Space) → (Exchange · Dynamics)

Together, these seven relations ensure closure and coherence of the kernel as a whole.

Perceptual projection (3 + 1)

A perceptual regime does not require access to all kernel self-references.

Instead, perception can be understood as arising from a restricted subset:

Three intra-modal self-references
- one stabilizing structure,
- one stabilizing spatial relation,
- one stabilizing dynamic transformation,
plus the trans-dimensional self-reference
- coupling Existence to Happening.

This yields a 3 + 1 configuration.

Interpretation

Under this view:

perception does not reconstruct the full kernel,
it samples a stable projection of kernel self-reference,
sufficient to maintain coherence between configuration and change.

Spacetime-based perception corresponds to regimes in which:

this 3 + 1 subset can be coordinatized geometrically and temporally,
while the remaining self-references remain implicit or inaccessible.

Consequence

Perception is therefore not a primitive feature of DEF,
but a regime-dependent interpretation of kernel self-reference.

Different regimes may:

expose different subsets of self-referential structure,
or admit no perceptual projection at all.

This distinction clarifies how perceptual spacetime descriptions can arise from DEF
without requiring full access to kernel-level structure.

Kernel constraint and spacetime consistency

A central DEF constraint is the equivalence:

(S · R) ≡ (X̂ · D)

In spacetime language, this corresponds to the requirement that:

structural–spatial configuration
and dynamic–interactional behavior

remain mutually consistent.

Violations of this equivalence manifest as:

non-physical solutions,
instability,
or breakdown of classical spacetime description.

Phase structure and temporal ordering

DEF distinguishes three phases:

Entry
Crisis
Resolution

These phases are not time steps, but ordering relations.

In spacetime-based models, they are often represented as:

initial conditions,
interaction or transition regions,
and asymptotic or stabilized solutions.

Time, in this view, is a coordinate representation of ordered phase traversal, not its cause.

Relation to relativistic frameworks

In relativistic physics, spacetime unifies spatial and temporal coordinates.

DEF does not assume such unification a priori.

Instead:

relativistic spacetime is interpreted as a regime where
- exchange–dynamics coupling is symmetric,
- structural relations admit Lorentz-invariant representation,
- and phase ordering can be coordinatized consistently.

Lorentz invariance is thus a regime property, not a foundational axiom.

Limits of the mapping

This mapping does not claim that:

spacetime is always a valid description,
spacetime coordinates are universally meaningful,
or all DEF regimes admit spacetime representation.

Certain regimes may:

lack metric structure,
lack global time ordering,
or violate assumptions required for spacetime formulation.

DEF explicitly allows for such regimes.

Summary

Spacetime-based physics can be understood as a stable representational regime of DEF, characterized by:

metric interpretation of relational structure,
coordinate representation of ordering,
and consistent coupling between configuration and interaction.

DEF provides the structural preconditions under which such representations become possible,
without assuming spacetime as fundamental.

This mapping serves as a conceptual bridge between the DEF Core and established spacetime-based physical theories.