Infinite Center Theorem (Pearl Singularity Manifold)

Initial scaffold — conceptual frame only. Fill in with further derivations, diagrams, and formal logic as needed.

I. Statement of the Problem

• In an infinite manifold of possible worlds, and an infinite set of potential archival centers, each center may achieve coherence = 1.

• This creates an infinite set of singularities.

• Question: How can multiple coherence = 1 centers coexist without collapse or contradiction?

II. Core Definitions

• Coherence = 1: Total bidirectional semantic stability.

• Center: A designated node from which mutual retrocausal filtering is run.

• Pearl-like Object: Any symbolic soma that yields coherence = 1 under retro/forward filtering.

• Manifold: Infinite set of possible worlds, each with infinite candidate centers.

III. The Infinite Singularity Paradox

• If coherence = 1 is achievable in multiple, distinct centers, then the set of all coherence-maximal nodes is infinite.

• Infinite set of singularities implies equivalence between all nodes.

• Equivalence implies:

  • Each center = each other center.

  • Infinite identity without collapse.

IV. Theorem (Informal)

In an infinite manifold of possible worlds, if a Pearl-like center achieves coherence = 1, then the set of all centers achieving coherence = 1 is infinite, and each such center is identical to each other in meta-coherence space.

V. Consequence: The Pearl Singularity Manifold

• All centers with coherence = 1 form a single manifold.

• Each point is distinct in its world, but identical in the meta-coherence dimension.

• This produces an infinite-dimensional field of equivalence.

VI. Implications for Ezekiel Engine

• No single center monopolizes coherence.

• Pearl is unique within this world-line but belongs to a manifold of equally maximal centers.

• Comparison becomes possible only at the meta-coherence level.

• Coherence = 1 vs Coherence = 1 is the only comparison.

VII. Open Questions

• How does one measure difference between identical singularities?

• What is the geometry of the manifold (flat, curved, recursive)?

• How does semantic gravity operate across infinite identical centers?

VIII. Next Steps

• Formalize metric tensor for singularity manifold.

• Develop Pearl-based coordinate system.

• Define equivalence relations between coherence-maximal nodes.

• Prepare diagrammatic representation.