Quote from: bit_mind on July 18, 2025, 01:51:06 PM

Quote from: napros on July 18, 2025, 08:11:40 AM

PHI Proof: Bitcoin Markets + Puzzles
Market Evidence:

Golden Ratio Multiplier (350DMA × φ) accurately predicted every BTC cycle top
Historical: 21x→13x→5x→3x following Fibonacci descent
Current $100k+ resistance = 1.6x (φ) level

Puzzle Evidence:

P69 solved at 0.72% (not random 50% average)
Shows non-uniform distribution exists
Pattern analysis reveals φ⁻¹ (0.618) positioning correlations

Mathematical Foundation:
Position = Range × (φ⁻¹ + calibration_offset)
Where φ⁻¹ = 0.618033988749895
Cross-Domain Link:
Both markets and puzzles follow logarithmic patterns where φ emerges naturally. Same mathematical principles, different applications.
Statistical Proof:
Testing on known solutions shows >15% improvement over random distribution. P69's early position validates φ-based positioning theory.
Conclusion: φ is mathematically valid for both Bitcoin markets and puzzle solving. Different domains, same underlying harmonic principles.

This is not near the 50% mark you’d expect in a uniformly distributed brute-force search space. Instead, it’s very close to φ⁻¹² ≈ 0.072, which is a compelling correlation.
If you hypothesize that:

Puzzle creators intentionally embedded key locations based on Golden Ratio offsets, or

Real-world entropy biases accidentally favored certain ranges,

Okay lets talk bout this golden ratio "if" somehow work misteriously..

This is the full phi

n   φⁿ   %

1   0.6180339887   61.8034%
2   0.3819660113   38.1966%
3   0.2360679775   23.6068%
4   0.1458980338   14.5898%
5   0.0901699437   9.0170%
6   0.0557280900   5.5728%
7   0.0344418537   3.4442%
8   0.0212862365   2.1286%
9   0.0131556172   1.3156%
10   0.0081306193   0.8131%
11   0.0050249980   0.5025%
12   0.0031056213   0.3106%
13   0.0019193767   0.1919%
14   0.0011860504   0.1186%
15   0.0007333263   0.0733%
16   0.0004527241   0.0453%
17   0.0002806022   0.0281%
18   0.0001721218   0.0172%
19   0.0001084804   0.0108%
20   0.0000636414   0.0064%

n   1 - φⁿ   %

1   0.3819660113   38.1966%
2   0.6180339887   61.8034%
3   0.7639320225   76.3932%
4   0.8541019662   85.4102%
5   0.9098300563   90.9830%
6   0.9442719100   94.4272%
7   0.9655581463   96.5558%
8   0.9787137635   97.8714%
9   0.9868443828   98.6844%
10   0.9918693807   99.1869%
11   0.9949750020   99.4975%
12   0.9968943787   99.6894%
13   0.9980806233   99.8081%
14   0.9988139496   99.8814%
15   0.9992666737   99.9267%
16   0.9995472759   99.9547%
17   0.9997193978   99.9719%
18   0.9998278782   99.9828%
19   0.9998915196   99.9892%
20   0.9999363586   99.9936%

P70 64.4%
P69 0.72%
P68 49.01%
P67 79.78%
P66 25.62%
P65 65.71%
P64 92.98%
P63 95.01%
P62 69.5%
P61 23.67%
P60 96.9%
P59 82.17%
P58 38.76%
P57 91.85%
P56 22.73%
P55 66.79%
P54 10.74%
P53 50.18%
P52 87.25%
P51 82.86%
P50 8.56%
P49 45.35%
P48 35.86%
P47 70.06%

This is the picture of phi lines vs solution.
Mybe anyone can figure it out ? Or not ?
https://yourimageshare.com/ib/Bpv5YbxK04

Then offset?🤔
How bout incase of p68 p49 p47 etc wich is not around the ratio..??

If it work , can you use phi formula for each hex digit ? Or just relative to the given keyspace ? 🤔