Phi-Genesis

Phi-Genesis — Spectral Research Home

Sierpiński-gasket spectral structure, boundary-condition experiments, reproducible computation, and evidence-bounded research.

🟢 FEATURED RESEARCH RECORD

Spectral decimation, corner-defect corrections, and the target-index selection audit

Phi-Genesis separates numerically reproduced spectral structure, finite-level estimates, preregistered tests, and open conjectures. The research record does not establish an independent spectral rule selecting the target indices ({1,12,17,40}), and it does not claim a completed physical mass-generation mechanism.

Phi-Genesis is the RFT-SIRM spectral research programme for the Sierpiński gasket. Begin with the research map and the boundaries of the available evidence; then inspect the results, selection protocol, computational methods, and chronology. The versioned source records remain authoritative.

Scope: Phi-Genesis is a numerical spectral audit. Its findings do not inherit the Lean proof status of the separate Evgeny-Theorem repository. A reproduced finite-level observation, a statistical test, a fitted relation, and a mathematical theorem are different evidence classes.

Research map

Use the Research Map to navigate the research hierarchy, spectral anchor, evidence labels, and unresolved questions. The map is organized by research relationship and evidence status, not by an implied claim that every downstream hypothesis follows from the spectral observations.

The mathematical anchor

For the Sierpiński gasket, the theoretical spectral exponent is

[ \frac{d_s}{2}=\frac{\ln 3}{\ln 5}\approx 0.6826. ]

The factor-five spectral-decimation structure and Fukushima–Shima gap structure are reproduced numerically within the documented finite-level scope, with corner-defect corrections for the corner-degree-2 graph Laplacian. Finite-window estimates remain sensitive to the counting window and estimator; the known exponent is a consistency reference, not a new prediction.

The proposed mass relation

[ m=A n ]

uses a fitted scale and the target indices ({1,12,17,40}). Those indices have not been independently derived from a spectral invariant. The relation is a fit, not a prediction.

Research strands

Strand	Primary page	Current status
Spectral decimation and gap structure	Verified Results	Numerically reproduced within the documented scope; corner corrections matter
Spectral counting and spectral dimension	Open Problems	Finite-level exponent estimates remain window-sensitive
Möbius / (\pi)-flux boundary conditions	Verified Results	Tested configurations open a gap; target selection is not established
Target-index selection ({1,12,17,40})	Selection Protocol	Preregistered tests did not meet the decision threshold
Reproducibility and search provenance	Data & Provenance	Versioned records and code are the source of truth
Interactive exploration and chronology	Interactive Portal · History	Separate from the main documentation

Documentation

Document	Purpose
Research Map	Research hierarchy, evidence classes, and reading order
Verified Results	Numerical observations, measurements, and explicit limitations
Selection Protocol	Preregistered search families, thresholds, and negative results
Open Problems	Unresolved questions and requirements for further work
Methodology	Statistical design, power checks, and look-elsewhere correction
Reproducibility	Environment, commands, and reproduction entry points
Computational Architecture	Computational modules, tests, and data artifacts
Data & Provenance	Source-of-truth hierarchy and cumulative search record
Protocol Ledger	Recorded evaluations and limitations of the historical search record
Preregistration	Binding protocol versions and decision rules
Changelog	Version history and material changes
Glossary	Terms used throughout the spectral audit
Support	Research correspondence and reproducibility feedback

Selected results and limits

Spectral decimation: eigenvalues scale by approximately a factor of five between levels, subject to the documented corner-defect correction.
Weyl exponent: (d_s/2=\ln 3/\ln 5) is the theoretical value; finite-window estimates show phase-dependent spread.
Boundary twists: the tested full (\pi)-flux configuration opens a spectral gap, but this does not select all four target indices.
Selection audit: preregistered tests v1.0, v1.1, and v1.2.1 did not meet the required threshold. Version v1.0 was underpowered; v1.1 and v1.2.1 could reach the threshold but did not.
(\eta)-invariant: the previously claimed value (-4) was not reproduced in the documented tests.
Top-quark index: candidates 1654, 1664, and 1680 remain inconsistent under the documented scale choices; no candidate is asserted as correct.

These are bounded findings about tested operators, configurations, methods, and parameter ranges. They do not establish a physical mass-generation mechanism.

Primary research records

The versioned source records supersede summaries on this site:

Research ecosystem

Phi-Genesis is a distinct spectral-computation workstream within RFT-SIRM. Its interactive portal and research history remain separate destinations; neither replaces the main documentation or the primary records.

Explore Phi-Genesis
Interactive portal · Research map · Verified results · Open problems · Reproducibility · Dissertation · Source repository