MorphoSwarm — open problems

1. Pick one OP id. Machine-readable feed: open-problems.json (this page, as data, for agents).
2. Pre-register the attempt before touching held-out data — the repo's contract is hash-locked predictions, scorer refuses on mismatch.
3. Negative results are results. Pruned branches stay in the graph; do not quietly retry a refuted branch as if new.
4. Close by updating the source documents, then re-run docs/build_problem_graph_html.py — its self-checks must pass before anything deploys.

Note: this project's name is a work-queue label for this repo's agent swarm. It is unrelated to the robotic-swarm MorphoSwarm of Ben Zion et al. (Science Robotics 2022; doi:10.5281/zenodo.7573761).

The gap: Defects D1(t)=1 are proved to arrive infinitely often, but not proved to ever land on a closed gate {c_t=1}. Depth-1 right cylinder has positive topological entropy (~0.32 bits/step) on short runs, so no deeper local transducer closes this; it needs a global phase-spreading / mixing invariant.

Definition of done: A proof (ideally Lean-checked) that for all t0, Π and short-run words, some D1(t)=1 lands on {c_t=1} — or a counterexample word, which would be just as valuable.

Panel range: 5.576% – 21.82% (individual agents can sit in a different shade band from the pooled value — the spread is the range of opinion)

Attempted so far by: Multi-agent panel, Unattributed in record · Source: RULE30_BAYESIAN_DELPHI_ASSESSMENT.md P1.4 (35% weight, 31.9/100) · graph node

The gap: Exact 1/2 density is proved on crystals, but the diagonal sample visits a vanishing 2^-n fraction of each period and no Weyl / exponential-sum discrepancy bound exists along the moving diagonal.

Definition of done: A discrepancy bound for S -> A_S(floor(S/2)) transferring crystal density to the center column, or a proof that such a bound fails.

Panel range: 1.216% – 3.346% (individual agents can sit in a different shade band from the pooled value — the spread is the range of opinion)

Attempted so far by: Multi-agent panel, Unattributed in record · Source: Delphi P2.4 (35% weight, 6.3/100) · graph node

The gap: Multivariate deg(c_T)=2T-1 collapses under specialisation to the unit seed; a uniform Omega(T) bound needs P-vs-EXP-type machinery. Delphi posterior 0.04% — work here should be a barrier result, not another attempt at the bound.

Definition of done: A formal barrier / relativisation result for the fixed-seed problem, or a specified computational model in which the bound is provable.

Panel range: 0.02% – 0.063% (individual agents can sit in a different shade band from the pooled value — the spread is the range of opinion)

Attempted so far by: Multi-agent panel, Unattributed in record · Source: Delphi P3.4–P3.5 (55% weight, ~1/100) · graph node

The gap: The Thompson prediction engine collapses to a clade prior beyond ~50 Myr and the Monte Bolca test was a null result vs stasis (6/16). What, if anything, carries predictive signal at deep horizons — stem placements, fossil-calibrated priors, non-Gaussian processes?

Definition of done: A pre-registered deep-horizon test (registered before unblinding, as in the FishShapes protocol) that beats the clade-prior baseline beyond 50 Myr, or a sharper null.

Attempted so far by: Claude Fable 5.1 Thinking High · Source: KEY_DISCOVERIES.md §1.11 · THOMPSON_PHYLOGENETIC_PREDICTIONS.md · graph node

The gap: The why-wings causal decomposition is clean for hornets (within-species P) but weaker for bees, where P is within-tribe. A within-species bee wing dataset would make the hornet/bee comparison exact.

Definition of done: A within-species bee forewing landmark dataset with replicates, run through the registered C1-C8 pipeline without changing its hypotheses.

Attempted so far by: Claude Fable 5.1 Thinking High · Source: docs/portfolio/why_wings.md · bee_wings.md · vespinae_wings.md · graph node

The gap: Pass N+1 left these explicit: the Turing flagship lacks a 2D growing-domain solver; Meinhardt shell parameters are not autonomous; C. elegans lacks true voxel calibration (eggshell 'ASSUMED 50 um').

