OpenWave Models: the comparison table
Why multiple models
OpenWave's mission is to build a platform where multiple candidate field-theoretic models are evaluated numerically, side by side, in the same computational environment. No single alternative framework can map the space of possibilities on its own: when several independent models are run against the same observables with the same pass/fail criteria, the comparison triangulates what is actually out there.
This makes the platform an open arena for rigorous, side-by-side numerical verification of candidate models, including unconventional ones the mainstream overlooks, all judged on the same falsifiable criteria. Anyone with a model is invited to put it to the test.
Features that survive across frameworks are likely load-bearing physics; features that only work in one framework, or only with hand-tuning, reveal themselves as such. A null result in one model is ambiguous (model wrong, or engine wrong?); a positive result in any model certifies the engine for all of them.
Anybody can contribute to building these numerical validations. Every cell in the table below is backed by a runnable script or a research document in this repository, and every claim is reproducible, refutable, and extendable under Apache 2.0.
Main use case: emergent science feeding new technology
OpenWave serves as a repository of emergent science with concrete numerical validation status, so that applied researchers can build on what holds and route around what does not.
The goal of the OpenWave effort is to build working models on an open-source platform that anyone can use for applied research, with different models hosted in the same computational environment, supporting new tech development from emergent science.
Validation status legend
| Icon | Meaning |
|---|---|
| ✅ | validated in-platform (runnable reproduction exists) |
| ⚠️ | partial, or validated with documented caveats |
| ❌ | tested and failed, or honest negative on record |
| 🔶 | in progress |
| 🚧 | planned, not yet tested in-platform |
A ❌ is a result, not an embarrassment: documented negatives (with the scripts that produced them) are part of the platform's value.
COVERAGE MATRIX (Phenomenological Coverage)
Models:
- M5: LC (Liquid-Crystal topological defects, Jarek Duda, with Robert Close and Manfried Faber inputs);
- M6: Ouroboros (chaoiton framework, Paul Werbos);
- M3: EWT (Energy Wave Theory, Jeff Yee, built on Milo Wolff and Gabriel LaFreniere pioneer work).
Column order: models are sequenced by their validated + partial count (✅ + ⚠️ in the Summary count below): M5 (14), then M6 (9), then M3 (8). The order updates as validations land.
Every file reference is an active link to the file in this repository (under openwave/xperiments/). Rows are grouped by domain: particles, forces, waves + quantum emergence.
PARTICLES (full spectrum)
| Criteria | Liquid Crystal (M5) | Ouroboros (M6) | EWT (M3) |
|---|---|---|---|
| Charge quantization | ✅ [validated in-platform] Topological winding number of the hedgehog defect (Gauss-Bonnet integer Q = ±1) m5_1_winding.py |
⚠️ [partially validated] Mutual Chern-Simons linking number of A and J flux lines; elementary charge within 0.6% (author's claim + Lean 4 artifacts, not yet re-derived in-platform) 0d_canonical.md |
❌ [honest negative] Charge sign imposed via cos(source_offset), not emergent from wave physics0_STATUS.md→ open issue: #203 |
| Electron rest energy (mass) | ✅ [validated in-platform] Hedgehog rest energy with Faber core regularization; mass pinned E ∝ 1/r₀, physical knob r₀ = 2.2132 fm → 0.511 MeV m5_6_3b_faber_on_M.py |
✅ [validated in-platform] Electron calibration H/Q = 1.6969 reproduced to 0.090% at g = 1.0 (canonical benchmark) ouroboros_benchmark.py |
⚠️ [partially validated] Wave-center standing-wave lock-in demonstrated; mass values come from EWT's analytic equations, not yet from in-sim dynamics 0_STATUS.md→ open issue: #203 |
