Reflector-Independence of a Frozen Codebook's Label-Free Commissioning Bound: No Geometric, Multiscale, Learned, or Ensembled Re-parameterization Confers Non-Obvious Label-Free Value

Reflector-Independence of a Frozen Codebook's Label-Free Commissioning Bound: No Geometric, Multiscale, Learned, or Ensembled Re-parameterization Confers Non-Obvious Label-Free Value Randolph James Ferlic, M.D. and Kimberly Kate Ferlic — Fieldstone Analytics, LLC, Austin, TX, USA Preprint · Zenodo DOI: 10.5281/zenodo.23788045 · CC-BY 4.0 · Community: spiral-domain-encoder-campaign · Follow-up to "Commissioning Without Labels" (Zenodo 10.5281/zenodo.23775800); characterizes a property of a previously filed and published method and discloses no new patentable subject matter. Abstract A frozen, deterministic single-token encoder maps each window of signal to one 8-bit token indexing a bounded ≤256-cell codebook; the table entry is the decision, computed bit-exactly in microseconds and sub-milliwatts. A companion study ("Commissioning Without Labels") showed this table can be built label-free only in a bounded regime, because one build step — a supervised linear projection that places the decision axis — needs labels, and no unsupervised stand-in reproduces it when the discriminative direction is a low-variance axis buried under nuisance variation. This record tests the most natural escape: could a cleverer re-parameterization of the signal — a "reflector" — make the class axis salient and unlock label-free commissioning for free? It pre-registers one decisive metric, G2 = the gain of label-free commissioning in a reflector's space over few-shot-supervised training on the same labels in the same space; a reflector is a genuine mechanism only if its G2 clears a margin that survives a step up in label budget. Across ten re-parameterizations (a semi-supervised discriminant regularizer, a geometric log-polar reflector, a multiscale wavelet-scattering reflector, a Fourier log-spectrum, a random projection, RBF random Fourier features, PCA whitening, a learned kernel embedding (Nyström), a trained autoencoder, and an ensemble stack) on 23 real multivariate datasets, the answer is a clean, mechanistic no: the commissioning bound is reflector-independent. Every family — including a representation learned from the data (a trained autoencoder, among the most negative of all) — sits below the non-obviousness margin, with bootstrap 95% confidence intervals to match. Highlights · The discriminant-regularizer adds nothing. Semi-supervised discriminant analysis (unlabeled data as a graph-Laplacian penalty on the projection) gains −0.017 over few-shot-supervised at a 64-label budget; the Laplacian term itself contributes only +0.008 over the unlabeled-variance baseline. · Geometric and multiscale reflectors are active but narrow — and they converge. Both genuinely shrink the label-free gap, but only on scale/periodic signals whose nuisance is a multiplicative scaling they linearize; the two independent families rescue the same two datasets (a bearing set and a periodic-motion set) and leave identity-confounded signals (ECG subject identity, activity-vs-subject) unmoved. The convergence sharpens the mechanism rather than broadening the capability. · The one apparent rescue is a label-budget mirage. On the bearing set, label-free in the best reflector space reaches 0.89 AUROC, while simply training on the same 64 labels reaches 0.95–0.97 (ceiling 0.997). Its decisive G2 is marginally positive only at the smallest budget (+0.034 at k=8, below +0.05) and negative at every larger budget. (One bounded industrial takeaway survives: for genuinely zero-label commissioning of scale-confounded signals such as bearings, a log-polar front end does lift commissioning from 0.82 to 0.89 by un-confounding the RPM/load scaling — a representation benefit confined to the zero-label regime, not a reduction in the label budget.) · The reflector zoo is uniform. Across nine reflector families and all 198 decisive comparisons, every family's mean G2 is negative at every budget; exactly three comparisons exceed the +0.05 margin — all at the smallest budget (k=8), and all three reverse to strongly negative at k=16. A trained autoencoder and an ensemble are no exception — the autoencoder is in fact among the most negative — and a 10,000-sample bootstrap places every reflector's 95% CI below the +0.05 margin (eight of nine significantly negative). · Reflector-independence. No task-agnostic re-parameterization — hand-designed, learned, or ensembled — supplies the information that identifies the class direction, because that information lives in the labels. The deployment recipe is unchanged and better defended: commission label-free where the few-label agreement