Collatz-Anchored Inversive Manifold Encryption (CAIME): A Cryptographic Primitive via Tension Symmetry

We present the Collatz-Anchored Inversive Manifold Encryption (CAIME) protocol, a cryptographic primitive grounded in three independent mathematical structures: the Collatz conjecture's convergence dynamics, complex circle inversion, and the Pearson skewness coefficient as a smoothness gate. The protocol defines a smooth seed pair (a, b) as one whose Collatz tension distribution satisfies Sk2 = 0. This anchor deterministically generates the parameters of a circle inversion transformation IM, whose inverse is computationally hard without knowledge of the anchor. Contributions:- Feedbackloop Lemma: structural invariant of the Collatz sequence (proven)- Smoothness condition: 1.4% rarity of smooth pairs (empirically demonstrated)- Forward-inverse asymmetry: O(1) encryption vs O(m²·r) brute-force inversion- Tamper detection via Euler-Feuerbach relation Related publications:NALP Paper: https://doi.org/10.5281/zenodo.20065953Canonical Audit: https://doi.org/10.5281/zenodo.20066792