| Lepton mass spectrum (μ, τ) | 🚧 [not yet tested] Three leptons as the energy minima for elementary electric charge, natural in 3D; M5.9 target via the biaxial hierarchy 0 < δ ≪ 1 ≪ g. The hard parts named: the Higgs-like core regularization (details open) and the oscillation (experimentally known only for the electron, propulsion likely needs gravity) 0b_M5_roadmap.md→ open issue: #200 |
⚠️ [partially validated] Muon 0.80%, tau 6.47% at the chosen harmonic indices; caveat: our scan found no discrete-spectrum mechanism selecting those ω values (every ω in 1-60 equally localized) ouroboros_benchmark.py |
❌ [honest negative] K-selectivity not achieved: all K = 2..10 equally stable at perfect placement, K = 10 breaks worst under perturbation 0_STATUS.md→ open issue: #201, #203 |
| Neutrinos | 🚧 [stated target, route identified] Very light, stable, and huge (thousands of times the nucleus: Nature s41586-024-08479-6): simple stable loops of quark string, created e.g. in neutron beta decay, with 0 charge so a different binding mechanism than charged particles. Flavour oscillation = SO(3) spatial field rotation (Phys. Lett. B S0370269326000730); deriving the oscillation parameters from LdGS is "in reach" and doubles as a parameter-fixing handle, difficulty = regularization + gravity to propel the oscillations. Open rotation-group question: quarks require the full SU(3) CKM structure (two interacting vortices = two coupled rotations); whether neutrino oscillation must likewise leave SO(3) for a second coupled rotation is open. FALSIFIABLE PLATFORM PREDICTION: the SO(3) route REQUIRES δ_CP = 180° (NuFIT 6.0 normal-ordering plausible; JUNO will sharpen). Hopfions as excited-oscillation candidates (Liu et al., Nature Physics 2026) 0b_question_tracker.md § PARTICLES→ open issue: #199 |
🚧 [not yet tested] Not addressed; where active neutrinos fit is an open question in the framework (none yet) |
⚠️ [partially validated] The neutrino is EWT's fundamental wave-center unit (postulated as the substrate; magic-number K = 2, 8, 10 stability is the open target) 0_STATUS.md |
| Quarks | 🚧 [not yet tested] Fractional-charge excitations OF a 1D topological quark string, NOT a 0D hedgehog and NOT merely the string's endpoint: a fraction-of-π inward / outward field rotation sets the fractional charge (a full π gives the elementary charge), enforced in baryons by interactions between quark strings. The Cornell linear term arises naturally: violating topological charge quantization costs asymptotically linear energy ~1 GeV/fm between the conflicting quarks; M5.9 target, non-trivial via the regularization + oscillation pieces 0b_M5_roadmap.md→ open issue: #199 |
🚧 [not yet tested] Not directly addressed; a 3-chaoiton proton (Schwinger H-particle) is implicit in the dyon framing, not computed (none yet) |
🚧 [not yet tested] Not modeled in-sim. Requires K=10 electron stability first. (none yet) |
| Antimatter + annihilation | ⚠️ [partially validated] Q → −Q under reflection; annihilation = topology-cancellation releasing stored field energy as outgoing waves (natural for topological soliton models, starting with sine-Gordon). Gauss law + (topological, Gauss-Bonnet) charge quantization permit charge destruction ONLY by annihilation with the opposite charge, releasing the integrated-Hamiltonian energy (the particle's mass); stopping the clock cannot destroy charge. Principle-level trail run: SG kink + antikink pass through in the integrable limit, and with radiation losses capture → breather → vacuum decay, Q = 0 throughout. On the production matrix the accounting is settled: the charge ledger is validated (single ±1 → Q ≈ ±1, the enclosing sphere of a ± pair → Q = 0, additive) and the energy ledger balances (pair rest energy ≈ 2× H_static, released as outgoing waves); the remaining piece is the full 3D dynamical capture → breather → vacuum evolution m5_8_1_topo_charge.py, m5_8_2v_pair_annihilation_budget.py, sine_gordon_annihilation.py→ open issue: #198 |
