Theory Grounding

OMEGA is a hardware interpretation of the OPH patch-net picture.

In OPH, no patch has the full state. A patch has local state, boundary data, records, and repair moves. Neighboring patches compare overlap-visible data. When a repair lowers declared mismatch and the branch has the right confluence properties, the network stabilizes a quotient normal form.

OMEGA uses the same structure as an engineering rule.

OPH object → OMEGA object

finite observer patch	chamber body
overlap boundary	optical port / host-routed interface
exposed readout	discharge trace, coupling scan, lock-in feature
mismatch potential	task score, verifier residual, calibration residual
repair move	scorebook update, boundary drive, threshold retune
record	run bundle, raw readout reference, candidate beam
normal form	exact-verifier accepted solution / replay-valid decision

Why mixed bodies

A single chamber geometry is the wrong abstraction for generic problem solving. OPH uses many patch roles. OMEGA should do the same.

Torus, the recurrent reservoir. Composes many weak constraints and fits proof-of-work and hard-search benchmarks.
Echosahedron, the clean symmetry reference body. Bounded OPH observer with interpretable symmetry; same-port reversible self-reading is a later hardware target.
Asymmetric mixer, the defect-rich critic. Deliberately breaks redundancy so generic constraints and future modes produce more distinguishable readouts.

Claim boundary

OMEGA does not claim that optics replaces exact computation. It claims that physical dynamics may enrich the candidate distribution before exact digital verification.

OMEGA measured candidate enrichment on task T under controls C, with exact verifier V confirming all reported hits.

The wrong claim form is:

OMEGA solved the hard problem directly.

Setup used

PYTHONPATH=src python3 -m omega_sim.cli optimize \
  --bits 20,24 --trials 2 \
  --architectures single-echosahedron omega-i1-five \
                  omega-research-12 omega-stretch-18 \
  --candidates 5000 --threshold 0.72 --seed 13 \
  --out results/hardware-optimization-smoke \
  --dump-candidates --candidate-dump-limit 0