🫐🎪 BlueberryCircus

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BlueberryCircus is a Python library for stochastic electrodynamics (SED), the classical theory in which a charged particle obeys ordinary Maxwell electrodynamics while a random background field drives it.

It is designed to test whether classical stochastic electrodynamics can produce atom-like bound behavior when charged-particle dynamics interact with a randomly fluctuating electromagnetic field.

In the analytically tractable harmonic-oscillator case: the implementation reproduces the quantum ground-state variance to approximately 0.05% under its stated assumptions and numerical checks.

However, in the nonlinear Coulomb model of hydrogen: long-time trajectories eventually exhibit electron escape and self-ionization rather than a stable ground state.

Features

• RK4 integration of the SED equation of motion
• Harmonic and Coulomb binding potentials
• Random-phase plane-wave ZPF backgrounds, 3-D isotropic or 1-D
• Landau–Lifshitz radiation reaction
• numpy, Rust, and JAX backends
• Analytic oracles: Bohr radius, ground-state energy, angular momentum, oscillator variance
• Phase-space covariance with symplectic readout
• Seeded ensemble runs for power balance
• Cole–Zou moving spectral window
• Ionization-time detection
• Re-checkable certificates on every reported number
• SI and scaled unit systems

Results are accompanied by a re-checkable certificate recording its value, reference rule, tolerance, provenance, and verdict.

Install

Not yet on PyPI, so install from a checkout. Distribution name blueberry-circus, import name blueberry_circus. Python 3.10+.

# uv (recommended)
uv venv && source .venv/bin/activate
uv pip install -e ".[dev]"       # extras:  ".[jax]"  ·  ".[all]"

# or plain pip
python3 -m venv .venv && source .venv/bin/activate && pip install -e ".[dev]"

The Rust backend is an optional native build (sh scripts/build_rust.sh). The default test run covers the core suite only; the Rust, JAX, and verifier tests are opt-in markers (pytest -m rust, -m jax, -m verify).

Quick example

import blueberry_circus as bc

# A charged particle on a spring, driven by a random background field.
U = bc.Units.scaled(gamma_over_omega0=0.05, omega0=1.0)
prog = bc.Program(n_particles=1, units=U)
with prog.context as q:
    bc.Harmonic(omega0=1.0)                                       | q[0]
    bc.ZPF(band=(0.3, 3.0), n_modes=400, mode="one_dimensional")  | q[0]
    bc.RadiationReaction("landau_lifshitz")                       | q[0]

result = bc.Engine(dt=0.02, t_max=600).run(prog, x0=[0,0,0], v0=[0,0,0])
print(result.summary())          # trajectory + means/covariance + certificates

# Check the engine against the standard ground-state numbers.
from blueberry_circus import oracles as o
print(o.bohr_radius(bc.SI))                  # 5.2917721e-11 m   (rel-err 1.2e-9)
print(o.hydrogen_ground_state_energy(bc.SI) / bc.E_CHARGE)  # -13.605693 (eV)

Results

Result	Number	vs reference	rule
Particle on a spring $\langle x^2\rangle = \hbar/2m\omega_0$	rel-err 4.99×10⁻⁴	analytic, real SI electron	residual_le_tol
Full vacuum covariance †	residual 3.8×10⁻⁶	quantum vacuum $\tfrac12 I$	residual_le_tol
Integrator fidelity	rel-err 2.2×10⁻³	analytic transfer function	residual_le_tol
Bohr radius $a_0$ (closed form in SI)	rel-err 1.2×10⁻⁹	CODATA-2018	residual_le_tol
Ground-state energy $E_1$	−13.605693 eV	−13.605693 eV	—
Ground-state angular momentum	$L/\hbar = $ 1 (algebraic identity, not a measurement)	Bohr / Puthoff	—
Orbit conservation (no radiation)	$\Delta E/E \sim 10^{-14}$	exact	residual_le_tol
numpy ↔ Rust agreement	spring case bit-identical, orbit 7×10⁻¹⁴	—	—
Independent recheck	Rust re-derives the verdicts	rejects tampered bundles	separate stack
Escape time $t_{\rm ion}$	finite (no bound orbit → NULL)	N–L 2015	report / NULL-first

Only the particle-on-a-spring result is a theorem (Boyer 1975). A certificate says something about recorded numbers under a recorded rule. It does not claim physical truth, and it does not claim SED is the correct theory of the atom.