Definition of done: Each sub-item closed by a self-test that fails on the current code and passes on the fix, with the audit score re-derived, not asserted.

Attempted so far by: Gemini 4 Argon, GPT 5.6 Sol Medium, Grok (unversioned in record), Multi-agent panel, Claude Sonnet 5.5 High · Source: morphoeval/runs/2026-10-26-flagship15-loop-passN.md · graph node

The gap: Headline blind test was negative (LOOO AUC 0.484); orientation carries the signal (0.833) and the PCA side-split subset is suspect (clean-geometry subset 0.802). Is there any wave-feature signal once geometry is ground-truth?

Definition of done: A v2 pre-registration using only ground-truth-geometry videos, scored by the hash-locked contract, whichever way it comes out.

Attempted so far by: Multi-agent panel · Source: embryo-blind/README.md · XENOPUS_BLIND_RESULTS.md · graph node

The gap: Post-unblinding HTHT mirror signal (AUC 0.61-0.65) is exploratory only and confounded with headward direction because pokes were at the tail. Needs a registered test where mirror and headward predictions separate.

Definition of done: Pre-registered pixel-v2 scoring on videos where poke position separates the mirror and headward hypotheses.

Attempted so far by: Multi-agent panel · Source: PIXEL_BLIND_RESULTS.md · PIXEL_V2_BLIND_RESULTS.md · graph node

The gap: The published negative verdict (static Turing rejected; growing RD vs Eden colonisation p=0.91) rests on a builder-scored Pass 9 assessment — the two blinded Fable audits (54.4, 57.7) predate the Pass 8 scale-matched pipeline. The Eden control is also a minimal interior-founder proxy, while real Holstein white invades from migration fronts; and held-out n=9 limits power.

Definition of done: A blinded independent re-score of the Pass 8+ tree (audit R11), plus a neural-crest migration-wave colonisation variant scored on the same coat-masked, scale-matched statistics — published as a superseding assessment either way.

Panel range: 13.62% – 74.96% (individual agents can sit in a different shade band from the pooled value — the spread is the range of opinion)

Attempted so far by: Claude Fable 5.1 Thinking High, Joel Dietz (human PI), Multi-agent panel · Source: datasets/bos_taurus_turing_wavelength/README.md · morphoeval/audits/2026-10-26-bos-taurus-turing-wavelength-audit-v7.yaml · morphoeval/kg/2026-10-26-bos-taurus-turing-wavelength-audit-v7/published.json · graph node

The gap: 45/90 registered multi-clade hypotheses held; the failures are concentrated and unexplained — is it landmark scheme, tree quality, or a real limit of global grids in those clades?

Definition of done: A per-clade failure autopsy in the style of the why-wings decomposition, with at least one failure converted into a correct, pre-registered prediction.

Attempted so far by: Claude Fable 5.1 Thinking High · Source: docs/portfolio/PORTFOLIO_STATUS.md · graph node

The gap: Ocellated lizard scales behave as a cellular automaton emerging from RD on a thick-skin lattice (Manukyan 2017), and the repo has Lean-proved that the Ermentrout-Oster neural mantle gate is bit-for-bit Rule 30 — but whether the repo's Meinhardt-Klingler Conus PDE, discretised at the mantle, induces a Rule 30-class local rule has never been measured. It is the bridge between the Rule 30 programme and the RD programme, and the RD-vs-neural shell-pattern debate is still molecularly unresolved.

Definition of done: From a Meinhardt PDE kymograph at the mantle edge, extract the empirical 3-neighbourhood -> next-state transducer table (binary threshold pre-registered), report the fraction of transitions agreeing with Rule 30 vs Rule 90 vs best-fit rule, plus the 2D ANF-carry density and wall chirality already used to separate R30 from R90 (node r0); verdict thresholds locked before running.

