Hypothesis

Compression Advantage of Antisymmetry.

For ensembles that support persistent localized structures, encodings with antisymmetric constraints achieve lower total description length than purely symmetric (bosonic) encodings.

Define the Competing Models

Define two strictly comparable representations

Bosonic

• State = multiset of modes

• No occupancy restriction

• Fully symmetric under exchange

Formally:

• coefficients \(c_k \in \mathbb{C}\)

• no constraint on reuse of modes

Fermionic / Antisymmetric

• State = antisymmetric combination of modes

• Enforced uniqueness / exclusion

• Order-sensitive with sign flips

Implementation-wise, we don’t need full QFT. We can approximate via bitstrings with no duplicate occupancy, or determinant-like encoding (Slater-style).

This corresponds to the structure behind the Pauli exclusion principle, but we’re testing it purely as an information constraint.

Define Description Length Operationally

Define a computable proxy for: \[L(\text{state})\]

Experimental Design (Minimal Viable Spike)

TODO

Code

TODO