Experimental BIP-39 research: prime-coordinate representation and entropy analysisI am sharing an independent experimental research project exploring a deterministic positional representation of the BIP-39 English word space and its relationship with prime-number coordinates.
The project maps each BIP-39 word position (1–2048) to the corresponding ordinal odd prime and extends the local 2048-position space into an absolute-coordinate model.
The purpose is
not to propose a replacement for BIP-39 or claim additional cryptographic entropy. The prime-coordinate mapping, absolute coordinates, structural filters and duplicate-history mechanisms do
not add entropy.
For the documented 12-word construction where the first BIP-39 word is fixed/known, that word fixes 11 bits and the remaining 117 entropy bits are generated using a cryptographically secure random source before the BIP-39 checksum is constructed.
The repository currently includes:
- 12-word and 24-word BIP-39 experimental generators
- absolute prime-coordinate representation
- bidirectional positional anchoring at a selected mnemonic slot
- BIP-39 checksum-preserving construction
- structural rejection filters
- SHA-256 + SQLite duplicate-history mechanisms
- automated exhaustive and randomized verification tests
- reproducible Python source code and research datasets
What I would particularly like the Bitcoin technical community to reviewI would appreciate criticism or independent verification concerning:
- entropy accounting when a mnemonic position is predetermined
- whether the absolute-coordinate representation introduces any overlooked statistical bias
- the mathematical implications of the structural rejection filters
- the BIP-39 checksum construction
- the reproducibility methodology and test coverage
The project is experimental research software and has not been audited for real wallet custody. Published/generated mnemonics must be treated as test material and should not be used to secure real funds.
Source code and reproducibility material:GitHub — BIP39 Prime Entropy ResearchArchived research release:Zenodo — DOI 10.5281/zenodo.22257814Article presenting the project:LinkedIn — Architecture of Infinity / BIP-39 researchI am especially interested in technical objections. If there is a flaw in the entropy reasoning, positional model, filtering methodology or implementation, I would prefer that it be identified explicitly so it can be tested and documented.
