# Environment AI writing code for simulations to test new models of particles

> Source: <https://github.com/openwave-labs/openwave/blob/main/MODELS.md>
> Published: 2026-06-18 06:12:37+00:00

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](/openwave-labs/openwave/blob/main/LICENSE).

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.

| 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.

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 (✅ + [Summary count](#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.

| 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` |
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 physics
`0_STATUS.md` |
| 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` |
Wave-center standing-wave lock-in demonstrated; mass values come from EWT's analytic equations, not yet from in-sim dynamics
`0_STATUS.md` |
| 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` |
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` |
| 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` |
🚧 [not yet tested] Not addressed; where active neutrinos fit is an open question in the framework (none yet) |
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` |
🚧 [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 | 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` |
🚧 [not yet tested] Q_CS = −1 positron analog identified, not yet computed numerically (none yet) |
Opposite-phase wave centers annihilate in-sim, with documented assists (0.5λ threshold, damping, velocity clamp)
`0_STATUS.md` |
| Magnetic moment μ + spin J | 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` |
| 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` |
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:
|
| 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` |
✅ [validated in-platform] Escape via oscillation: true neutral ground state found by BVP (zero sign changes, K₁ exponential tail)
`sandbox_v11/` |
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` |
| 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/` |
🚧 [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:
|
| 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) |
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` |
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) |

| 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` |
🚧 [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` |
| Magnetic force | 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` |
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:
|
| Strong force / confinement | 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 | 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` |
🚧 [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 | 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) |

| 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` |
✅ [validated in-platform] A_μ is the electromagnetic four-potential by construction; delocalized J-field wave modes coexist with solitons
`0d_canonical.md` |
Scalar wave propagation only (no polarization structure)
`research/` |
| 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` |
🚧 [not yet tested] QM not derived; the classical field carries the e^{iωt} ansatz, quantum behavior is outside current scope (none yet) |
The scalar wave equation is the postulated substrate, not an emergent result
`0_WAVE_EQUATION.md` |
| 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/` |
🚧 [not yet tested] Not addressed (none yet) |
Standing-wave lock-in demonstrated: same-phase wave centers sit in energy wells at λ separation; selectivity fragile under perturbation
`0_STATUS.md` |

| Status | Liquid Crystal (M5) | Ouroboros (M6) | EWT (M3) |
|---|---|---|---|
| ✅ validated in-platform | 8 | 4 | 0 |
| 6 | 5 | 8 | |
| ❌ honest negative | 0 | 0 | 3 |
| 🔶 in progress | 0 | 0 | 0 |
| 🚧 planned / not yet | 7 | 12 | 10 |
Total criteria |
21 |
21 |
21 |

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.

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 units
`4c_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 script
`0a_equations.md` |
| Formal artifacts | Every claim backed by a runnable open script + research note; documented negatives (M5.2, the M5.7 nulls) preserved as results
`10_summary_report.md` |
Author's Lean 4 proof artifacts (linking number, mountain-pass existence, power counting) + our independent numerical reproduction of the canonical profile and benchmark
`0d_canonical.md` |
Runnable scripts + an explicit honest-blockers status doc
`0_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` |
Author's roadmap: NEGF vertex check, sub-MeV searches, six-peak Gaia-stream annual modulation of the J-field flux
`0e_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` |
n/a |

| Model | Deep dive |
|---|---|
| Liquid Crystal (M5) |
`10_summary_report.md` |

[: full program;](/openwave-labs/openwave/blob/main/openwave/xperiments/m5_liquid_crystal/research/0b_M5_roadmap.md)

`0b_M5_roadmap.md`

[: emergence catalog + open questions](/openwave-labs/openwave/blob/main/openwave/xperiments/m5_liquid_crystal/research/0b_question_tracker.md)

`0b_question_tracker.md`

[: canonical numerical specification](/openwave-labs/openwave/blob/main/openwave/xperiments/m6_ouroboros/research/0d_canonical.md)`0d_canonical.md`

[: targets, achieved, honest blockers](/openwave-labs/openwave/blob/main/openwave/xperiments/m3_wolff_lafreniere/research/0_STATUS.md)`0_STATUS.md`

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](/openwave-labs/openwave/blob/main/CONTRIBUTING.md) and

[for structure, and open an issue to propose a new column.](/openwave-labs/openwave/blob/main/SYS_ARCH.md)

`SYS_ARCH.md`