screen clears, else label a few examples and train. The transferable lesson A label-free method that improves under a clever representation must always be measured against few-shot-supervised in that same representation — any representation that aids unsupervised clustering is equally available to a supervised learner, and the supervised learner, told which direction is the class, wins. Read constructively, the result states exactly what it would take to commission this codebook without labels, and each option is labels in disguise: spend more labels (then it is supervised commissioning), design a class-preserving augmentation (declaring which transforms preserve the class is weak supervision), or supply a domain-specific prior (task knowledge, re-chosen per deployment). There is no fourth option, because the one missing quantity — which of the many directions in the data is the decision — is defined only by the labels. What this record contains · Manuscript_Paper68.pdf / .docx — the manuscript (four figures; the six pre-registrations, the SDA probe, the spiral and scattering arms, the decisive gain test, the nine-reflector hardening zoo (with a trained autoencoder and bootstrap confidence intervals), a discussion of the mechanism, generality boundary, and deployment implication, and a skeptic Q&A). · PAPER_68_ZENODO_ARCHIVE.zip — the reproducibility archive: the six frozen pre-registrations, the campaign runners (the SDA probe, the spiral and scattering arms, the spiral gain test, and the nine-reflector tiers) plus the program's shared machinery, the per-probe result records (JSON), the four 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). Reflector-Independence of a Frozen Codebook's Label-Free Commissioning Bound. Zenodo. https://doi.org/10.5281/zenodo.23788045 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 — whether any task-agnostic re-parameterization can relax the label-free commissioning bound — of a previously filed and published method (the class-discriminant single-token codebook and its deployment-sizing law). The logarithmic-spiral / log-polar transform, wavelet scattering, Fourier features, random projections, random Fourier features, kernel PCA / Nyström, PCA whitening, semi-supervised discriminant analysis, and reflector ensembling are established prior art or standard tools, used only as instruments or comparators; each candidate was tested against a few-shot-supervised baseline and conferred no budget-robust non-obvious gain. 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. © 2026 Fieldstone Analytics, LLC and the authors. Inquiries: randolphf@fieldstoneanalyticsllc.com. Companion deposits (spiral-domain-encoder-campaign) · Commissioning Without Labels — the companion study whose label-free commissioning bound this record tests against reflectors (doi:10.5281/zenodo.23775800). Is continuation of. · The Deployment-Sizing Law — established the codebook's commissioning label-hunger (doi:10.5281/zenodo.23323323). References. · When Does a Frozen One-Byte Token Suffice? — the separability law and its screen (doi:10.5281/zenodo.23288053). References. · Watch the Input — the finding that a foundation-model embedding underperforms domain features for a task-specific role, cited for the learned reflector (doi:10.5281/zenodo.23351878). References. · Class-discriminant single-token codebook — the base encoder (doi:10.5281/zenodo.20788187). References. Data and reproducibility All datasets are public and are not redistributed — point the loaders at a local copy: the UEA and UCR time-series archives, and the standard CWRU, MFPT, UCI-HAR, MIT-BIH ECG, and robot force–torque and EMG sets. The decisive comparisons focus on the eleven "collapse" datasets (where label-free fails and a reflector could help), with GroupKFold entity-disjoint folds, multiple seeds, and macro-AUROC; each study fixes its seeds and its a-priori bands. Absolute paths and handles are scrubbed; no company name appears. Keywords frozen token; single-token encoder; class-discriminant codebook; label-free commissioning; reflector-independence; re-parameterization; inductive bias; representation learning; log-polar transform; logarithmic spiral; wavelet scattering; Fourier features; random projection; random Fourier features; kernel PCA; Nyström method; PCA whitening; semi-supervised discriminant analysis; few-shot supervised; non-obviousness; label budget; pre-registration; unsupervised learning; deployment sizing; bearing fault diagnosis; multivariate time series classification; UEA archive; UCR archive; CWRU; MFPT; MIT-BIH ECG; deterministic inference; auditable AI; edge AI; honest negative; reproducibility; autoencoder; no-free-lunch; self-supervised learning; contrastive learning; deep cluster