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Woven Continuous Frames in Hilbert Spaces

2025· article· W4416785430 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

venuePublished in a venue whose home country is Canada.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueInternational Journal of Analysis and Applications · 2025
Typearticle
Language
FieldMathematics
TopicMathematical Analysis and Transform Methods
Canadian institutionsnot available
Fundersnot available
KeywordsWeavingHilbert spaceFrame (networking)Relational frame theoryDual (grammatical number)Space (punctuation)

Abstract

fetched live from OpenAlex

In this present paper we introduce weaving Hilbert space frames in the continuous case, we propose new approaches for manufacturing pairs of woven continuous frames, and we obtain new properties in continuous weaving frame theory related to dual frames. Also, we provide some approaches for constructing continuous weaving frames by using small perturbations. These methods not only enhance the understanding of frame theory but also open avenues for practical applications in signal processing and data representation. Future research may further explore the implications of these findings in more complex systems and their potential interdisciplinary benefits.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.917
Threshold uncertainty score0.831

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0020.002
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.014
GPT teacher head0.363
Teacher spread0.349 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it