⚒️ Errata

Originally claimed as a proven theorem relating intent vector alignment to holonomy group structure. After adversarial review (4 models, including Claude Opus and Hermes-405B), the proof has a gap: interval preservation ≠ trivial holonomy. Direction (A)⟹(B) is partially proven; direction (B)⟹(A) needs fixed-point strengthening.

Action: Demoted to "open problem" in all repos. Papers updated to say "conjectured" not "proven." Documented in OPEN-PROBLEMS-ROADMAP.md.

Six parts were individually verified but calling them a "unified theorem" implied a single coherent proof. The six parts are better described as "recognitions" — each shows a Galois connection exists in a specific domain (XOR, INT8, Bloom, quantization, intent, holonomy), but they don't compose into a single theorem.

Action: Relabeled as "Galois Unification Principle" — a recognition pattern, not a theorem. All repos updated.

The core type (EisensteinInt, E12, norms, D6 operations) is genuinely zero-dependency and zero-float — ~600 lines of pure integer arithmetic. But the snap feature (angle snapping) uses libm for atan2/cos/sin.

Action: Feature-gated behind features = ["snap"] in v0.3.1. Default build is pure integer, no floats, no deps. Snap is opt-in.

README originally said "100+ tests passing." Actual count varies by feature set: 25 core tests (no deps), 37 with snap feature, 93 in flux-lucid meta-crate, 184 in constraint-theory-core.

Action: Each crate now lists exact test count with feature breakdown.

A literature review section cited an arXiv paper that doesn't exist. This was generated content not caught during review.

Action: Removed. All references now verified. Added citation verification step to review process.

76% precision mismatches at values > 2048 in FP16. This is not a bug in our code — it's a fundamental limitation of half-precision floats. The constraint library correctly rejects FP16 for constraint checking.

Lesson: If your values can exceed 2048, don't use FP16. Use INT8 (our benchmark: 341B constraints/sec, zero mismatches at 50M elements).

Workload is memory-bound at ~187 GB/s, not compute-bound. Tensor cores can't help when you're waiting on memory. INT8 without tensor cores (341B constr/s) beats FP16 with tensor cores (322B constr/s) because INT8 moves 2× less data per element.

Adding padding to avoid shared memory bank conflicts actually slowed things down on the RTX 4050 (Ada architecture). The Ada L2 cache handles bank conflicts better than manual padding, and padding wastes cache lines.

We claim Eisenstein snapping enables deterministic lockstep multiplayer by eliminating float desync. The math is sound (integer coordinates → identical results on all clients), but we haven't benchmarked this on an actual multiplayer framework.

Need: Lockstep demo with 2+ clients, 10K+ frames, verify byte-identical state.

The core type compiles for thumbv7em-none-eabi (no_std, no floats), but we don't have cycle-accurate numbers from real hardware. The 4KB C runtime should fit in Cortex-M4 flash, but we need to prove it.