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9711af2427
python/chiral_spectral_lut.py: - Maps 65,536 chiral configurations → 5 spectral fingerprints - Integer arithmetic only: block eigenvalues = 273 ± w, w rational - Regime classification: CANONICAL (6.1%), ROSSBY (93.8%), SCARRED (0.1%) - Example: AAAAAAAA→λ=[17,529] CANONICAL, LLLLLLLL→λ=[-111,657] ROSSBY Receipt: signatures/chiral_spectral_lut.json
88 lines
3.5 KiB
Python
88 lines
3.5 KiB
Python
#!/usr/bin/env python3
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"""
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Chiral Spectral LUT — mapping 8-strand chiral configuration → spectral state.
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8 strands × 4 chiral labels = 4⁸ = 65,536 states
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Collapses to exactly 5 distinct spectral fingerprints.
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The LUT maps any configuration to its eigenvalue pair {λ_min, λ_max}
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using pure integer arithmetic (zero floats).
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"""
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import json, time
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# Chiral weights as rational pairs (num, den) — integer arithmetic, zero floats
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CHIRAL = {"A": (1, 1), "S": (1, 2), "L": (3, 2), "R": (3, 2)}
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NAMES = ["A", "S", "L", "R"] # achiral, scarred, left_bias, right_bias
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def compute_spectral(chi8):
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"""
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Compute {λ_min, λ_max} for an 8-char chiral string like 'AASSSLLR'.
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Integer arithmetic only — zero floats.
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The Cartan matrix is 4×2×2 block-diagonal: pairs (0,1), (2,3), (4,5), (6,7).
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Each block [[273, w], [w, 273]] has eigenvalues {273+w, 273-w}
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where w = 128 × (chiral[num]/chiral[den] average of the pair).
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"""
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pairs = [(0,1), (2,3), (4,5), (6,7)]
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all_lo, all_hi = [], []
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for a, b in pairs:
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an, ad = CHIRAL[chi8[a]]
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bn, bd = CHIRAL[chi8[b]]
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# w = 128 × (an/ad + bn/bd) = 128 × (an×bd + bn×ad) / (ad×bd)
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num = 128 * (an * bd + bn * ad)
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den = ad * bd
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w = num // den
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all_lo.append(273 + w)
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all_hi.append(273 - w)
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return max(all_lo), min(all_hi)
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def build_lut(save=True):
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"""Build the full 65,536-entry LUT."""
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t0 = time.time()
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lut = {}
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for mask_int in range(4**8):
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chi = "".join(NAMES[(mask_int >> (i*2)) & 3] for i in range(8))
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lam_max, lam_min = compute_spectral(chi)
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lut[chi] = {"lambda_max": lam_max, "lambda_min": lam_min}
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t1 = time.time()
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# Classify into regimes
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regimes = {}
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for chi, spec in lut.items():
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key = (spec["lambda_min"], spec["lambda_max"])
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regimes.setdefault(key, [])
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regimes[key].append(chi)
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print(f"LUT built in {t1-t0:.1f}s — {len(lut):,} entries, zero floats")
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print(f"\nSpectral regime distribution ({len(regimes)} regimes):")
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for (lo, hi), configs in sorted(regimes.items(), key=lambda x: -len(x[1])):
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regime = "CANONICAL" if lo == 17 else "ROSSBY" if lo < 0 else "SCARRED" if lo > 17 else "OTHER"
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name = {"CANONICAL": "achiral ground state",
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"ROSSBY": "nonabelian (Rossby-active)",
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"SCARRED": "sub-critical (scarred)"}.get(regime, regime)
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print(f" λ=[{lo:>4}, {hi:>4}] {len(configs):>5} configs ({len(configs)/len(lut)*100:5.1f}%) {name}")
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if save:
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receipt = {
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"schema": "chiral_spectral_lut_v1", "zero_float": True,
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"entries": len(lut), "regimes": len(regimes),
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"regime_labels": ["CANONICAL", "ROSSBY", "SCARRED"],
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"compute_time_s": round(t1-t0, 2),
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"note": "Integer arithmetic only. Block eigenvalues = 273 ± w, w = 128 × avg(chi)"
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}
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with open("signatures/chiral_spectral_lut.json", "w") as f:
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json.dump(receipt, f, indent=2)
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print(f"\nReceipt: signatures/chiral_spectral_lut.json")
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return lut, regimes
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if __name__ == "__main__":
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lut, regimes = build_lut()
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# Example lookups
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print("\nExample lookups:")
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for chi in ["AAAAAAAA", "SSSSSSSS", "LLLLLLLL", "AASSLRRL", "AASSAASS"]:
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spec = lut.get(chi, {})
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regime = "CANONICAL" if spec.get("lambda_min") == 17 else "ROSSBY" if spec.get("lambda_min", 0) < 0 else "SCARRED"
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print(f" {chi} → λ=[{spec.get('lambda_min')}, {spec.get('lambda_max')}] {regime}")
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