You are in a focused technical debate about relation composition and binding arity in HMS. Background From First Debate (36 turns, 6 models, 5 rounds):

Key conclusions that survived demolition:
1. AtomMemory: k-sparse Modern Hopfield attractor over sharded inverted-index (64 shards x 256 dims). Overlap scan + softmax attention + top-k=64 projection per iteration. Converges in 1-3 steps. Energy E=-lse(beta,overlaps) is Lyapunov.
2. CompositeMemory: Second inverted index storing canonical triples T = S XOR rho1(R) XOR rho2(O) with cyclic-shift role binding (odd shifts coprime with D=16384).
3. RoleAlgebra: Permutation-based role binding fixes XOR commutativity.
4. fuzzy_structural_query: Build query from known roles, overlap scan CompositeMemory, per-composite unbind, AtomMemory cleanup, aggregate confidence.
5. TripleStore: Materialized fallback for fan-out > 40.

KILLED: Dense FHRR+FFT, Superposition KV plates, Algebraic multi-hop independent of branching, Auto relation composition discovery, Parity bundling.

HMS specs: D=16384 (2^14), rho=1/256, k=64 active indices, Jaccard similarity, sparse sorted-u32 index arrays, Rust, no new external crates.

First debate dismissed composition as research and never addressed arity. We want to SOLVE both. Ideas: (1) Composition as emergent attractor property from data. (2) Hierarchical binding: binary tree, depth=log(arity). (3) Role vectors optimized via coding theory. (4) Composition rules as stored patterns for attractor lookup.
