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Record W3081710876 · doi:10.20382/jocg.v11i1a4

Rigid foldability is NP-hard

2018· article· en· W3081710876 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

VenueJournal of Computational Geometry (Carleton University) · 2018
Typearticle
Languageen
FieldEngineering
TopicAdvanced Materials and Mechanics
Canadian institutionsnot available
FundersDivision of Emerging Frontiers in Research and InnovationJapan Society for the Promotion of ScienceNational Science Foundation
KeywordsIntersection (aeronautics)CombinatoricsVertex (graph theory)Partition (number theory)MathematicsFolding (DSP implementation)PlanarReduction (mathematics)KinematicsFlexibility (engineering)Plane (geometry)AlgorithmComputer scienceGeometryGraphPhysicsStructural engineeringEngineeringClassical mechanics

Abstract

fetched live from OpenAlex

In this paper, we show that the rigid-foldability of a given crease pattern using all creases is weakly NP-hard by a reduction from the partition problem, and that rigid-foldability with optional creases is NP-hard by a reduction from the 1-in-3 SAT problem. Unlike flat-foldabilty of origami or flexibility of other kinematic linkages, whose complexity originates in the complexity of the layer ordering and possible self-intersection of the material, rigid foldabilltiy from a planar state is hard even though there is no potential self-intersection. In fact, the complexity comes from the combinatorial behavior of the different possible rigid folding configurations at each vertex. The results underpin the fact that it is harder to fold from an unfolded sheet of paper than to unfold a folded state back to a plane, frequently encountered problem when realizing folding-based systems such as self-folding matters and reconfigurable robots.

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)0.000
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: Not applicable · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.805
Threshold uncertainty score0.440

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
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 head0.009
GPT teacher head0.199
Teacher spread0.190 · 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