Phi-Genesis
Glossary
Spectral decimation
A recursive relation connecting spectral data at successive graph approximations. In this project, the principal scaling factor is approximately five, with corrections for the corner-degree-2 Laplacian.
Sierpiński gasket (SG)
The self-similar graph used as the main spectral substrate for the documented computations.
Spectral dimension
The exponent associated with spectral counting. For the Sierpiński gasket, the theoretical value used here is (d_s/2=\ln 3/\ln 5\approx0.6826).
Fukushima–Shima gaps
Forbidden spectral intervals associated with the spectral-decimation structure. The repository reports their finite-level numerical reproduction within the documented setup.
Möbius / (\pi)-flux boundary condition
A boundary twist used to study how flux changes the graph spectrum. The tested full (\pi)-flux configuration opens a gap, but this does not establish the target mass-index rule.
Target indices
The four integers ({1,12,17,40}) used in the proposed mass relation. Their independent derivation from a spectral invariant has not been established.
Look-elsewhere effect
The statistical inflation of apparent significance when many configurations, rules, or parameter choices are tested. Phi-Genesis records configuration counts and preregistered decision thresholds to make this risk explicit.
Null-only power check
A check, designed without looking at target outcomes, that establishes whether a protocol could reach its decision threshold under an idealized target-compatible result.
Inertia count
The number of eigenvalues below a chosen threshold, computed from the inertia of a shifted matrix. The project’s sparse-LU method is numerical and floating-point based, not a machine-checked proof.
Evidence labels
- Reproduced numerically: observed again with documented computation and scope.
- No evidence: the tested protocol did not meet its predeclared threshold.
- Not reproduced: a prior claim was not obtained in the documented tests.
- Open: current evidence does not settle the question.
- Fit, not prediction: parameters or target indices were chosen using the data being matched.
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