01 / 05
The missing information is a loop phase
In the magnetic Aharonov–Bohm idealization, a charged wave can travel through a region where the accessible magnetic field vanishes while paths enclose excluded magnetic flux. The relative phase is fixed by the flux. Gauge-invariant holonomy records this information around a noncontractible loop. The phase depends on the charge convention; observable interference is gauge invariant.
This is established ordinary-space quantum mechanics. The project’s progress was to correct its observation contract: retain the quantum preparation and connection together, up to gauge, including noncontractible holonomies. It was not a new explanation requiring a fourth physical spatial direction.
02 / 05
A point detector became a finite aperture
The punctured-grid benchmark has 72 vertices, 120 links and 48 independent faces, leaving one hole and one independent loop phase. At its specified time, zero flux and half an electron flux quantum give different point-detector probabilities; cutting the loop removes the flux dependence. A separate implementation checks the finite evolution.
The finite-width follow-up supplied an annular Schrödinger problem in dimensionless units. At time 6 on the finest first-run mesh, the integrated detector-sector probabilities were 0.2238462247 at zero flux and 0.0425240701 at half flux. The central point is dark at half flux, while nearby probability still enters a finite sector. Those are finite-model values, with no certified continuum error bound at that late time.
03 / 05
The first acceptance test failed
Full-wave spatial reduction ratios of roughly 2.17–2.20 missed the first frozen minimum of 2.5. A separately frozen deeper challenge, using up to 512 radial intervals and 1,024 angles, reached 2.60–2.71 and passed its scoped minimum. It remained short of a factor-four full-wave regime. Selected low eigenvalues converging near factor four do not certify the complete evolving packet.
The original failed gate stays in the record. Independent small-grid sparse propagation, gauge checks and selected-mode checks support specific numerical statements; they cannot be substituted for a convergence theorem or a calibrated apparatus.
04 / 05
A proposed lens baseline needed a correction
The lens audit reproduced the published Lentzen correction to an ideal toroidal-lens calculation. For a contractible rectangle entirely inside its smooth field-free bore, the corrected loop integral vanishes, with a normalized numerical residual at most 1.55×10⁻¹⁵. Reversing radial signs creates a persistent artifact. Ordinary AB holonomy around excluded flux remains intact.
Eighteen checksum-verified historical detector frames form nine pairs. A simple radial-dilation estimator proved unstable on nickel-ring profiles, explaining only about 9.7–17.9% of processed radial contrast. These fits do not supply an accepted physical lens parameter or evidence for another dimension. The correction reproduces published work; it is not claimed as an original discovery.
05 / 05
The next observation must include the apparatus
The next physical test needs an open-propagation model with independently bounded beam coherence, specimen and support, fringing fields, imaging transfer, pixel response and calibration correlations. Freeze its prediction and uncertainty distribution before scoring newly reserved frames. Already inspected images remain development evidence.
The interactive phase figure on this page shows ideal equal-arm, point-readout interference only. It is an illustration of the imported phase law, not the finite-aperture PDE, the microscope model, or an experimental result.
Evidence & sources
Source-bound editorial synthesis of the cited record. The claim classes above separate imported physics, conditional mathematics, finite simulations, historical measurements and prospective tests.
- Aharonov & Bohm, 1959 ↗
- Lentzen correction, 2024 ↗
- Finite-width report and failed gate —
AB_Continuum_Report.md
Reviewed source record · full text outside this preview - Lens correction and measured-data limits —
AB_Lens_Results.md
Reviewed source record · full text outside this preview - Punctured-grid benchmark —
Aharonov_Bohm_Report.md
Reviewed source record · full text outside this preview