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The 36-month research path
Seven proposed work packages: management and open science (WP1), four research work packages matching SO1–SO4 (WP2–WP5), integration (WP6) and DeepRAP portfolio activities (WP7); 135 person-months over 36 months.
ANULUM / RESEARCH
Explore KYMA
An educational phase-locking lab, the preliminary probe results and the proposed work plan of the submitted KYMA proposal.
Submitted · under evaluation · no funding awarded · Updated 18 October 2026 · Proposed duration: 36 months
01 / AN EDUCATIONAL MODEL
When do two rhythms lock?
Two oscillators have different natural frequencies. Coupling can make their phase difference settle. Try stronger coupling, greater detuning or a different starting phase.
Prediction: stable locking is possible when |Δω| < 2K.
Changing a parameter resets the experiment. Animation starts only when you choose Run; Pause stops it. The controls stay local to your browser.
- Simulation time
- 0.00 s
- Phase difference
- 120.0°
- Coherence R
- 0.500
High coherence at one instant is not proof of frequency locking. Observe whether the phase difference settles over time.
The equations and their scope
θ̇₁ = 1 − Δω/2 + K sin(θ₂ − θ₁)
θ̇₂ = 1 + Δω/2 − K sin(θ₂ − θ₁)
δ̇ = Δω − 2K sin δ
For K > 0 and |Δω| < 2K, the locally stable fixed point is δ* = arcsin(Δω/2K). At the equality boundary the linear attraction vanishes. With no coupling and equal frequencies, the initial phase difference is preserved; it is not attracted to a learned motif.
This two-unit deterministic model has no training, relation gating or checker. It illustrates phase locking; it does not reproduce the KYMA probes or demonstrate reasoning, transferable abstraction or an energy advantage. The proposed programme tests those questions separately.
02 / PRELIMINARY TOY-SCALE PROBES
A result needs its conditions.
Inspect each experiment together with its assumptions and what it leaves open. Scores belong to different tasks; compare methods within the selected probe.
v2 — oscillator-generated labels
17 oscillators with per-relation gated coupling and five training seeds. The labels come from an oscillator system.
| Method | Accuracy | Spread or note |
|---|---|---|
| See original results | Source files linked below | |
What this supports
Pass of the frozen contract on this task.
What it does not establish
Transfer to other task families, the role of the dynamics and energy use.
All protocols were frozen before training. The first probe (v1, July 2026) did not pass its contract and was published with its diagnosis. Where the ground truth had cyclic structure, the phase model beat every generic learned baseline we trained; on two first tests with other structure, phase and conventional models were close, and tests of this size decide nothing in either direction. The hypothesis that a phase representation acts as a symmetry prior was formulated after these results; the proposed research tests it with predictions frozen before each run.
Read the original public result files without interactive controls
- v2 results
- v2.1 controls and leave-one-out results
- v3 results at a pinned revision
- v3 dynamics ablation at a pinned revision
- Three-valued logic and NoRA: numbers in the submitted proposal; replication bundle released with deliverable D2.1.
03 / THE PROPOSED WORK PLAN
What happens before a claim?
Choose a work package to see its planned outputs and dependencies. Month numbers are relative to a proposed start; they are not calendar dates or evidence of completed work.
THE M12 DECISION (MS1)
Go or adapt.
If SO1 fails the MS1 gate, the comparison and the negative report are published, and SO2–SO4 continue on the validation-selected conventional representation, with phase modules only where they were shown to help. This does not meet the central target of SO1 and will not be reported as if it did. The trust spine (SO3), the certificate interface (SO2) and the energy protocol (SO5) do not depend on the outcome of SO1.