Claim C-0001 — The Soft Cohesion Field is Primitive

Statement#

The soft cohesion field $u_t:X_t\to [0,1]$ is the ontological primitive of the theory. Objects are derivative — they are distinguished regions where $u$ is high, stable, and temporally persistent.

ID: C-0001 · Status: validated · Confidence: 100% · Proposed: 2026-03-26 Evidence: A-0001, Canonical Spec §2–3 · Depends on: Q-0001

Rationale#

Avoids circular presupposition: Starting from objects presupposes that individuation is already complete. The theory needs to account for how individuation emerges, not assume it.

Captures pre-objective states: Graded fields can represent partially-formed, ambiguous, or transitional coherence states that discrete objects cannot express.

Empirical adequacy: Soft fields naturally match neural population codes, visual saliency maps, and other biological instantiations.

Evidence#

• Theoretical: A-0001 (axiom of ontological primitivity); full formalization in Canonical Spec §3
• Conceptual: §2 Foundational Orientation provides philosophical justification
• Computational: scc/graph.py, scc/operators.py implement $u_t$ as central data structure

Assumptions#

1. Relational support space X_t is well-defined (sites can be identified even if objects cannot)
2. Graded membership (degree ∈ [0,1]) is meaningful for cohesion
3. Temporal evolution $u_t\to u_{t+1}$ can be formally specified

Limitations#

• Does not address where X_t itself comes from (that is a separate modeling choice)
• Requires formal specification of operators (closure, distinction, aggregation) to be non-vacuous
• Does not automatically resolve what threshold makes a "crisp object" — that remains a downstream question

Related Claims#

• C-0002: Objects are distinguished formations (not primitives)
• C-0003: Formations are defined by proto-cohesion (Bind ∧ Sep ∧ Artic ∧ Persist)

Validation Status#

Confidence Assessment#

Current confidence: 100% (foundational axiom, validated by entire theory)

Factors increasing confidence:

• Used consistently across all theorems
• No counterexamples
• Explains pre-objective phenomena
• Enables graded representations

Factors decreasing confidence:

• (None known)

Next Steps#

This claim requires no further validation. It is canonical.

Last Updated: 2026-05-04 Status: Canonical (CV-1.5.2 §3)