Most accounts of perception start from objects and ask how they relate. This track starts one step earlier and asks: what holds anything together enough to become an object in the first place?
The answer offered here is Soft Cognitive Cohesion (SCC). Its primitive is a graded field
over a relational support space, where measures the degree to which site participates in a cohesive formation. It is not a probability, not a segmentation mask, and not a clustering assignment. Objects are a distinguished limit of this formation space, not its starting point.
Formal structure in one paragraph
A phase transition separates the two regimes:
Commitments that shape the theory
State of play
Sixty-eight theorems are proved fully (Category A) — including existence (T1), closure fixed-points (T6a/T6b), phase transition (T8-Core), axiom consistency (T20), non-idempotent metastability advantage (T7-Enhanced), Γ-convergence (T11), gradient flow convergence (T14), the W4 Pre-Objective Mechanism cluster (T-PreObj-1 + T-PreObj-1G + Lemma 4), the W4-extended Goldstone result (T-V5b-T), the W5 multi-formation count bridge T-L1-F, the W6 additions (CV-1.6–CV-1.11): hard-depth topological locking (T-ST-5a), boundary precision (T-OP6-B, resolving OP-0006), and the stochastic foundation P-F-A1 Package I — well-posed reflected SDE on (T-PF-A1-AR + T-PF-A1-SDE), unique Gibbs invariant measure (T-PF-A1-GI), and exponential ergodicity with explicit Poincaré constant (T-PF-A1-PE), plus Gibbs measure continuity at (T-P-F-ε0), and the W7 additions (CV-1.12–CV-1.17): existence of the temporal correspondence T-Temporal-Identity (a) via H-SINK (Bigot–Cazelles–Papadakis Sinkhorn Lipschitz, in the SCC cost class). Nineteen are proved with a structural parameter (Category B) — including the W6 additions smooth-depth barrier raising (T-ST-5b), Kramers exponent stability (T-P-F-ε0-K), equilibrium K-selection partially resolving OP-0005-EQ (T-K-Select-PF), observation-conditioned K-selection partially resolving OP-0005-OBS (T-K-Select-OBS), and the W7 additions kernel-composed compositional consistency (T-CC-StableK-Kernel, closing H-COMP-KERNEL at CV-1.17) plus the conditional lift T-ACT-KERNEL-COMP→REL (CV-1.15 → activated at CV-1.17). Six remain conditional (Category C) — including the temporal-identity interior persistence part (c) (CV-1.12, blocked by OP-0011). Totalling 98 formal claims, ~70% fully proved. Five claims have been retracted.
The Observer Moduli Space (OMS-2.0) reached Accepted — Full at W6 close: the space of symmetry-inequivalent critical formations is proved finite and stratified, with both the static branch decomposition ( generic symmetry, codim-1 strata) and the temporal extension (, 19-branch Δ³ map) established. Appendix OMS (§A–§M) is now part of the canonical specification.
Per Commitment 16 (CV-1.5.1, 2026-04-29), the formation count decomposes into (architectural cap, modeling-layer commitment) and (dynamic stratum index, derived diagnostic), resolving the long-standing OP-0009-K ontological ambiguity.
The larger goal
SCC is the pre-objective layer of a larger design target: a single cognitive-reasoning architecture that unifies SCC with Ontology Neural Networks. The north-star document for that unification is Integrated Architecture — SCC × ONN as one cognitive-reasoning system. Everything on this page is in service of the integration claim there.
Papers on this track
- An Axiomatic Framework for Understanding Relations via Gauge-Invariant Cohomology — the formal bridge from SCC to RelationWorld.
- In preparation: the two principal SCC manuscripts (mathematical and cognitive-science treatments) are being revised for submission.
Related
- Ontology Neural Networks — how the outputs of SCC become inputs to learned semantic reasoning.
- Mathematical foundations — the RelationWorld framework that gives SCC a concrete relational substrate.