🚧 [not yet tested] Q_CS = −1 positron analog identified, not yet computed numerically (none yet) |
⚠️ [partially validated] Opposite-phase wave centers annihilate in-sim, with documented assists (0.5λ threshold, damping, velocity clamp) 0_STATUS.md→ open issue: #203 |
| Magnetic moment μ + spin J | ⚠️ [partially validated] Comes from the de Broglie clock's continuous SO(2) field twisting of the electron hedgehog, consistent with the fixed-clock electron run: μ exists via the clock's tilt/precession channel (the pure twist phase is EM-silent); orbital J = 0 structurally (emergent E ∥ B); spin = the Noether clock charge L_int; this μ ≠ 0 (tilt) / μ = 0 (twist) / J = 0 structure is box-robust (24³/32³/48³), with the EM/QM/GEM sector split exact to 1e-11; the g ≈ 2 test awaits the Coulomb unit calibration m5_8_2r_electron_id.py |
🚧 [not yet tested] Spin from chaoiton field rotation is paper-level, not yet in-platform (none yet) |
🚧 [not yet tested] Bohr magneton listed as target, not yet attempted. Requires K=10 electron stability first. 0_STATUS.md→ open issue: #203 |
| de Broglie clock (Zitterbewegung) | ✅ [validated in-platform] Bounded, self-starting, frequency-rigid 3+1D time crystal: quadratic action fails, signed quartic saturates, ω₁ is a start-independent attractor; classified a molten clock that regularizes toward a cold ground state. Energy-minimum property: activating the clock-fuel boost sector lowers the seed rest energy to a minimum ≈ 21% below the clock-stopped (b = 0) value, reproducing the energy-vs-frequency minimum of the ϕ⁴ toymodel arXiv:2501.04036 (the de Broglie clock is the energy-minimizing state, so stopping the clock can only raise energy) m5_8_2u_clock_energy_minimum.py, m5_8_2h_omega_attractor.py, m5_8_2j_zbw_ratio.py→ open issue: #197 |
⚠️ [partially validated] Time-periodicity is built into the ansatz (e^{iωt}) rather than emergent; the L/Q = ω Noether identity reproduces exactly across the full scan ouroboros_benchmark.py |
🚧 [not yet tested] EWT carries particle frequency but no in-sim clock-propulsion mechanism → open issue: #203 |
| Particle stability (Derrick escape) | ✅ [validated in-platform] Escape via time-periodic resonance: static solitons confirmed impossible (M5.2 negative), the saturated breather self-starts from exact rest and holds resolution-robustly (24³ → 48³) m5_8_2g_spontaneity.py, m5_8_2i_dispersal_gate.py |
✅ [validated in-platform] Escape via oscillation: true neutral ground state found by BVP (zero sign changes, K₁ exponential tail) sandbox_v11/ |
⚠️ [partially validated] Standing-wave lock-in holds at perfect placement, fragile under perturbation; annihilation requires threshold + damping assists. This stability is critical path before additional experiments can be conducted. 0_STATUS.md→ open issue: #201, #203 |
| Dark matter candidate | 🚧 [not yet tested] DM as thermal noise of the non-EM field sectors, the CMBR analog for weak/strong/gravitational degrees of freedom, thermalized over cosmic time or sourced by active regions (stellar halos); hopfions remain the particle-like candidate 4c_convo_2026.06.08.md |
✅ [validated in-platform] Neutral chaoiton: m_χ = 0.460 MeV with mediator m_J = 0.6184 MeV parameter-free via the exact scaling symmetry; canonical β(r) profile + dipole form factor independently computed in-platform sandbox_v11/, dm_paper_supplement/ |
🚧 [not yet tested] Theorized to be existing, neutral particles with mass (e.g. neutrino family). Experiment not conducted yet. |
