🫐🎪 BlueberryCircus

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BlueberryCircus is a Python laboratory for testing stochastic electrodynamics, not a proof that classical vacuum noise reproduces hydrogen. Its linear oscillator remains an exact benchmark, while its Coulomb sector evaluates three narrower claims: Puthoff’s circular-orbit absorption and radiation balance, Nieuwenhuizen’s near-ionization rectification threshold (L_c=16/(5\pi\sqrt3)), and Setterfield’s proposed static vacuum co-scaling, which leaves dimensionless hydrogen dynamics unchanged after time rescaling. The v0.1.0 escape run is retained only as an accelerated numerical stress test because its damping ratio is about 13,000 times the physical Bohr-unit value and it unbinds in less than one tenth of an orbit, so it cannot stand as a reproduction of physical hydrogen self-ionization; certificates verify numerical claims under explicit assumptions, not the truth of SED itself.

Version 0.3.0 adds an energy-audited hypothesis tournament. It computes the complete point-charge D(E,L) surface before testing a driven Setterfield map, a reciprocal finite shell, an inverse-square control, and a conservative multipole-storage surrogate. Its finite-mode statistics validate the perturbative response kernel, not a nonlinear long-time trajectory. See the tournament specification.

Artifact label: simulation-repo

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
• Physical Bohr units and an independently integrated near-ionization threshold
• Static Setterfield co-scaling map with a trajectory-conjugacy regression test
• Complete point-charge drift surface with perihelion-adapted quadrature
• Seven-channel energy ledgers and a closed five-state classification vocabulary
• Four preregistered hypothesis arms with exact zero-parameter recovery controls
• Chunkable 32-seed/2,048-mode research command with deterministic JSON/NPZ output
• Phase-space covariance with symplectic readout
• Seeded ensemble runs for power balance
• Cole–Zou moving spectral window
• Generic unbinding-time diagnostics for bounded numerical windows
• Re-checkable certificates on every reported number
• SI and physical Bohr units; accelerated scaled units for oscillator/stress tests

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	—
Puthoff circular balance $P_{\rm abs}=P_{\rm rad}$	residual <10⁻¹²	circular harmonic approximation	residual_le_tol
Ground-state angular momentum	$L/\hbar = $ 1 (algebraic identity, not a measurement)	Bohr / Puthoff	—
Rectification threshold	$L_c=$ 0.5880841551	independent improper quadrature vs $16/(5\pi\sqrt3)$	residual_le_tol
Critical perihelion	$r_p=$ 0.172921 $a_0$	$L_c^2/2$ near-ionization asymptote	—
Setterfield static co-scaling	trajectory conjugacy <10⁻⁹	$x_U(Ut)=x_1(t)$ and mapped velocities	regression
Point-charge drift surface	18 preregistered cells	full Eq. (2.34), both endpoint limits	regression
Inverse-square defining maximum	$H_{\max}=$ 7.327 at $\mu\approx0.590$	printed kernel gives $d_c\approx-53.69$, not prose −35.8	quadrature
Multipole closed Hamiltonian	relative total-energy error <10⁻⁶	no ZPF or damping	conservation
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
Accelerated stress unbinding	0.0696 orbit at 13,368× physical damping	v0.1.0 fixture only	diagnostic, not physical

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
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	near-ionization rectification threshold	quadrature recovers $L_c$ within $10^{-8}$; drift changes sign there	A

O2 remains the normalization gate: if the simulated field does not give $\hbar/2m\omega_0$ for the spring, every Coulomb result downstream is meaningless. O5 is now the primary reproducible Coulomb result: a conditional near-zero-energy drift asymptote, not a stationary distribution.

Limitations

• The published long-duration 3-D studies report self-ionization, including later relativistic and renormalized-noise attempts. BlueberryCircus does not claim to reproduce those physical timescales with its accelerated fixture.
• Nieuwenhuizen rectification is a conditional drift in energy space. It does not establish equilibrium vacuum-energy extraction, usable net work, or evasion of detailed balance; broken symmetry alone is insufficient.
• Setterfield co-scaling is represented as a speculative static hypothesis. Its invariants and trajectory conjugacy show that the static profile is dynamically inert after time reparameterization.
• A time-dependent Setterfield profile is an externally driven variable-mass Hamiltonian; any apparent suppression with nonzero parameter work is classified ACTIVE_CONTROL.
• The finite-shell and multipole arms are response/surrogate models. They are not validated electron or proton structure models. The stochastic tournament is perturbative and does not replace a physical-timescale nonlinear ensemble.
• Direct quadrature of Nieuwenhuizen's printed inverse-square kernel gives $d_c\approx-53.69$, while the paper's prose quotes −35.8 from its endpoint. Both are retained explicitly; neither establishes a physical inverse-square force.
• Matching the quantum 1s density remains 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).
• T. M. Nieuwenhuizen, On the stability of classical orbits of the hydrogen ground state in Stochastic Electrodynamics, Entropy 18, 135 (2016), arXiv:1611.10200.
• B. Setterfield, ZPE and Atomic Constants’ Behavior, behaviorzpe3.html (speculative scaling proposal, tested here as a hypothesis only).
• T. M. Nieuwenhuizen, Stochastic Electrodynamics: Renormalized Noise in the Hydrogen Ground-State Problem, Front. Phys. 8, 335 (2020), doi:10.3389/fphy.2020.00335.
• G. Moddel & O. Dmitriyeva, Extraction of Zero-Point Energy from the Vacuum, arXiv:0910.5893 (equilibrium/detailed-balance assessment).
• J. A. E. Rodríguez, extended-charge motivation, arXiv:1201.6168 (the implemented multipole oscillator is a clearly labeled surrogate).

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: 134 passed, 2 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_rectification.py      # certified Puthoff + O5 threshold
python examples/demo_hydrogen_coulomb.py   # accelerated Coulomb stress fixture
python examples/demo_hypothesis_tournament.py # reduced schema/ledger smoke
blueberry-tournament --profile preregistered --arm all # manifest only

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

Nanarch Technologies — Photonic & Quantum Intelligence Systems