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Record W7118052205

Thin Tree Verification is coNP-Complete

2025· article· W7118052205 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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueArXiv.org · 2025
Typearticle
Language
FieldComputer Science
TopicComplexity and Algorithms in Graphs
Canadian institutionsUniversity of Waterloo
Fundersnot available
KeywordsK-ary treeInterval treeTree (set theory)GraphSegment treeGomory–Hu treeKruskal's algorithmSpanning tree
DOInot available

Abstract

fetched live from OpenAlex

An $α$-thin tree $T$ of a graph $G$ is a spanning tree such that every cut of $G$ has at most an $α$ proportion of its edges in $T$. The Thin Tree Conjecture proposes that there exists a function $f$ such that for any $α> 0$, every $f(α)$-edge-connected graph has an $α$-thin tree. Aside from its independent interest, an algorithm which could efficiently construct an $O(1)/k$-thin tree for a given $k$-edge-connected graph would directly lead to an $O(1)$-approximation algorithm for the asymmetric travelling salesman problem (ATSP)(arXiv:0909.2849). However, it was not even known whether it is possible to efficiently verify that a given tree is $α$-thin. We prove that determining the thinness of a tree is coNP-hard.

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)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Observational · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.502
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0000.002
Science and technology studies0.0010.001
Scholarly communication0.0000.001
Open science0.0030.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.001

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 head0.066
GPT teacher head0.286
Teacher spread0.219 · 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