RLWC 2.0 — Vantamere Transport Certifier
Scalar transport envelopes, defect-depth analysis, and exact-rational finite-time leakage certificates.
Author line: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Version: 2.0.0 · Date: 2026-10-05 · Status: research software / unreviewed mathematical manuscript
RLWC takes a finite-dimensional, controlled coupling model and answers a practical question:
How much population can reach a forbidden output during a specified schedule, even if the dynamics inside the intervening modules are unknown or strong?
The release supplies proofs, a Python package, a command-line interface, exact-rational JSON certificates, examples, regression tests, and reproducibility records. It is not an experimentally validated device, a certified industrial safety product, a general quantum computer simulator, or a proven state-of-the-art improvement.
What changed from version 1
The main result is no longer a renamed trace-norm identity or a claim of new Aharonov–Bohm caging. Version 2 develops a trajectory-dependent scalar-envelope theorem: under independent bounds on inter-block coupling norms, any block-population trajectory of a coherent system has a real scalar-network realization. Conversely, scalar controls embed in a block network. Thus the universal worst-case population envelope, for a pure input and the stated unrestricted uncertainty class, is independent of the internal block dimensions.
A second result makes this useful without solving an optimal-control problem. On a chain of algebraically generated defect layers, let b_j(t) bound coupling from layer j to j+1. Set z_0=1 and z'_k=b_(k-1) z_(k-1). Transfer into layer d or beyond is at most min(1,z_d(T)^2). For constant equal couplings this is min(1,((b T)^d/d!)^2).
A residual budget handles skipped-layer couplings instead of silently discarding them. The exact-rational engine has no floating-point rank decisions, underflow, sampled-time maxima, or floating-point norm estimates. Its guarantee is for the supplied exact model; accurate hardware modeling remains the user's responsibility.
Installation and first run
Python 3.10 or later:
python -m pip install .
python -m rlwc demo --output results/my_demo.json
python -m rlwc bound examples/six_barriers.json --output results/my_certificate.json
python -m rlwc design --exposure 0.2 --probability 1e-12
Run the complete tests:
python -m pip install ".[verify]"
python -m pytest -q
Windows users can run run_demo_windows.bat from the extracted release directory. It creates a local virtual environment and installs dependencies; it does not upload files or request credentials. Linux/macOS users can run bash run_demo.sh. Windows execution itself was not available for testing; the Python commands and an isolated installation were tested on Linux.
Verified example
Six boundaries, each with dimensionless integrated coupling b T = 0.05, give the exact bound
probability <= 1 / 2123366400000000000000
<= 4.70950279706790124e-22
This is an upper bound, not a claimed measured error rate. It assumes no unmodeled bypass and the coherent dynamics specified in the model. A direct extra coupling of 0.0001 is detected and dominates the certificate; see results/shortcut_certificate.json.
The same two couplings, opened in opposite temporal orders, give a forward upper bound of 0.0036 and an exact reverse-order bound of zero. Their static interaction graph is identical.
Entry points
rlwc.rational.certify_model: exact-rational coordinate-block bounds; real symmetric inputs; decimal/rational strings required.rlwc.algebra.analyze_depth: automatic nominal-algebra orbit closure and defect layers; complex Hermitian inputs; numerical rank estimates.rlwc.exact.exact_depth: small exact symbolic depth and a minimum-defect word witness; optional SymPy.rlwc.bounds.certificate_for_schedule: residual-aware numerical certificate for arbitrary orthogonal layers, input and output subspaces.rlwc.envelope.population_projection: trajectory-dependent scalar probability-current representation.rlwc.envelope.scalar_chain_probability: one feasible scalar-control trajectory, not an optimized upper bound.rlwc.capacity.breach_capacity: legacy algebraic envelope with its correct limitations.
Read docs/USER_GUIDE.md for the model format and paper/manuscript.pdf for the full statements and proofs.
Practical scope
Directly applicable as mathematics to finite-dimensional coherent quantum networks and lossless linear coupled-mode models written as i dx/dt=H(t)x, with Hermitian H. Potential uses include crosstalk screening, pulse-schedule review, coupled-resonator isolation, and selecting a minimum number of barriers for a prescribed risk budget. These are demonstrated model-level uses, not industrial deployments.
The ordered bound also extends to block-local Lindblad noise. For skipped-layer Hamiltonian residuals, the noisy and coherent residual corrections differ; both are explicitly returned. Inter-block relaxation, jumps, gain, nonlinear dynamics and non-Hermitian effective Hamiltonians are not covered by the coherent bound.
Evidence and limits
results/pytest.txt records 100 passing tests in the release environment, including exact rational calculations, randomized complex-Hermitian cases, symbolic witnesses, shortcuts, temporal reversal, the scalar-current identity, and block-local dephasing.
A cached schedule-screening benchmark is included. It excludes structure discovery and coupling-norm computation and compares upper-bound evaluation with dense SciPy simulations of a different task. It is not a universal speedup claim.
Novelty is not independently established. Probability-current speed limits, graph-distance short-time laws, invariant-subspace methods, noiseless subsystems, non-Abelian caging, and nested quantum superswitches all have prior art. docs/PRIORITY_AUDIT.md identifies the overlaps. The candidate contribution is their carefully delimited synthesis into a scalar-envelope / algebraic-depth / residual-certified workflow.
Attribution and license
MIT license applies to this release, including source and the supplied original documentation. Author metadata follows the requested author line and is not an institutional affiliation or a claim that a human researcher independently verified the work. This is AI-developed research. No external publication, DOI registration, peer review, or hardware validation has been performed by this package.