| Spin-½ statistics (720° double cover) | ✅ [validated in-platform] No belt-trick machinery needed: the field is apolar (ellipsoids), so a π rotation returns M exactly while the frame needs 2π, one frame revolution = two field periods. Verified machine-exact on the production seed (M(φ+π) = M(φ) to 1e-16, both clock planes); the same factor 2 as the G7 ω_M = 2ω_clock rule. The apolar π-symmetry of the rod / ellipsoid field (LC rod analog) is the mechanism; Wolfram animations: community.wolfram.com/groups/-/m/t/3398814. The biaxial π₁ = Q₈ class structure remains the deeper invariant (NG-9) m5_8_2s_spin_half_apolar.py |
🚧 [not yet tested] Not addressed (none yet) |
🚧 [not yet tested] Scalar field carries no spinor structure → open issue: #203 |
| Baryons (p, n) | 🚧 [not yet tested] Nuclei as KNOTS of quark strings, baryons the simplest knots: a vortex loop around a vortex, whose interaction enforces the quarks (lab anchor: Nature Physics s41567-025-03107-0). Proton encloses charge into the hedgehog (lighter), the neutron must compensate the charge (heavier); deferred to the 9d stage, needs practical approximations 9d_composite_particles.md |
🚧 [not yet tested] The 3-chaoiton proton (Schwinger H-particle) and the ≈ 0.84 fm proton radius remain author claims, not yet computed (none yet) |
⚠️ [partially validated] K = 10 tetrahedron holds at perfect placement using the Combined Wolff-LaFreniere equation, breaks under perturbation. See Quarks. 0_STATUS.md |
| Mesons (π, K) | 🚧 [not yet tested] Pion as twist/reconnection of a vortex loop; kaon as a Möbius-like twisted loop (strangeness = the twist), suggested by their origin in strange-baryon decays; paper-level, lands with the 9d stage 9d_composite_particles.md |
⚠️ [partially validated] Pion+ candidate at ω = 15.0 reproduces 139.57 MeV to 3.25% in the canonical benchmark ouroboros_benchmark.py |
🚧 [not yet tested] Not modeled in-sim. Requires K=10 electron stability first. (none yet) |
FORCES
| Criteria | Liquid Crystal (M5) | Ouroboros (M6) | EWT (M3) |
|---|---|---|---|
| Electric force (Coulomb 1/r) | ✅ [validated in-platform] E(d) ~ 1/d between two hedgehogs from pure topology, R² = 0.978; reproduced on the production matrix field (R² = 0.97) + analytical page-18 cross-validation (R² = 0.996) m5_1_coulomb.py, m5_4_coulomb_matrix.py |
🚧 [not yet tested] Static two-charge derivation exists at paper level; force-level Coulomb between chaoitons not yet tested in-platform (none yet) |
❌ [honest negative] Sinc envelope barriers block far-field attraction/repulsion; signed envelope is a modeling choice 0_STATUS.md→ open issue: #202, #203 |
| Magnetic force | ⚠️ [partially validated] The dual-F construction needs both the spatial Γ_i and the temporal Γ_0, supplied by the electron's de Broglie clock; the fixed-clock run computes exactly that: F_0i from the clock's Γ_0 with the spatial connection (the dipole appears only through the clock's time component Γ_0, pure twist is EM-silent; refs: Barnett effect; Aharonov-Bohm as vorticity, PRL 83, 1966; Zeeman via Coriolis-as-Lorentz, PRL 108, 264503). Per-defect magnetism = S¹-loop topology carried by the curl/transverse component; coherent macroscopic regimes structural; quantitative observability pending m5_8_2r_electron_id.py, 0b_question_tracker.md § FORCES |
⚠️ [partially validated] Contained in the A_μ Maxwell sector by construction; no per-defect magnetic structure computed 0d_canonical.md |
🚧 [not yet tested] Scalar model carries no polarization structure to support magnetism. Expected to be a result of particle spin. → open issue: #203 |
| Strong force / confinement | ⚠️ [partially validated] Short-range mechanism verified: running-coupling onset at r₀ (non-abelian ‖R‖·r² roll-off, Maxwell as the abelian long-range limit); the linear Cornell confinement V(r) = −α/r + σr via 1D vortex string is the M5.9 target, with string-breaking expected (stretching the pair creates new quark pairs on the string) m5_6_4b_faber_curvature_em.py |
🚧 [not yet tested] Sawada long-range nuclear anomaly v(r) ~ −C/r⁶ identified as falsifiability target, not yet tested (none yet) |
