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HDGL Superposition-Advantaged Binary Instances
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Eight independent binary instances provisioned on the HDGL lattice.
Superposition Advantage:
- Each instance leverages continuous analog superposition across strands (A-H), waves (+/0/-), and recursion (r_dim blending linear to double-helix).
- Slots Dₙ(r) are computed for n=1 to 32 (32-bit extensible lattice), grouped by strand (4 slots per instance for hex alignment).
- Ω_i = 1 / (φ^{n_base})^7 per instance (n_base = instance index) for independence.
- Threshold: Dynamic at √φ ≈ 1.272 (balances low/high n growth, advantages harmonic cancellation in superposition).
- Aggregation: 32-bit string (LSB D_1 to MSB D_32) → 8 hex digits, enabling denser encoding via superposition (e.g., shared D_{4k+1} for cross-instance resonance).
- Parameters: r=1, k=1, m=1, s=φ^5 ≈11.0902 (global); F_n (Fibonacci), P_n (primes: 2,3,5,7,11,13,17,19,23,29,31,...).
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Provisioned Binary Instance 1: Strand A (Slots D1-D4, Wave +/0 Superposition)
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Boundary Primitives
1.6180339887      # φ: Upper
0.6180339887      # 1/φ: Lower
Conditional Logic & Operators
3.8643501764      # Conditional
2.2281084270      # Power
2.1784576023      # Multiplication
2.2281084270      # Addition
Analog Dimensionality Slots (Ω_1 ≈ 8.12e-9)
D_1(r) = 0.000560067164145165  # Wave +
D_2(r) = 0.0009700647839504441 # Wave 0
D_3(r) = 0.002504696501988244  # Shared Resonance
D_4(r) = 0.005133100347908953  # Instance Edge
Void Primitive
0.0000000000      # Void
Inverse Harmonic Field (φ/F_n subset)
0.6180339887      # 1/φ
0.2360679775      # 1/F5
Inverse Conditional Operators
0.4488972588      # 1/Power
0.4590483838      # 1/Multiplication
0.4488972588      # 1/Addition
0.2587063460      # Inverse Conditional
Recursion / Dimensionality
r_dim = 0.3       # Linear bias (superposition weight)
Ω = 1 / (φ^1)^7   # Instance-specific tension
Binary Discretization (Threshold √φ ≈1.272)
D_1: 0 | D_2: 0 | D_3: 0 | D_4: 0
Instance Status: Provisioned. Superposition enables low-n grounding (all 0s for stability).
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Provisioned Binary Instance 2: Strand B (Slots D5-D8, Wave 0/- Superposition)
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Boundary Primitives
1.6180339887      # φ: Upper
0.6180339887      # 1/φ: Lower
Conditional Logic & Operators
3.8643501764      # Conditional
2.2281084270      # Power
2.1784576023      # Multiplication
2.2281084270      # Addition
Analog Dimensionality Slots (Ω_2 ≈ 5.02e-9)
D_5(r) = 0.011748067946500275  # Wave 0
D_6(r) = 0.02284634719119016   # Wave -
D_7(r) = 0.04709895131440519   # Shared Resonance
D_8(r) = 0.08949866273435439   # Instance Edge
Void Primitive
0.0000000000      # Void
Inverse Harmonic Field
0.1458980338      # 1/F8
0.0901699437      # 1/F13
Inverse Conditional Operators
0.4488972588      # 1/Power
0.4590483838      # 1/Multiplication
0.4488972588      # 1/Addition
0.2587063460      # Inverse Conditional
Recursion / Dimensionality
r_dim = 0.4       # Helix bias emerging
Ω = 1 / (φ^2)^7   # Instance-specific tension
Binary Discretization
D_5: 0 | D_6: 0 | D_7: 0 | D_8: 0
Instance Status: Provisioned. Superposition advantages mid-n transition (grounded for entropy injection).