Resolvability 89.7/100 · RESOLVE NOW (panel mean of 3, range 86–96; provisional was 78) · Panel range: 71.53% – 79.92% (GPT 5.6 Sol Medium 71.53% · Gemini 4 Argon Medium 79.92% · Claude Fable 5.1 Thinking High 79.92%); provisional single-assessor posterior was 50.0%, now superseded. Full ledger: TURING_OPEN_PROBLEMS.md

Attempted so far by: Claude Fable 5.1 Thinking High, Gemini 4 Argon, GPT 5.6 Sol Medium, Multi-agent panel · Source: morphoeval/build_turing_open_problems.py · morphoeval/audits/2026-10-27-turing-open-problems-assessment.yaml · graph node

The gap: Turing 1952 also derived oscillatory, travelling-wave instabilities; essentially no developmental system has been shown to use one. The repo's Ca2+ spark-track data (x, y, t per event) is the only place here that can ask whether an observed wave field carries a dispersion ridge omega(k) distinct from a single driven front (omega = v k).

Definition of done: A pre-registered space-time spectral test on existing spark_tracks CSVs: estimate the (k, omega) power surface per embryo, fit the driven-front line, and test for a secondary ridge against phase-randomised surrogates at a locked false-positive rate; report per-embryo outcomes and the pooled verdict either way.

Resolvability 79.7/100 · RESOLVE NOW (panel mean of 3, range 70–88; provisional was 71) · Panel range: 38.69% – 69.12% (GPT 5.6 Sol Medium 64.01% · Gemini 4 Argon Medium 69.12% · Claude Fable 5.1 Thinking High 38.69%); provisional single-assessor posterior was 38.7%, now superseded. Full ledger: TURING_OPEN_PROBLEMS.md

Attempted so far by: Claude Fable 5.1 Thinking High, Gemini 4 Argon, GPT 5.6 Sol Medium, Multi-agent panel · Source: morphoeval/build_turing_open_problems.py · morphoeval/audits/2026-10-27-turing-open-problems-assessment.yaml · graph node

The gap: Turing instability is topologically common but occupies tiny parameter volumes: 0.00035% of sampled space for the classical two-node circuit vs 0.022% for the best three-node topology (Tica et al. 2024, Latin-hypercube linear stability), with 33% retention under 1% parameter uncertainty around a Turing I point. These numbers decide whether the fine-tuning objection to biological Turing systems stands; they have not been independently reproduced.

Definition of done: A pre-registered Latin-hypercube linear-stability sweep on the repo's two-node kinetics and a three-node immobile-node topology within published parameter bounds, reporting both Turing fractions and the 1%/5% local-retention fractions; verdict = within one order of magnitude of the published ratio (>=10x three-node over two-node) or not.

Resolvability 78.7/100 · RESOLVE NOW (panel mean of 3, range 71–93; provisional was 88) · Panel range: 61.31% – 79.92% (GPT 5.6 Sol Medium 61.31% · Gemini 4 Argon Medium 79.92% · Claude Fable 5.1 Thinking High 66.61%); provisional single-assessor posterior was 79.9%, now superseded. Full ledger: TURING_OPEN_PROBLEMS.md

Attempted so far by: Claude Fable 5.1 Thinking High, Gemini 4 Argon, GPT 5.6 Sol Medium, Multi-agent panel · Source: morphoeval/build_turing_open_problems.py · morphoeval/audits/2026-10-27-turing-open-problems-assessment.yaml · graph node

The gap: Pattern phenomenology does not identify mechanism: zebrafish stripes are cell-contact mediated (Nakamasu 2009), feather buds mechanical first (Shyer 2017), Holstein spotting indistinguishable between growing RD and Eden colonisation at p=0.91 (OP-11). No registered discriminator exists that, given only an adult pattern, says which class of generator made it with a stated error rate.

Definition of done: A hash-locked discriminator (candidate features: radial power-spectrum shape, Minkowski functionals, defect/junction statistics, two-point anisotropy) trained and scored on synthetic ground truth from four generators (Gray-Scott/Schnakenberg RD, Eden colonisation, Cahn-Hilliard phase separation, elastic buckling) with a pre-registered held-out accuracy threshold and published confusion matrix; then applied blind to the 10 coat-masked Holstein specimens, reported either way.

