Entropy Diagonal Analysis

Given N binary sequences S₁, S₂, ..., S_N (length L), the Cantorian diagonal inversion is:

D = [¬S₁[1], ¬S₂[2], ..., ¬S_m[m]], where m = min(N, L)

For a binary matrix M ∈ {0,1}^{N×L}, D extracts the (i,i)-th bit of each row, inverts it, and scores entropy H(D). Entropy collapse (H << 1) signals hidden structure.

Submitting for public and technical review. I already have it under review at a journal, but I am too curious on the publics opinion to stay quiet in the meantime. This is the first empirical validation of Entropy Diagonalization Analysis (EDA), a method for exposing latent structure in large datasets that standard randomness tests ignore. You extract the diagonal from a stack of binary sequences, invert those bits, and measure Shannon entropy. True randomness yields entropy ~1; structure or bias manifests as a sudden drop.

I ran three experiments over the past year, each with full control runs (random/synthetic and shuffled):

Bitcoin blockchain: I processed 800,000+ block hashes (each 256 bits), forming sliding 256×256 matrices. For each, extracted and inverted the diagonal, then hashed that string with SHA-256 and counted leading zeros. True randoms (synthetic or shuffled) always match the geometric null; real data shows a heavy tail of high-leading-zero events, especially during difficulty jumps, confirming protocol-aligned structural bias.

Global seismic data: I ran a 42-day live deployment ingesting continuous broadband waveforms from hundreds of stations. Each station was processed independently in rolling windows, diagonalized, inverted, and tracked for persistent entropy drops. Drops cluster across stations, and the system triangulates probable earthquake origins. During the trial, entropy collapse predicted earthquake onsets with median lead time ~22 minutes (max ~45 min, matched 96% of catalogued events at high station counts). Control clusters and unmatched events were extensively analyzed.

SETI/FRB radio astronomy: I pulled two rare, multiband .fil filterbank files (256×1024 chunks) from the Green Bank Telescope containing known FRB121102 bursts. Each chunk was binarized, diagonals extracted/inverted, and entropy scored. Out of thousands of candidate events, only eight showed >5σ entropy drops, and every one matched a catalogued FRB burst. There were no false positives and no anomalies in quiet controls. Heatmaps make the result visually obvious.

All code and algorithms are fully documented. Null distributions, shuffled controls, and synthetic data are all included. The method is open, Lean formalized, and reproducible. If youre interested in seeing the paper let me know, I am seeking genuine feedback and can provide all information to back my claims.