If gravity is not a force, and mass is not an intrinsic property but resistance to reconstrual, then the familiar appeal to curvature must be handled with care.
Curvature is often treated as the sophisticated replacement for force: no longer an attraction, but a bending of spacetime itself. From a relational ontology, this move is an improvement — but not yet a solution. It retains a container, merely refined.
The task of this post is precise: to show how curvature emerges without spacetime, and without any geometric object doing explanatory work.
Why spacetime curvature will not do
Spacetime curvature explanations presuppose:
a manifold that exists independently of phenomena,
a metric structure that encodes distances and durations,
and a rule that tells phenomena how to move within that structure.
However elegant, this grammar still relies on a background arena — something that is, bends, and then guides motion. The ontology we are working with does not allow this.
There is no spacetime in which cuts occur. There are only cuts, coordinated under constraint.
If curvature is to survive, it must be reconceived as a feature of relational orderings, not of a container.
Recalling the dual orderings
Earlier, we established that:
time is the ordering of dependency between cuts,
space is the ordering of incompatibility between cuts.
These are not dimensions but structural relations that must hold if a phenomenon is to persist across perspectives. They are the minimal orderings required for coherence.
Relational thickening, introduced in the previous post, directly affects these orderings.
What curvature becomes
When a high-mass configuration thickens the surrounding relational architecture, it does not bend a manifold. It produces asymmetry in the availability of ordered sequences of cuts.
Specifically:
Certain dependency chains become easier to sustain than others.
Certain incompatibilities become sharper, closing off alternative co-actualisations.
The space of viable sequences becomes directionally biased.
This bias is what curvature is in a relational ontology.
Curvature is not shape. It is uneven permissibility.
Direction without geometry
A common objection arises here: without spacetime, how can there be direction at all?
The answer is that direction is not primitive. It is an emergent feature of ordered constraints.
Where relational thickening is present:
sequences of cuts resolve preferentially along paths of least resistance,
dependency orderings funnel persistence toward stable configurations,
incompatibility orderings close more rapidly in some relational directions than others.
These patterned asymmetries give rise to what we later describe phenomenally as direction, trajectory, and path — without any geometric substrate.
Curvature as perspectival, not global
Another consequence follows immediately.
Curvature, so construed, is not a global property of a universe-sized structure. It is local to regions of relational thickening.
Different configurations experience different curvatures because:
they participate in different dependency chains,
they face different incompatibility constraints,
and they encounter thickening from different perspectival positions.
This preserves the relational commitment: there is no view from nowhere, no universal geometry underlying all cuts.
Holding the line
At this point, several temptations must be resisted:
to draw diagrams that resemble manifolds,
to speak of bending or warping as physical actions,
to let geometry quietly resume explanatory authority.
None of this is needed.
Everything we require follows from one claim:
High resistance to reconstrual produces asymmetric constraint on the ordering of possible cuts.
That asymmetry is curvature.
Preparing the next step
We now have all the pieces required to dissolve motion itself.
If curvature is asymmetric constraint, and if sequences of cuts persist preferentially along certain orderings, then what we call motion is not something that happens in a curved space. It is the name we give to constrained re-cutting over successive perspectives.
The next post will take this step carefully:
Post 4 — Motion as Constrained Re-Cutting.
For now, the central claim stands:
Curvature does not belong to spacetime. It belongs to the architecture of relational possibility.
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