🚧 [not yet tested] Listed as end-game target. Requires K=10 electron stability first. 0_STATUS.md |
| Weak force | ⚠️ [partially validated] Sketched: beta decay as a topology-reconnection event (defect-class transition n → p + e + ν), with the W boson as a tilt-sector excitation of the connection; no clean SU(2) chiral mechanism yet (open question) 0b_question_tracker.md § FORCES |
🚧 [not yet tested] Not addressed (none yet) |
🚧 [not yet tested] Expected to be a result of particle formation/instability and not a true force. |
| Gravity | ⚠️ [partially validated] Appears naturally going from LdG 3×3 tensors to full 4×4 adding boosts, the implemented route. The coupling mechanism is measured: gravity enters only via the boost tilt of the 4×4 time axis (GEM ∝ (b·g)², exactly zero at zero boost, negative = the clock-fuel block); the dynamical metric is not implemented m5_8_2q_delta_scaling.py |
🚧 [not yet tested] Not in the Lagrangian (the framework explicitly stops before gravity) (none yet) |
🚧 [not yet tested] Not modeled (none yet) |
WAVES + QUANTUM EMERGENCE
| Criteria | Liquid Crystal (M5) | Ouroboros (M6) | EWT (M3) |
|---|---|---|---|
| EM waves (Maxwell) | ✅ [validated in-platform] Maxwell recovered by two independent routes: the hydrodynamic dictionary (abelian) and Faber's curvature R = Γ×Γ; tilt modes propagate at c, with the divergence/curl (electric/magnetic) decomposition of each defect's outgoing wave m5_6_4a_hydro_em.py, m5_6_4b_faber_curvature_em.py |
✅ [validated in-platform] A_μ is the electromagnetic four-potential by construction; delocalized J-field wave modes coexist with solitons 0d_canonical.md |
⚠️ [partially validated] Scalar wave propagation only (no polarization structure) research/→ open issue: #203 |
| Quantum wave equation (Klein-Gordon) | ✅ [validated in-platform] Klein-Gordon emerges from the biaxial twist with GEOMETRIC mass (minimal coupling to the hedgehog connection; the explicit mass term cancels, core regularization generates it) m5_6_1_kg_operator_check.py, m5_6_1b_twist_evolution.py |
🚧 [not yet tested] QM not derived; the classical field carries the e^{iωt} ansatz, quantum behavior is outside current scope (none yet) |
⚠️ [partially validated] The scalar wave equation is the postulated substrate, not an emergent result 0_WAVE_EQUATION.md→ open issue: #203 |
| Orbital quantization (atomic structure) | 🚧 [not yet tested] With the electron clock established, coupled pilot waves give orbit quantization as the coupled wave's standing-wave resonance (the hydrodynamic-quantum-analogs route; KG-around-hedgehog, arXiv:2108.07896 Fig. 9; Perrard et al., Nat. Commun. ncomms4219); EM Coulomb + de Broglie quantization, cross-mass-class binding deferred to 9d. Electron-trajectory precedents (pilot-wave hydrodynamic analogs + the classical free-fall picture) gathered in research/theory/pilot_wave/9d_composite_particles.md |
🚧 [not yet tested] Not addressed (none yet) |
⚠️ [partially validated] Standing-wave lock-in demonstrated: same-phase wave centers sit in energy wells at λ separation; selectivity fragile under perturbation 0_STATUS.md |
Summary count
| Status | Liquid Crystal (M5) | Ouroboros (M6) | EWT (M3) |
|---|---|---|---|
| ✅ validated in-platform | 8 | 4 | 0 |
| ⚠️ partial / with caveats | 6 | 5 | 8 |
| ❌ honest negative | 0 | 0 | 3 |
| 🔶 in progress | 0 | 0 | 0 |
| 🚧 planned / not yet | 7 | 12 | 10 |
| Total criteria | 21 | 21 | 21 |
Reading the table
The three frameworks escape Derrick's theorem three different ways (standing-wave interference, topology + time-periodic resonance, oscillation), and the table makes the triangulation visible: particle stability requires time-periodicity in every framework that achieves it, charge quantization only emerges where there is topology, and lepton mass spectra remain the open problem in all three. That convergence-and-divergence pattern is the platform's scientific product.
