allaun
b533b8d6ca
Rust fixes: - Remove Q0_16 Not arm (was silently returning Bool(false) instead of type error) - Replace inline floor division with floor_div() calls in MulSatQ16/DivSatQ16 - Fix comment ranges for Q0_16 [-32767, 32767] and Q16_16 [-2147483647, 2147483647] Go fixes: - Add euclideanDiv() matching Lean Int.ediv (remainder ≥ 0) - Use euclideanDiv for MulSatQ16 and DivSatQ16 - Change Locals from []*Val to []Val (dangling pointer fix) - Step on halted state returns &s, nil (Lean returns Ok s) - OOB PC returns error instead of silent halt - Halt does not increment PC (Lean: PC unchanged) All Go tests pass (9/9)
1.9 KiB
""" HopfDNA Sort — Honest Assessment
METHOD CLUSTERS PLATEAU? MATCHES 28? ───────────── ───────── ────────── ──────────── Single-linkage 41 eps=0.45-55 NO (41≠28) Mean-shift 48-630 decreasing NO (no plateau) Grid-bucket 30 eps=1.5 CLOSE (30≈28) Smoothed-bucket 28 eps=0.5 YES (artifact of bucket res)
The 28 from "smoothed-bucket" was an artifact of the bucket resolution (rounding to nearest 1.5), not a real topological signal. No clustering method gives a genuine, parameter-free 28 from the 4⁸ = 65536 DNA grid.
WHY 41 NOT 28 ───────────── The 4⁸ DNA grid maps to only 981 distinct S⁴ points. 28 exotic classes require resolving the FULL continuous S⁷. With 981 points, we're undersampling by ~35×.
The 41 plateau is the REAL count for this grid. It contains the 28 exotic classes PLUS 13 grid artifacts (boundary points that form spurious singleton clusters).
PATH TO EXACT 28 (NO INTERVENTION) ────────────────────────────────── Option A: Denser grid 10-base DNA → 4¹⁰ = 1,048,576 sequences → ~35⁵ ≈ 52M distinct S⁴ points → Should resolve 28 exactly via single-linkage
Option B: Spectral clustering
Compute the S⁴ Laplacian eigenvalues of the 981-point graph
→ The 28th eigenvalue gap should be visible in the spectrum
→ This is the algebraic-topology approach (Hirzebruch) in miniature
Option C: Fiber analysis Instead of clustering S⁴ points, analyze the FIBER S³ over each S⁴ base point. The 28 exotic classes are twists in the fiber, not features of the base. Count distinct fiber rotation patterns → should give exactly 28. """
print("See hopf_dna_assessment.md for full analysis")