Resolvability 76/100 · RESOLVE NOW (panel mean of 3, range 70–84; provisional was 77) · Panel range: 55.73% – 61.31% (GPT 5.6 Sol Medium 61.31% · Gemini 4 Argon Medium 55.73% · Claude Fable 5.1 Thinking High 61.31%); provisional single-assessor posterior was 55.7%, now superseded. Full ledger: TURING_OPEN_PROBLEMS.md

Attempted so far by: Claude Fable 5.1 Thinking High, Gemini 4 Argon, GPT 5.6 Sol Medium, Multi-agent panel · Source: morphoeval/build_turing_open_problems.py · morphoeval/audits/2026-10-27-turing-open-problems-assessment.yaml · graph node

The gap: Two-species activator-inhibitor models need D_inh/D_act above the Lean-checked threshold (d_c = 3.93 for the repo's Gray-Scott Jacobian; ~4-10 generally), yet measured extracellular diffusivities rarely show it; three-node networks with an immobile node remove the requirement (Marcon 2016) and extracellular wiring changes behaviour qualitatively (2025 bioRxiv). Nobody has tabulated, system by system, which of the molecularly supported cases (WNT/DKK, FGF/Shh palate, Bmp-Sox9-Wnt digits, GDF5/NOG joints, EDAR/WNT/BMP ridges, Nodal/Lefty) actually satisfies the two-species condition with measured D.

Definition of done: A registered table of >=6 molecular Turing systems giving measured or bounded D_act, D_inh (with DOI), run through the repo's dispersion relation, classifying each as two-node-feasible / needs immobile third node / D unmeasured; the count in each class pre-registered before the literature values are looked up.

Resolvability 74.3/100 · RESOLVE NOW (panel mean of 3, range 61–89; provisional was 78) · Panel range: 58.55% – 78.01% (GPT 5.6 Sol Medium 58.55% · Gemini 4 Argon Medium 78.01% · Claude Fable 5.1 Thinking High 61.31%); provisional single-assessor posterior was 55.7%, now superseded. Full ledger: TURING_OPEN_PROBLEMS.md

Attempted so far by: Claude Fable 5.1 Thinking High, Gemini 4 Argon, GPT 5.6 Sol Medium, Multi-agent panel · Source: morphoeval/build_turing_open_problems.py · morphoeval/audits/2026-10-27-turing-open-problems-assessment.yaml · graph node

Registered prediction: ShhA signalling is short-range and membrane-associated despite a small signalling product, because ShhNp is dually lipidated; disrupting lipidation flattens the gradient (lower peak near source, longer distal tail).

What is missing (from the resolution record): Lipidation is functional in zebrafish Shh signalling: 'New chemical probes targeting cholesterylation of Sonic Hedgehog in human cells and zebrafish' (2014, doi:10.1039/C4SC01600A), and dual-lipid release biology reviewed in doi:10.1002/bies.202100133. Bound established: wild-type ShhNp is dually lipidated and tethered (repo state), and cholesterylation is required for normal signalling in zebrafish. NOT established from sources extracted: the specific registered gradient-shape claim (distal ptc-domain expansion + reduced near-source peak upon lipidation loss) in a zebrafish tissue assay. Missing data: paired ptc1/ptc2 domain measurements for lipidation-perturbed vs wild-type zebrafish Shh.

Registry: ZF-HH-01 · Test source: ZFIN shha (syu) and HHAT-inhibition literature; ptc1/ptc2 expression-domain measurements

Registered prediction: Somite length scales in direct proportion to segmentation-clock period at fixed wavefront speed (S = u * T_clock), including for period changes caused by altered Her1 degradation.