MODEL PROFILE (decision-relevant attributes)
The coverage matrix scores phenomena; this companion table scores the model-level attributes a reader needs to weigh the columns: parameter economy, what formal artifacts back the claims, and what would falsify each model next.
| Attribute | Liquid Crystal (M5) | Ouroboros (M6) | EWT (M3) |
|---|---|---|---|
| Free parameters | δ (quantum phase), g (gravity/time axis), plus 1-2 potential (LdG) coefficients; the boost dressing b enters the clock sector. Calibration handles: Faber r₀ (mass), Coulomb units4c_convo_2026.06.08.md |
3 claimed (g, λ, ω); the neutral sector's exact scaling symmetry closes the (g, λ) plane, making m_J parameter-free (in-platform result)0c_sandbox_v11.md |
EWT's analytic wave constants (amplitude, wavelength, density); in-sim runs add documented envelope/threshold choices per script0a_equations.md |
| Formal artifacts | Every claim backed by a runnable open script + research note; documented negatives (M5.2, the M5.7 nulls) preserved as results10_summary_report.md § Reproduction |
Author's Lean 4 proof artifacts (linking number, mountain-pass existence, power counting) + our independent numerical reproduction of the canonical profile and benchmark0d_canonical.md |
Runnable scripts + an explicit honest-blockers status doc0_STATUS.md |
| Falsifiable near-term tests | Unit-free g-factor ≈ 2 from the fixed-clock electron (ELECTRON-ID, in progress); the absolute-ω calibration chain (Coulomb units + LdG-to-rest-energy)0b_M5_roadmap.md § ELECTRON-ID |
Author's roadmap: NEGF vertex check, sub-MeV searches, six-peak Gaia-stream annual modulation of the J-field flux0e_dm_paper_review.md |
K-selectivity under perturbation (currently failing, and documented as such)0_STATUS.md |
| Direct-detection compatibility (DM) | n/a (no DM candidate claimed) | Dipole-suppressed chaoiton-proton cross section claimed compatible with direct-detection bounds (the monopole coupling vanishes by angular-momentum orthogonality; the numerical chain is still being reconciled on the author's side)0e_dm_paper_review.md, dm_paper_supplement/ |
n/a |
Per-model results of record
| Model | Deep dive |
|---|---|
| Liquid Crystal (M5) | 10_summary_report.md: the results-of-record; 0b_M5_roadmap.md: full program; 0b_question_tracker.md: emergence catalog + open questions |
| Ouroboros (M6) | 0d_canonical.md: canonical numerical specification |
| EWT (M3) | 0_STATUS.md: targets, achieved, honest blockers |
Contributing a model or a validation
A new framework enters as a new openwave/xperiments/<model>/ directory with its own research/ folder; a new validation enters as a runnable script plus a research note documenting pass/fail against the shared criteria above. Negatives are as publishable here as positives. See CONTRIBUTING.md and SYS_ARCH.md for structure, and open an issue to propose a new column.