FQFT Prediction Ledger & Empirical Calibration Register

7-Tier Prediction Taxonomy, Parameter Accounting & Empirical Verification Status

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Research Root · FQFT Frontier · Prediction Ledger & Empirical Accounting

Institutional Authority: Global Institute of Logic & Cybernetics (GILC)
Parent Framework: Fractal Quantum Field Theory (FQFT)
Corpus Layer: Empirical Confrontation & Falsifiable Science

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1. Epistemic Law & Prediction Taxonomy

In strict accordance with scientific integrity, the corpus enforces the fundamental demarcation:

$$\boxed{{\displaystyle \text{Fit}\ne \text{Retrodiction}\ne \text{Cross-Validation}\ne \text{Prospective Prediction}\ne \text{Empirical Confirmation}}}$$

Every quantitative statement is classified into exactly one tier of the 7-Tier Prediction Taxonomy:

Tier	Epistemic Classification	Scientific Definition	Current Examples
P0	FORMAL_IDENTITY	Exact mathematical identity derived purely from axioms without parameter tuning.	Shifted Laplacian spectrum $\lambda ({\mathrm{\Delta }}_5)=5-\lambda (A_5)$
P1	NUMERICAL_BENCHMARK	Computational verification of equations on synthetic or toy substrates.	KKT saddle-point residual $|Cu|<{10}^{-12}$, graph cycle space dimension
P2	CALIBRATED_RETRODICTION	Reproduction of known empirical values through parameter tuning / fitting.	3-generation mass relation ($q=5,D_H^{\ast }=27.6,{\mathrm{\Lambda }}_{\sigma },m_0$)
P3	HELD_OUT_VALIDATION	Testing calibrated models on empirical data held out during parameter fitting.	Validation across held-out neutrino mass splittings (Target)
P4	PROSPECTIVE_PREDICTION	Pre-registered, sealed prediction of an unmeasured physical observable.	Pre-registered LIV photon arrival delay or new resonance
P5	EMPIRICAL_TEST_RESULT	First direct observational confrontation of a P4 prospective prediction.	Observational comparison against Fermi-LAT or electron $g-2$ data
P6	REPLICATED_EMPIRICAL_RESULT	Independent, cross-instrument confirmation of an empirical finding.	Replicated multi-observatory confirmation

Epistemic Hard Rule

A quantity obtained after tuning against measured values may never be subsequently called a prediction of those same values. The 3-generation mass relation remains P2 CALIBRATED_RETRODICTION.

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2. Parameter Accounting & Degrees of Freedom

For the current FQFT mass scaling relation $m_k^2=m_0^2+{\mathrm{\Lambda }}_{\sigma }^2{\lambda }_k^{D_H^{\ast }/2}$:

Parameter / Choice	Formal Role	Value / Specification	Calibration vs Derivation Status
$q=5$	Graph Vertex Degree	$5$ (Integer)	Selected model assumption (FQFT-R1)
${\lambda }_1,{\lambda }_2,{\lambda }_3$	Spectral Eigenvalues	$\{2.403,5.000,7.597\}\in [1,9]$	Symmetrically selected eigenvalues of ${\mathrm{\Delta }}_5$
$D_H^{\ast }$	Effective Dimension	$27.6\pm 0.3$	Fitted parameter (UNRESOLVED_NUMERICAL_CLAIM)
${\mathrm{\Lambda }}_{\sigma }$	Energy Scale	$\sim 1.0\times {10}^{-5}\text{ MeV}$	Calibrated scale parameter
$m_0$	Base Mass	$0.511\text{ MeV}$	Externally supplied boundary condition (electron mass)
Particle Mapping	Generation Index	Lepton / Quark Sector	Assumed mapping heuristic

Degrees of Freedom Ledger:

• $N_{\text{data}}$ (Data points fitted): $3$ (Lepton masses $e,\mu ,\tau$)
• $N_{\text{free}}$ (Free/tuned parameters): $3$ ($D_H^{\ast },{\mathrm{\Lambda }}_{\sigma },m_0$)
• $N_{\text{effective}}$ (Effective degrees of freedom): $N_{\text{data}}-N_{\text{free}}=0$
• $N_{\text{heldout}}$ (Held-out test observables): $0$
• Conclusion: $\text{PROSPECTIVE\_PREDICTIVE\_EVIDENCE}=\text{NONE}$ (Fit quality cannot substitute for prospective confirmation).

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3. Experimental Access Channels

Observational confrontation is partitioned into three rigorous experimental channels:

graph TD
    CH1["Channel E1: Lorentz-Invariance Violation (LIV)"] --> GRB["Archival Fermi-LAT GRB Data: E_QG,1 > 7.6 E_Pl"]
    CH2["Channel E2: Electron Magnetic Anomaly (g-2)"] --> G2["Harvard / LKB Precision Measurements: a_e = a_e(SM) + delta a_e(FQFT)"]
    CH3["Channel E3: Particle Mass Spectra"] --> P2["Calibrated Retrodiction vs Held-Out Tests"]

3.1 Channel E1: Lorentz-Violating Photon Dispersion

• Status: INACTIVE pending formal derivation of energy-dependent photon group velocity $v(E)=c[1-{\xi }_1(E/E_{\text{QG}})]$.
• Benchmark Boundary: Fermi-LAT 95% CL limit $E_{\text{QG},1}>7.6E_{\text{Pl}}$ sets a strict ceiling on allowable linear dispersion.

3.2 Channel E2: Electron Magnetic Moment ($g-2$)

• Status: INACTIVE pending derivation of explicit FQFT loop correction $\delta a_e^{\text{FQFT}}$.
• Independence Rule: Must use independently measured fine-structure constant $\alpha$ (e.g., from Cs/Rb atom recoil experiments), avoiding circular reliance on global CODATA adjustments.

3.3 Channel E3: Particle Mass Spectra

• Status: P2 CALIBRATED_RETRODICTION.

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4. Canonical Continuations

Domain	Resource	Focus
FQFT Master Node	Fractal Quantum Field Theory	Parent framework and scale-recursive field grammar
Falsifiability Matrix	FQFT Falsifiability Matrix	Pre-registered failure criteria and adversarial null tests
Artifact Dependency Map	FQFT Artifact Map	Computational code, prediction ledger, and review routes
Computational Companion	FQFT Computational Companion	Reproducible prediction verification protocol and Zenodo bridge
DOI Locking Protocol	FQFT DOI Locking Protocol	Metadata verification and provenance locking rules
Formal Mathematics	Mathematics Gateway	28 machine-verified Lean 4 proofs across 9 modules