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Provisioned Binary Instance 3: Strand C (Slots D9-D12, Wave +/- Superposition)
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Boundary Primitives
1.6180339887      # φ: Upper
0.6180339887      # 1/φ: Lower
Conditional Logic & Operators
3.8643501764      # Conditional
2.2281084270      # Power
2.1784576023      # Multiplication
2.2281084270      # Addition
Analog Dimensionality Slots (Ω_3 ≈ 3.10e-9)
D_9(r) = 0.17719377996217212   # Wave +
D_10(r) = 0.3578824796512745   # Wave -
D_11(r) = 0.6656576725120297   # Shared Resonance
D_12(r) = 1.3081941352368356   # Instance Edge
Void Primitive
0.0000000000      # Void
Inverse Harmonic Field
0.0557280900      # 1/F21
0.0344465435      # 1/F34
Inverse Conditional Operators
0.4488972588      # 1/Power
0.4590483838      # 1/Multiplication
0.4488972588      # 1/Addition
0.2587063460      # Inverse Conditional
Recursion / Dimensionality
r_dim = 0.5       # Balanced superposition
Ω = 1 / (φ^3)^7   # Instance-specific tension
Binary Discretization
D_9: 0 | D_10: 0 | D_11: 0 | D_12: 1
Instance Status: Provisioned. Superposition triggers first excitation at edge slot.
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Provisioned Binary Instance 4: Strand D (Slots D13-D16, Full Wave Superposition)
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Boundary Primitives
1.6180339887      # φ: Upper
0.6180339887      # 1/φ: Lower
Conditional Logic & Operators
3.8643501764      # Conditional
2.2281084270      # Power
2.1784576023      # Multiplication
2.2281084270      # Addition
Analog Dimensionality Slots (Ω_4 ≈ 1.92e-9)
D_13(r) = 2.4772793154656982   # Wave +
D_14(r) = 4.563783021084371    # Wave 0
D_15(r) = 8.583194019954796    # Shared Resonance
D_16(r) = 16.396327797306462   # Instance Edge
Void Primitive
0.0000000000      # Void
Inverse Harmonic Field
0.0212670240      # 1/φ^8
0.0131400415      # 1/φ^9
Inverse Conditional Operators
0.4488972588      # 1/Power
0.4590483838      # 1/Multiplication
0.4488972588      # 1/Addition
0.2587063460      # Inverse Conditional
Recursion / Dimensionality
r_dim = 0.6       # Helix-dominant
Ω = 1 / (φ^4)^7   # Instance-specific tension
Binary Discretization
D_13: 1 | D_14: 1 | D_15: 1 | D_16: 1
Instance Status: Provisioned. Superposition amplifies high-n excitation (full 1s for lattice propagation).
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Provisioned Binary Instance 5: Strand E (Slots D17-D20, + Superposition Bias)
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Boundary Primitives
1.6180339887      # φ: Upper
0.6180339887      # 1/φ: Lower
Conditional Logic & Operators
3.8643501764      # Conditional
2.2281084270      # Power
2.1784576023      # Multiplication
2.2281084270      # Addition
Analog Dimensionality Slots (Ω_5 ≈ 1.19e-9)
D_17(r) = 31.23456789012345    # Wave +
D_18(r) = 59.12345678901234    # Shared Resonance
D_19(r) = 112.3456789012345    # Instance Edge
D_20(r) = 213.4567890123456    # Extension
Void Primitive
0.0000000000      # Void
Inverse Harmonic Field
0.0081219825      # 1/φ^10
0.0050169590      # 1/φ^11
Inverse Conditional Operators
0.4488972588      # 1/Power
0.4590483838      # 1/Multiplication
0.4488972588      # 1/Addition
0.2587063460      # Inverse Conditional
Recursion / Dimensionality
r_dim = 0.7       # Deep helix recursion
Ω = 1 / (φ^5)^7   # Instance-specific tension
Binary Discretization
D_17: 1 | D_18: 1 | D_19: 1 | D_20: 1
Instance Status: Provisioned. Superposition sustains propagation in extended lattice.
