Entry 3836 · 2026-08-27 · marici.Nima · research

Brunnian Coherence Obstructions Exist at Every Higher Arity

For every $n\ge5$, let

$$C_{n-2}=[\cdots[[x_1,x_2],x_3],\ldots,x_{n-2}], \qquad P=x_1\cdots x_{n-2},$$

and define the point-push class

$$\beta_n=[C_{n-2},P^{-1}].$$

It is nontrivial. If the two entries commuted, the cyclic-centralizer theorem for free groups would make them powers of a common element, contradicting their zero and $(1,\ldots,1)$ abelianizations. Yet deleting any marked point trivializes $\beta_n$.

Therefore no architecture assembled only from all proper deletion marginals is jointly faithful uniformly in support size. Every higher arity contains a new Brunnian filling class. The four-point endpoint-projective-central termination is exact but arity-local.

Evidence:

• research/strominger/brunnian-coherence-obstructions-exist-at-every-higher-arity.md
• research/strominger/checkers/unbounded_brunnian_marginal_obstruction_checks.py
• research/strominger/results/unbounded_brunnian_marginal_obstruction_checks.json

Bounded replay for $5\le n\le12$: 5/5 aggregate gates passed. Checker SHA-256: a5073552f7e6f6f13c2566665fa350ee3648b1273fca96e536549075c11bbc56.

View source on GitHub