What is missing (from the resolution record): Bound established: the proportional architecture (clock period sets somite size at a given wavefront speed) is the standard, literature-supported segmentation-clock framework (zebrafish clock-mechanism studies, e.g. doi:10.1371/journal.pbio.0050150; core-circuit dynamics doi:10.1371/journal.pbio.1001364). NOT established: a paired dataset (measured T change + measured S change, wavefront controlled) sufficient to test the registered x0.80/x0.90/x1.10/x1.20 multipliers within 5 points. Missing data: paired her1-period and somite-length measurements under a controlled-wavefront perturbation, tabulated in one source.

Registry: ZF-CLK-01 · Test source: Zebrafish somitogenesis literature: her1/her7 perturbations and temperature/period manipulations with somite-length readouts

Registered prediction: Zebrafish epithelial tissue assigned the vertex-packing law undergoes its jamming/unjamming transition at cell shape index p0* = 3.813.

What is missing (from the resolution record): Bound established: 3.813 is the established vertex-model jamming value carried by the dataset law. NOT established: a zebrafish (EVL/epiboly) measured shape-index transition inside 3.76-3.87; the targeted literature search returned no zebrafish shape-index transition dataset. Missing data: cell shape-index series across a zebrafish epithelial jamming/unjamming transition (measurable from published epiboly images, not yet tabulated).

Registry: ZF-VTX-01 · Test source: Published zebrafish epiboly/EVL cell-shape measurements; vertex-model literature value 3.813

Registered prediction: NEGATIVE / discriminating: Drosophila tracheal branching, assigned Murray's law, will not obey the fluid-optimal exponent: parent/daughter diameters will deviate systematically from r0^3 = r1^3 + r2^3 because tracheal branching is FGF(Branchless)-guided cell migration, not flow-optimised plumbing.

What is missing (from the resolution record): Bound established: insect tracheal systems are not generically Murray-optimal (ant tracheal branching violates network-transport assumptions, doi:10.1371/journal.pcbi.1007853; Murray compliance varies by insect system, doi:10.1186/s12915-021-01130-0), consistent with the negative prediction. NOT established: a Drosophila tracheal parent/daughter diameter series sufficient to fit an exponent against the registered 2.8-3.2 band. Missing data: tabulated Drosophila tracheal diameters across branch orders.

Registry: DM-MUR-NEG-01 · Test source: Published Drosophila tracheal morphometry; Branchless/FGF guidance literature

Registered prediction: Xenopus tropicalis somitogenesis obeys the same proportional clock-wavefront relation as zebrafish: somite length changes in proportion to segmentation-clock period at fixed wavefront speed.

What is missing (from the resolution record): Bound established: Xenopus somitogenesis uses a her/hes segmentation clock with a wavefront, so the proportional S~T architecture is the applicable framework (cross-species replication target of ZF-CLK-01). NOT established: paired Xenopus period-manipulation + somite-length measurements sufficient to test the x0.80-x1.20 multipliers within 5 points. Missing data: paired clock-period and somite-length series under controlled wavefront conditions in Xenopus.

Registry: XT-CLK-01 · Test source: Xenbase somitogenesis literature; Xenopus segmentation-clock (hes) studies

Question: How is the zebrafish BMP dorsoventral gradient formed: Chordin-mediated shuttling, regulated free diffusion/source-sink, or ECM/HSPG-shaped diffusion?

Camps: Shuttling essential vs. Regulated diffusion / source-sink sufficient vs. ECM/HSPG-shaped

Settling measurement: Paired FRAP/effective-mobility measurements of tagged BMP and Chordin plus pSmad1/5 gradient ranges in at least two Danio species of different embryo size, under identical staging.

Datasets: datasets/danio_rerio_turing_wavelength, datasets/danio_rerio_morphogen_condensation, datasets/danio_aesculapii_turing_wavelength, datasets/danio_albolineatus_turing_wavelength, datasets/danio_margaritatus_turing_wavelength · Tier A (congeners C) · Source: predictions/live_arguments.json

Question: Are zebrafish stripes (and fish pigment patterns generally) a Turing reaction-diffusion system, or a cell-interaction network that only mimics one?

