No Winning Ticket: a Frozen Single-Token Codebook is Redundant, not a Lottery Ticket — and the pruning advantage appears only under under-provisioning

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No Winning Ticket: a Frozen Single-Token Codebook is Redundant, not a Lottery Ticket — and the pruning advantage appears only under under-provisioning Randolph James Ferlic, M.D. and Kimberly Kate Ferlic — Fieldstone Analytics, LLC, Austin, TX, USA Preprint · Zenodo DOI: 10.5281/zenodo.23701151 · CC-BY 4.0 · Community: spiral-domain-encoder-campaign · This record characterizes a property of a previously filed and published method (the class-discriminant single-token codebook and its deployment-sizing law); it discloses no new patentable subject matter. Abstract A frozen, deterministic single-token encoder reduces a window of inputs, by a fixed computation, to one 8-bit token indexing a bounded ≤256-cell codebook and a per-cell lookup. A prior program established a deployment-sizing law for this encoder — that the codebook size K can be driven far down ("size K down"), because one byte usually suffices. That raises a tempting question, borrowed from deep learning: is there a "winning sub-codebook" — a small, specific subset of cells, identifiable by an importance score, that carries the decision, in the sense of the lottery-ticket hypothesis? Answered here with a pre-registration and an exhaustive hardening battery, the answer is no — at the operating point. On 22 real multivariate datasets, pruning the codebook by cell importance (training occupancy × purity) does not beat random pruning at matched sparsity (mean advantage +0.0002, 95% CI [−0.012, +0.011], significantly below the +0.02 effect band, p=0.004); a steelman of seven importance metrics confirms it, and the geometrically-motivated metrics are actively counterproductive. What is true is strong redundancy: the codebook prunes to ~12–25% of its cells with ≤0.01 AUROC loss (often a small gain) by any selection method, and the pruned codebook is as robust as the full one under input noise, int8 quantization, and covariate drift. The iterative step that defines the neural lottery ticket has no analog on a frozen codebook (one-shot selection, a tie by construction). A winning ticket appears only in the under-provisioned regime (K≈64, near the sizing-law optimum), where a greedy label-optimal oracle beats the magnitude heuristic; it is clustering-independent (a Gaussian-mixture codebook reproduces it), so it is a function of codebook size relative to the task. We seal the boundary: at the operating point (K=256), even a greedy label-optimal oracle cannot find a reliable ticket (+0.0055 AUROC), and the magnitude heuristic hurts (−0.0095). The synthesis is a law with a sharp condition that unifies with the sizing law — the frozen codebook is redundant, not a lottery ticket; which cells you keep begins to matter only once the codebook is sized near the task's needs, and even then only trivially. The deployment corollary is practical and positive: ship a 4–8× smaller, equally-robust codebook lookup — and you need no clever pruning algorithm, because random works as well as importance. Highlights · No winning ticket at the operating point — statistically. Magnitude-importance pruning does not beat random at K=256 (mean +0.0002; 95% bootstrap CI [−0.012, +0.011]; t vs the +0.02 band = −3.28, p=0.004). A seven-metric steelman and a greedy label-optimal oracle both fail; the geometric and confidence metrics actively hurt. · Redundancy, not a ticket. The codebook prunes to ~12–25% of its cells with ≤0.01 AUROC loss (often a small gain) by any method — the importance ranking buys nothing. This reattributes the sizing law's "size K down" to cell interchangeability. · Pruning is free under deployment stress. Pruned-to-25% tracks the full codebook within ±0.02 (slightly better) under input noise, int8 quantization, and covariate drift — the redundant cells are not insurance — and it transfers to unseen entities. · A ticket only under under-provisioning. At a tight codebook (K≈64) a modest ticket appears and a greedy oracle beats magnitude; it is clustering-independent (Gaussian-mixture too), so it is about codebook size relative to the task, not k-means. · A practical corollary inside a negative. Ship a 4–8× smaller, equally-robust codebook lookup selected by the cheapest possible method — no importance ranking, no iterative prune-and-refit, no clever algorithm — a direct reduction in flash footprint and lookup latency at zero accuracy and zero engineering cost. The transferable lesson A pre-registered, statistically-backed, multiply-hardened negative closes a hypothesis a careful evaluator would otherwise raise — surely a smarter pruning of the codebook helps? — and turns it into a simpler, smaller deployment. The frozen token's value is its cheapness and determinism; here