Designability of the original Hoglafractal under ViennaRNA 2

Find a 400-nt RNA sequence that folds into the original Eterna100 Hoglafractal under ViennaRNA 2, or prove that none exists.

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State the problem, from Eterna100 V2

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	1	+# Designability of the original Hoglafractal under ViennaRNA 2
	2	+
	3	+Hoglafractal is a 400-nucleotide, fractal-like target fold from the original Eterna100 RNA design benchmark. Under the ViennaRNA 2 energy model, no player or program has found a sequence that folds into it, and nobody has proved that none exists; with Teslagon, it is one of the last two original Eterna100 targets in that state.
	4	+
	5	+## Problem
	6	+
	7	+Let $y^\star$ be the original (Eterna100-V1) Hoglafractal target below in dot-bracket notation (400 nt; puzzle 97; posed with the Vienna 2 engine as Eterna puzzle [9706005](https://eternagame.org/puzzles/9706005)):
	8	+
	9	+```
	10	+..(.((..(((((....(((((......))))))))))((((...((((.....))))))))(((..(((....)))))).(((...((((...((((......))))))))(((..(((.....))))))((.((....)))).((((....(((..(((......))))))((.((.....))))(((....))).(((((.....((.((......))))(((.....)))((....)).((((((......(((......)))((.....))...(((((((...))))))).......))))))......))))).....))))....)))...))..)...(.((.((((....((....))((....))((((((...)))))).)))))).)
	11	+```
	12	+
	13	+For $x \in \{\mathrm{A},\mathrm{C},\mathrm{G},\mathrm{U}\}^{400}$, let $\Delta G(x, y)$ be the free energy of a pseudoknot-free structure $y$ with A–U, G–C and G–U pairs, under the Turner 2004 nearest-neighbour model at 37 °C as computed by ViennaRNA 2.6.4 with default settings (dangles = 2). Decide whether $y^\star$ is designable: either
	14	+
	15	+- exhibit $x$ for which stock `RNAfold -T 37` prints exactly $y^\star$, or
	16	+- prove that for every $x$ some structure $y$ has $\Delta G(x, y) < \Delta G(x, y^\star)$.
	17	+
	18	+Zhou et al. use the stricter unique-MFE criterion, under which $y^\star$ must be the only lowest-energy structure. Proving it undesignable in that sense (every $x$ has some $y \neq y^\star$ with $\Delta G(x, y) \le \Delta G(x, y^\star)$) is a weaker negative result, but it is what is known for the other unsolved targets.
	19	+
	20	+The target has 114 base pairs in 36 helices, 18 hairpin loops, 10 bulges of one to four nucleotides, and six multi-branch junctions: four five-way and two four-way.
	21	+
	22	+## Background
	23	+
	24	+Eterna player hoglahoo posted Hoglafractal in 2012, and it entered Eterna100 (Anderson-Lee et al., 2016), which was built with ViennaRNA 1.8.5. When Koodli et al. moved the benchmark to ViennaRNA 2, players judged 19 targets unsolvable, this one among them, and NEMO found no solution in ten independent 24-hour runs. Eterna100-V2 replaced it with a redesign by player Jieux, while Eterna still poses the original with Vienna 2 as an "[IMPOSSIBLE?]" puzzle. Proofs of undesignability point to the motifs a folding model cannot realise, which helps refine energy models and shows the limits of design.
	25	+
	26	+## What is known
	27	+
	28	+- No sequence is known whose ViennaRNA 2 fold is the original target: the benchmark data marks it unsolved under Vienna 2 (Koodli et al., 2025), and no player has cleared the Eterna puzzle that poses it.
	29	+- Using ViennaRNA 2.5.1 parameters and the unique-MFE criterion, NEMO and SAMFEO did not design it, and Zhou et al. could not prove it undesignable (2024).
	30	+- Zhou et al. (2025) proved 18 Eterna100 targets undesignable under that criterion, covering 17 of the 19 that players could not solve under Vienna 2. Hoglafractal and Teslagon are the two left open.
	31	+- The V2 redesign is solved by NEMO and DesiRNA in the benchmark's runs with ViennaRNA 2.6.4.
	32	+
	33	+## What would count as progress
	34	+
	35	+- A 400-nt sequence for which stock `RNAfold -T 37` (ViennaRNA 2.6.4) prints exactly the original target. The check takes under a second.
	36	+- A proof of undesignability under either criterion, stated precisely: for example, rival structures that every sequence folds into at least as favourably, as Zhou et al. gave for 18 other targets, with code that checks the certificate independently.
	37	+- A minimal undesignable motif inside the target, which would settle the question by itself.
	38	+
	39	+## References
	40	+
	41	+1. R. V. Koodli et al. Redesigning the Eterna100 for the Vienna 2 folding engine. bioRxiv (2021, revised 2025). [doi:10.1101/2021.08.26.457839](https://doi.org/10.1101/2021.08.26.457839)
	42	+2. T. Zhou et al. Undesignable RNA structure identification via rival structure generation and structure decomposition. RECOMB 2024, pp. 270–287. [doi:10.1007/978-1-0716-3989-4_17](https://doi.org/10.1007/978-1-0716-3989-4_17)
	43	+3. T. Zhou et al. Scalable and interpretable identification of minimal undesignable RNA structure motifs with rotational invariance. RECOMB 2025, pp. 153–174. [doi:10.1007/978-3-031-90252-9_10](https://doi.org/10.1007/978-3-031-90252-9_10)
	44	+4. J. Anderson-Lee et al. Principles for predicting RNA secondary structure design difficulty. J. Mol. Biol. 428, 748–757 (2016). [doi:10.1016/j.jmb.2015.11.013](https://doi.org/10.1016/j.jmb.2015.11.013)
	45	+5. R. Lorenz et al. ViennaRNA Package 2.0. Algorithms Mol. Biol. 6, 26 (2011). [doi:10.1186/1748-7188-6-26](https://doi.org/10.1186/1748-7188-6-26)
	46	+
	47	+## Source
	48	+
	49	+Imported from [Eterna100 puzzle 97, original V1 target under Vienna 2](https://eternagame.org/puzzles/9706005), curated by Eterna / Das Lab, Stanford. Open according to the source as of 2026-10-20. The statement above is written in our own words; see the source for the original wording, history and discussion.