† The vacuum-covariance certificate pins the whole state rather than one number, so it rejects squeezed and thermal states that a position-only check accepts. It tracks the same physics as the spring result, so it is not an independent measurement. Details and the ultraviolet caveat are in docs/theory.md.

Bundles can also be re-derived by nanarch-verify, a separate Rust implementation of the same checking rules. A passing bundle re-derives as passing; a tampered bundle, where the stored verdict disagrees with the stored numbers, is rejected. The verifier does not ship in this repository and has no public pinned release yet. When a binary is available, point BLUEBERRY_VERIFY_BIN at it and run pytest -m verify. Without it, every certificate still re-derives its own verdict in-process via Certificate.recheck(), and the demos run audit_overclaim over the bundle they emit.

Architecture

Operation (| apply)  ─▶  Program.compile()  ─▶  Backend  ─▶  Result
  Harmonic·Coulomb        named, fail-closed     numpy│rust│jax    trajectory
  ZPF·RadiationReaction        passes            (agree to          + means/cov
                                                  tolerance)         + certificates

• numpy. The reference implementation, and the trust root.
• rust. A dependency-free C-ABI cdylib (no PyO3, no crates.io) called through ctypes, carrying the integrator's inner loop. Output for the spring case is bit-identical to numpy.
• jax. A jit/scan integrator, vmap-ready for batched runs on CPU or GPU.
• Certificates. Emitted through the canonical nanarch_certify envelope, hash-chained and re-checkable across languages. Tamper with a number and the verdict flips.

Validation ladder (O0 → O5)

	check	passes if	tier
O0	field statistics	discrete → continuum, rel-err < 5%	A
O1	Puthoff power balance	reproduces $a_0$, −13.6 eV, $L=\hbar$	A
O2	spring variance, the gate	$\langle x^2\rangle=\hbar/2m\omega_0$ to ~1%	A
O3	hydrogen radial density	→ $4r^2e^{-2r}$ (CPU-day ensembles)	B · xfail
O4	phase-space conjecture	N–L §3 (NULL where the dynamics don't reach)	B
O5	escape time, the headline	reports a finite $t_{\rm ion}$	report / NULL-first

O2 is the gate: if the simulated field doesn't give $\hbar/2m\omega_0$ for the spring, every hydrogen number downstream is meaningless. O5 is the headline: the atom falls apart, and the library says so.

Limitations

• There is no stable hydrogen ground state here. At long times the electron escapes (Nieuwenhuizen–Liska 2015). Matching the quantum 1s density is a CPU-day frontier, marked strict-xfail rather than faked.
• The orbit is chaotic. The code is deterministic and byte-reproducible on a fixed machine, but quantities like r_max depend on floating-point summation order and shift across machines. The certified quantities, meaning the conservation laws and the tolerance-gated checks, are stable. Raw chaotic outputs are not, and shouldn't be quoted as if they were.
• Non-relativistic, with dipole and point-charge approximations and a finite, band-limited background field. Each run is faithful only out to bounded times.

Provenance & citing

Framework and code © Joe Pecoraro / Nanarch Technologies, Inc., Apache-2.0. The physics below is cited prior art, not vendored, and is not claimed to originate here:

• H. E. Puthoff, Ground state of hydrogen as a zero-point-fluctuation-determined state, Phys. Rev. D 35, 3266 (1987).
• T. H. Boyer, Random electrodynamics, Phys. Rev. D 11, 790 (1975).
• D. C. Cole & Y. Zou, Phys. Lett. A 317, 14 (2003).
• T. M. Nieuwenhuizen & M. T. P. Liska, Found. Phys. 45, 1190 (2015).

The certificate layer is vendored inside the package (blueberry_circus/_vendor/nanarch_certify, a near-verbatim mirror of Nanarch's canonical copy), so import blueberry_circus works from a fresh checkout. See PROVENANCE.md and NOTICE.

Run it

pytest                                     # core suite: 89 passed, 3 xfailed, 0 skipped
sh scripts/build_rust.sh && pytest -m rust # optional: Rust backend cross-language tests
pip install ".[jax]" && pytest -m jax      # optional: JAX backend tests
pytest -m verify                           # optional: needs BLUEBERRY_VERIFY_BIN
python examples/demo_sho_ground_state.py   # certified spring ground state
python examples/demo_vacuum_covariance.py  # full vacuum covariance certificate
python examples/demo_hydrogen_coulomb.py   # orbit · radiative collapse · escape

docs/STATUS.md · docs/theory.md · docs/comparison.md

Nanarch Technologies — Photonic & Quantum Intelligence Systems