RECORD / 01
Selection protocol
Predeclared targets, null ensembles, look-elsewhere correction, and a shared p ≤ 0.01 decision threshold.
Spectral research · documented status v2.2.1
Evidence first.
Every spectrum auditable.
An interactive map of spectral decimation, boundary-condition experiments, and preregistered tests on the Sierpiński gasket—with a clear record of what has and has not been established.
NUMERICAL EVIDENCE · PREREGISTERED TESTS · EXPLICIT LIMITATIONS
01 / Research pathway
From graph spectrum to evidence audit
Select a stage to reveal its role, evidence status, and the next place to inspect.
Graph and operator. The base object is the Sierpiński-gasket graph Laplacian. Operator convention and corner-degree-2 corrections matter; numerical claims are scoped to the implemented graph and boundary conditions. Open research map →
02 / Mathematical anchor
The known exponent is a reference point
Separate established mathematical structure from finite-level estimation and physical interpretation.
Sierpiński gasket · theoretical spectral exponent
\[\frac{d_s}{2}=\frac{\ln 3}{\ln 5}\approx0.6826\]
The factor-5 decimation structure produces log-periodic signatures. Numerical estimates at finite graph levels depend on the chosen estimator and counting window; agreement with the known exponent is a consistency check, not a new prediction.
The proposed mass relation \(m=A n\) uses a fitted scale and target indices \(\{1,12,17,40\}\). The indices have not been independently derived from a spectral invariant. The relation is a fit, not a prediction.
03 / Evidence status
What the record supports
Each statement is bounded by its tested operator, graph level, estimator, and preregistered scope.
Spectral decimation and gaps
ReproducedFactor-5 scaling and Fukushima–Shima gap structure are numerically reproduced with documented corner-defect corrections for the graph Laplacian.
Finite-level spectral exponent
OpenThe theoretical value is known, but broader finite-level estimates remain sensitive to window width and phase. More levels alone do not resolve estimator dependence.
Target-index selection
No evidenceThe preregistered tests did not reach the decision criterion. This is a bounded negative result for the tested families, not proof that no possible rule exists.
η-invariant claim −4
Not reproducedThe documented tests did not reproduce the claimed value. The repository does not present it as an established topological invariant.
04 / Protocol and reproducibility
Negative results stay in the record
The search history is part of the evidence, not an appendix to be hidden.
RECORD / 02
Reproducibility
Environment setup, test commands, fixed-seed protocol runs, and estimator-study reproduction instructions.
RECORD / 03
Data provenance
Preregistration, code, data artifacts, cumulative ledger, methodology, and versioned project summary.
05 / Research chronology
From coincidence to bounded conclusion
Earlier apparent matches are retained alongside the methodological reassessment that changed their interpretation.
PHASE 01
Spectral observation
Explore graph spectra, decimation structure, and possible integer-index correspondences.
PHASE 02
Family search
Test twist, potential, product-operator, and carpet configurations.
PHASE 03
Preregistration
Fix target rules, null pools, thresholds, and power checks before evaluation.
PHASE 04
Reassessment
Correct for search multiplicity and record underpowered or unsuccessful tests honestly.
PHASE 05
Current status
No independent target-index rule established; the finite-window exponent question remains open.
06 / Related foundational work
Research dissertation
A separate RFT-SIRM research work on recursive graph operators, spectral trace defects, and higher-moment recurrence. It provides broader mathematical context but is not itself a Phi-Genesis result or evidence for the target-index selection claim.
DISSERTATION · VERSION 1.0
Recursive Graph Operators, Spectral Trace Defects, and Higher-Moment Recurrence
By Evgeny Zaprudnov · RFT-SIRM · 15 October 2026
Read the dissertation ↗Open dissertation repository ↗06 / Source of truth
The repository remains authoritative
This interactive portal is a navigation and explanation layer. It does not replace the primary records or upgrade numerical evidence into a theorem.