Logan Lewis

Alix Petit, Mai Lang, Logan Lewis et al.

This paper studies Set Shaping Theory (SST) in a database-index setting under a revised interpretation: SST is not treated as a competing hashing method, but as a structural pre processing layer that can be applied before an existing indexing algorithm. The experimental question is therefore whether a method improves when it is used with SST rather than with out it. The study compares linear probing, double hashing, quadratic probing, and Robin Hood hashing against their corresponding SST-augmented variants for shaping orders K = 2,4,8. Beyond mean time, the benchmark reports mean successful probes, 95th and 99th percentile probes, collisions per stored record, and maxi mum cluster length. Experiments cover load factors from 0.75 to 0.95, database sizes from M =5000 to M =500000, query multipliers up to 200 lookups per stored record, and both uniform and hotspot query distributions. The results highlight two fundamental advantages. First, SST reduces the number of RAM accesses required during retrieval. By prevent ing clusters and long probe chains from forming at insertion time, the lookup phase requires fewer memory jumps, lower probe counts, and reduced tail latency. Second, the method introduces a new way of thinking about data storage: the data are not treated as fixed objects that must be placed passively into a table, but as reversible representations that can be struc turally adapted before being written. A small metadata tag records which transformation was selected, allowing the original key to remain recoverable and the lookup process to remain deterministic.This article is connected to the Set Shaping Theory simulator project, available online at https://sst-simulator.github.io/Set-Shaping-Theory-Simulator/ where it is possible to simulate part of the results presented in the article.

Aida Koch, Logan Lewis, Lily Scott et al.

This paper studies the use of Set Shaping Theory (SST) as a reversible payload-shaping layer for least significant bit (LSB) image steganography. The proposal is not intended to replace existing steganographic methods or to compete with them as a new embedding scheme. Instead, SST is positioned as a complementary preprocessing stage that makes an existing embedding method easier to apply with lower statistical disturbance. The SST transformation increases the message length by K symbols and is implemented with the approximate and fast transformation algorithm developed by Glen Tankersley. Although the embedded payload is lengthened from N to N+K bits, the selected representation can reduce D_KL(P||Q) and therefore make the subsequent steganographic insertion less detectable under histogram-based criteria. Across 1,800 controlled simulations on four synthetic cover-image models, SST reduced D_KL(P||Q) by an average of 25.16 percent relative to a fair N+K LSB baseline, with a 95 percent confidence interval of +/- 1.22 percent. For K=8, the average reduction reached 42.81 percent. Additional robustness simulations with keyed random embedding paths confirmed the effect across several distances: at K=8, SST reduced KL divergence by 42.44 percent, Jensen-Shannon divergence by 29.62 percent, total variation by 12.41 percent, and symmetric chi-square distance by 28.30 percent. An additional image-based matrix-embedding/STC-like simulation showed that SST also reduces the minimum weighted insertion cost: relative to the unshaped K=0 reference, K=8 reduced the cost by 6.93 percent.