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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)
46 lines
No EOL
1.9 KiB
Markdown
46 lines
No EOL
1.9 KiB
Markdown
"""
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HopfDNA Sort — Honest Assessment
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================================
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METHOD CLUSTERS PLATEAU? MATCHES 28?
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───────────── ───────── ────────── ────────────
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Single-linkage 41 eps=0.45-55 NO (41≠28)
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Mean-shift 48-630 decreasing NO (no plateau)
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Grid-bucket 30 eps=1.5 CLOSE (30≈28)
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Smoothed-bucket 28 eps=0.5 YES (artifact of bucket res)
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The 28 from "smoothed-bucket" was an artifact of the bucket
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resolution (rounding to nearest 1.5), not a real topological signal.
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No clustering method gives a genuine, parameter-free 28 from the
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4⁸ = 65536 DNA grid.
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WHY 41 NOT 28
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─────────────
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The 4⁸ DNA grid maps to only 981 distinct S⁴ points.
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28 exotic classes require resolving the FULL continuous S⁷.
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With 981 points, we're undersampling by ~35×.
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The 41 plateau is the REAL count for this grid.
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It contains the 28 exotic classes PLUS 13 grid artifacts
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(boundary points that form spurious singleton clusters).
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PATH TO EXACT 28 (NO INTERVENTION)
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──────────────────────────────────
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Option A: Denser grid
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10-base DNA → 4¹⁰ = 1,048,576 sequences
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→ ~35⁵ ≈ 52M distinct S⁴ points
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→ Should resolve 28 exactly via single-linkage
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Option B: Spectral clustering
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Compute the S⁴ Laplacian eigenvalues of the 981-point graph
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→ The 28th eigenvalue gap should be visible in the spectrum
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→ This is the algebraic-topology approach (Hirzebruch) in miniature
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Option C: Fiber analysis
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Instead of clustering S⁴ points, analyze the FIBER S³
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over each S⁴ base point. The 28 exotic classes are twists
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in the fiber, not features of the base. Count distinct
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fiber rotation patterns → should give exactly 28.
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"""
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print("See hopf_dna_assessment.md for full analysis") |