Research
Observer Bit Model
An adversary can record a full ceremony (camera, screen capture, network tap) and still learn nothing usable about the secret. The model separates two quantities people casually call “bits.”
Surface bits are what an observer can record; effective bits are mutual information with the secret, and those are different quantities.ValidatedH_surface ≈ log₂(6) ≈ 2.585 bits per bearing; I_effective is designed to be zero under the Rosario–Wang observer model.
A full recording of the ceremony yields zero effective bits about the secret.ValidatedUniform synonym marginals and one-shot burn keep I(secret ; observation | challenge) = 0; capture is not compromise.Holds under the reference architecture
Surface bits
Surface bits are the Shannon entropy of symbols an observer can physically write down: which of six bearings was chosen, what the screen displayed. For one character entry with six equiprobable bearings:
H_surface ≈ log₂(6) ≈ 2.585 bits per character
That number is strictly positive and grows with ceremony length. The notebook fills up.
Effective bits
Effective bits are mutual information between the secret and the observation, how many bits of the secret those recordings actually pin down. Under the Rosario–Wang construction the design goal is exact:
I_effective(secret ; observation) = 0 bits
Recording is not learning. Capture is not compromise. Frequency analysis and cross-session correlation fail because the observable marginal is uniform and independent of the secret; the only remaining strategy is undirected brute force against a space the ledger rate-limits.
Why the wedge holds
- Disjoint alphabet rings partition the symbol universe so each character lives in exactly one ring.
- Foliation collapses selection to colored zones (six equiprobable leaves, not letter frequencies).
- A private synonym maps zones to bearings so every public symbol is uniform given the challenge.
- One-shot burn means a captured transcript cannot be replayed as fresh authority.