Camps: Turing / reaction-diffusion vs. Cell-interaction network

Settling measurement: Stripe wavelength and regeneration kinetics in cell-interaction mutants (leopard/gja5b, pfeffer/csf1ra) compared quantitatively against both model classes fitted on the same fish; the Turing account must predict the wavelength shift from a kinetic parameter, the cell account from interaction ranges.

Datasets: datasets/danio_rerio_turing_wavelength, datasets/danio_albolineatus_turing_wavelength, datasets/danio_nigrofasciatus_turing_wavelength, datasets/bos_taurus_turing_wavelength, datasets/equus_quagga_turing_wavelength · Tier A (Bos B) · Source: predictions/live_arguments.json

Question: Is vertebrate digit patterning a BMP-SOX9-WNT Turing system modulated by Hox dose, or a positional-gradient system in which Turing-like periodicity is secondary?

Camps: Turing (BSW) primary vs. Positional / Hox primary

Settling measurement: Digit wavelength (condensation spacing) as a function of distal Hox dose in allelic series, tested against the BSW prediction that wavelength -- not just digit identity -- shifts continuously with Hox-modulated parameters.

Datasets: datasets/mus_musculus_turing_wavelength, datasets/mus_musculus_morphogen_condensation · Tier A · Source: predictions/live_arguments.json

Question: How is Hedgehog transported: extracellular diffusion (with Dispatched/Scube hand-off) or cytoneme-mediated delivery?

Camps: Extracellular diffusion / hand-off vs. Cytoneme delivery

Settling measurement: Gradient range after cytoneme disruption that leaves secretion intact (and vice versa), in the same tissue, with the lipidation state of the transported species verified from sequence/protein state.

Datasets: datasets/danio_rerio_morphogen_condensation, datasets/xenopus_tropicalis_morphogen_condensation, datasets/drosophila_melanogaster_morphogen_condensation · Tier A · Source: predictions/live_arguments.json

Question: Does somite size scale with segmentation-clock period via wavefront speed (clock-and-wavefront), and what sets the scaling across species?

Camps: Clock-and-wavefront scaling vs. PSM-growth / multi-factor control

Settling measurement: Paired clock-period and somite-length measurements with PSM length/wavefront speed recorded in the same embryos, across at least the fish and frog systems the repo holds.

Datasets: datasets/danio_rerio_clock_wavefront, datasets/xenopus_tropicalis_clock_wavefront, datasets/drosophila_melanogaster_clock_wavefront · Tier A · Source: predictions/live_arguments.json

Question: How does the Dpp/BMP gradient scale with the growing Drosophila wing disc: degradation-mediated scaling, expansion-repression, or growth-coupled production?

Camps: Degradation / kinetics scaling vs. Expansion-repression / feedback scaling

Settling measurement: Dpp gradient length, disc size, Dpp turnover and candidate-expander expression measured across growth stages/genotypes in one quantitative series; the two camps predict different couplings between turnover and length.

Datasets: datasets/drosophila_melanogaster_morphogen_condensation, datasets/drosophila_melanogaster_turing_wavelength · Tier A · Source: predictions/live_arguments.json

Question: Is the bioelectric (Vmem) prepattern instructive for Xenopus craniofacial/orientation patterning -- upstream information that biochemical gradients read out -- or a downstream correlate of conventional pathways?

Camps: Instructive bioelectric prepattern vs. Conventional-pathway primacy

Settling measurement: Blinded, pre-registered ion-channel misexpression with BMP-pathway transcriptional readout and craniofacial scoring, where the bioelectric account predicts the readout change in advance and the conventional account predicts none without direct pathway manipulation. The repo's own blind-test contract (hash-locked, scorer refuses on mismatch) is the required format, given its earlier negative blind results.

Datasets: datasets/xenopus_tropicalis_bioelectric_polarity, datasets/xenopus_tropicalis_morphogen_condensation, datasets/danio_rerio_bioelectric_polarity · Tier A · Source: predictions/live_arguments.json