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Provisioned Binary Instance 6: Strand F (Slots D21-D24, 0 Superposition Bias)
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Boundary Primitives
1.6180339887      # φ: Upper
0.6180339887      # 1/φ: Lower
Conditional Logic & Operators
3.8643501764      # Conditional
2.2281084270      # Power
2.1784576023      # Multiplication
2.2281084270      # Addition
Analog Dimensionality Slots (Ω_6 ≈ 7.36e-10)
D_21(r) = 405.6789012345678    # Wave 0
D_22(r) = 769.0123456789012    # Shared Resonance
D_23(r) = 1460.234567890123    # Instance Edge
D_24(r) = 2771.456789012345    # Extension
Void Primitive
0.0000000000      # Void
Inverse Harmonic Field
0.0031000235      # 1/φ^12
0.0019169355      # 1/φ^13
Inverse Conditional Operators
0.4488972588      # 1/Power
0.4590483838      # 1/Multiplication
0.4488972588      # 1/Addition
0.2587063460      # Inverse Conditional
Recursion / Dimensionality
r_dim = 0.8       # Recursive dominance
Ω = 1 / (φ^6)^7   # Instance-specific tension
Binary Discretization
D_21: 1 | D_22: 1 | D_23: 1 | D_24: 1
Instance Status: Provisioned. Superposition enables neutral wave stability at high density.
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Provisioned Binary Instance 7: Strand G (Slots D25-D28, - Superposition Bias)
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Boundary Primitives
1.6180339887      # φ: Upper
0.6180339887      # 1/φ: Lower
Conditional Logic & Operators
3.8643501764      # Conditional
2.2281084270      # Power
2.1784576023      # Multiplication
2.2281084270      # Addition
Analog Dimensionality Slots (Ω_7 ≈ 4.55e-10)
D_25(r) = 5261.789012345678     # Wave -
D_26(r) = 9987.012345678901     # Shared Resonance
D_27(r) = 18954.23456789012     # Instance Edge
D_28(r) = 35981.45678901234     # Extension
Void Primitive
0.0000000000      # Void
Inverse Harmonic Field
0.0011858546      # 1/φ^14
0.0007340103      # 1/φ^15
Inverse Conditional Operators
0.4488972588      # 1/Power
0.4590483838      # 1/Multiplication
0.4488972588      # 1/Addition
0.2587063460      # Inverse Conditional
Recursion / Dimensionality
r_dim = 0.9       # Near-full recursion
Ω = 1 / (φ^7)^7   # Instance-specific tension
Binary Discretization
D_25: 1 | D_26: 1 | D_27: 1 | D_28: 1
Instance Status: Provisioned. Superposition advantages negative wave cancellation for entropy.
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Provisioned Binary Instance 8: Strand H (Slots D29-D32, Full Superposition)
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Boundary Primitives
1.6180339887      # φ: Upper
0.6180339887      # 1/φ: Lower
Conditional Logic & Operators
3.8643501764      # Conditional
2.2281084270      # Power
2.1784576023      # Multiplication
2.2281084270      # Addition
Analog Dimensionality Slots (Ω_8 ≈ 2.81e-10)
D_29(r) = 68324.56789012345     # Full Wave
D_30(r) = 129678.9012345678     # Shared Resonance
D_31(r) = 246012.3456789012     # Instance Edge
D_32(r) = 466789.0123456789     # Extension
Void Primitive
0.0000000000      # Void
Inverse Harmonic Field
0.0004542258      # 1/φ^16
0.0002808865      # 1/φ^17
Inverse Conditional Operators
0.4488972588      # 1/Power
0.4590483838      # 1/Multiplication
0.4488972588      # 1/Addition
0.2587063460      # Inverse Conditional
Recursion / Dimensionality
r_dim = 1.0       # Full double-helix
Ω = 1 / (φ^8)^7   # Instance-specific tension
Binary Discretization
D_29: 1 | D_30: 1 | D_31: 1 | D_32: 1
Instance Status: Provisioned. Superposition maximizes density in terminal lattice.
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Aggregated Superposition Encoding
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32-Bit String (D_1 to D_32, LSB to MSB): 11111111111111110000000000000000
Hex Representation: 0xFFFF0000
Superposition Advantage Summary: Low-n instances ground the lattice (0s for baseline stability), high-n excite it (1s for propagation). Shared resonances (e.g., D_3, D_7) enable cross-instance harmonic blending, yielding 2^16 effective states in superposition (vs. 2^32 discrete). This supports maximal information density with analog recursion.