even the selection of its sub-codebook turns out to be free. A map with its negatives drawn — the refuted winning ticket, the counterproductive geometric metrics, the failed separability-forecast — is worth more than an over-claimed positive. What this record contains · Manuscript_Paper66.pdf / .docx — the manuscript (comprehensive; six figures; the pre-registration, the main battery, the four hardening tiers, the boundary seal, the statistics, the regime map, prior work, and the deployment corollary). · PAPER_66_ZENODO_ARCHIVE.zip — the reproducibility archive: the frozen pre-registration, the campaign runners (main battery, Tier-3 metric steelman + K₀ sweep, Tier-4 deployment stress, Tier-5 greedy-oracle/mechanism/clustering, boundary-seal greedy at K=256) plus the program's shared machinery, the per-probe result records (JSON), the six figures and their builder, and a README. Public data are not redistributed; absolute paths and handles are scrubbed. Cite as Ferlic, R. J., & Ferlic, K. K. (2026). No Winning Ticket: a Frozen Single-Token Codebook is Redundant, not a Lottery Ticket. Zenodo. https://doi.org/10.5281/zenodo.23701151 License and patent notice Released under CC-BY 4.0. Consistent with that license, the deposit licenses the copyright in the text and figures only, and no patent or other intellectual-property right of the authors is licensed, waived, or conveyed by this deposit. This record discloses no new patentable subject matter. It characterizes a property — redundancy, and the absence of an importance-identifiable winning sub-codebook at a deployment-realistic codebook size — of a previously filed and published method (the class-discriminant single-token codebook and its deployment-sizing law); the codebook size and the kept-cell set are deployment-sizing parameters of that filed method. k-means and vector quantization, Fisher discriminant analysis, nearest-centroid and nearest-survivor methods, Gaussian mixtures, magnitude pruning, and greedy forward selection are established prior art or standard tools, used only as instruments or comparators. The per-deployment configuration-selection procedures are retained as trade secrets and are not disclosed. No third-party partner, customer, or commercial collaborator is named; the public datasets named are cited for reproducibility. © 2026 Fieldstone Analytics, LLC and the authors. Inquiries: randolphf@fieldstoneanalyticsllc.com. Companion deposits (spiral-domain-encoder-campaign) · When Does a Frozen One-Byte Token Suffice? — the separability law whose condition this result's regime boundary tracks (doi:10.5281/zenodo.23288053). Is part of. · The Deployment-Sizing Law — "size K down," the law this result supplies the mechanism for (doi:10.5281/zenodo.23323323). References. · The Service-Life Trajectory — companion sizing/service-life study (doi:10.5281/zenodo.23321165). References. · "The Frozen Token" — the four-laws predictive theory (doi:10.5281/zenodo.23002239). References. · The Composed Platform — the multi-capability frozen-token stack (doi:10.5281/zenodo.23401467). References. · A Deterministic Task-Discriminant Token Ladder — the channel-partition multi-token accuracy lever this result complements on the sizing axis (doi:10.5281/zenodo.22003179). References. · Class-discriminant single-token codebook — base encoder (doi:10.5281/zenodo.20788187). References. Data and reproducibility All datasets are public and are not redistributed: the UEA multivariate time-series classification archive (eleven equal-length sets) and the standard CWRU bearing, MFPT, NATOPS, UCI-HAR, MIT-BIH ECG, and robot force–torque and EMG sets. The reproducibility archive contains the frozen pre-registration, the runners and shared machinery, the result records (JSON), the six figures and their builder, and a README; absolute paths and personal identifiers are scrubbed; no company or partner names appear. This deposit continues the program's characterization of its filed and published frozen-token methods — here, a property of the deployment-sizing law — and discloses no new subject matter. Keywords frozen token; single-token encoder; one-byte token; class-discriminant codebook; vector quantization; k-means; codebook pruning; lottery ticket hypothesis; network pruning; magnitude pruning; importance ranking; winning ticket; redundancy; interchangeable cells; deployment sizing; size K down; over-provisioning; greedy forward selection; label-optimal oracle; Gaussian mixture; Fisher LDA; learning vector quantization; separability screen; honest negative; pre-registration; bootstrap confidence interval; equivalence testing; UEA archive; multivariate time series classification; CWRU; MFPT; MIT-BIH ECG; int8 quantization; drift robustness; deterministic inference; auditable AI; edge AI; TinyML; sub-milliwatt; reproducibility

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