FQFT Falsifiability Matrix & Pre-Registration Protocol

Pre-Registered Failure Criteria, Adversarial Null Tests & Empirical Refutation Boundaries

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Research Root · FQFT Frontier · Falsifiability Matrix & Refutation Boundaries

Institutional Authority: Global Institute of Logic & Cybernetics (GILC)
Parent Framework: Fractal Quantum Field Theory (FQFT)
Corpus Layer: Empirical Methodology & Falsification Protocols

PRE_REGISTRATIONCRYPTOGRAPHICALLY SEALED

NULL_BENCHMARKS4 RIGOROUS ENSEMBLES

NULL_HYPOTHESISp_null = 0.62 (AGREED)

OBSERVATIONAL_CEILINGFermi-LAT LIV ENFORCED

EPISTEMIC_RULEPOST_SEAL_MUTATION = 0

REFUTATION BOUNDARIES // SECTION 01USER SELECTOR: SECTOR

Active Pre-Registered Falsification Matrix

SECTOR 01

FQFT-R1 Spectral Generations

ADVERSARIAL_NULL_TEST_ACTIVE

INVESTIGATED HYPOTHESIS:

3-band structure is a non-trivial graph property (H₁).

PRE-REGISTERED FALSIFICATION THRESHOLD:

Null model test: ΔAIC ≤ 0 or p_null ≥ 0.05 against degree-preserving randomized graphs.

SEALED IN OMEGA283B-AG5G CANONICAL ARTIFACT

Open FQFT Master Node →

ADVERSARIAL NULL CONTROLS // SECTION 02NULL CONTROL BENCHMARKS

Negative Control Ensembles & Benchmark Results

NEGATIVE RESULTS DISCLOSED

NULL 01DISCRIMINATION_MARGINAL

Regular Graph Null Ensemble

Baseline Tested:5-regular canonical authorial graphs.

Adversary Ensemble:Degree-preserving rewired random graphs.

Observed Outcome:Eigenvalue gap Δλ = 0.082 vs 0.079 randomized.

NULL 02NULL_NOT_REJECTED (p = 0.62)

Spectral Partition Null

Baseline Tested:Authorial three-band spectral centroids.

Adversary Ensemble:Random 3-band partition algorithms.

Observed Outcome:p_null = 0.62 agreement with null hypothesis.

NULL 03POSITIVITY_CONFIRMED

KP Nonlocal Operator Control

Baseline Tested:Nonlocal fractional kernel (-Δ_G)^s.

Adversary Ensemble:Standard combinatorial graph Laplacians.

Observed Outcome:Discrete green kernel positivity holds for s in (0, 1].

NULL 04FOLIATION_PRESERVED

Constrained FFE Control

Baseline Tested:Constrained saddle-point variational solution.

Adversary Ensemble:Unconstrained gradient descent relaxation.

Observed Outcome:Constraint penalty residual ‖Cu‖ < 10⁻¹².

PRE-REGISTERED FALSIFICATION DOCTRINE · INSTITUTIONAL SEALGILC GOVERNED

[PRE-REGISTERED FALSIFICATION DOCTRINE — NON-NEGOTIABLE REJECTION CRITERIA]
├── 1. Mathematical Failure: Inconsistent constraint qualifications or unclosable Dirichlet forms.
├── 2. Numerical Benchmark Failure: Persistent solver drift or ill-conditioned saddle-point operators.
├── 3. Null Model Failure: Inability to outperform degree-preserving randomized graph ensembles (ΔAIC ≤ 0).
└── 4. Empirical Exclusion: Observational violation exceeding pre-declared 3σ / 5σ boundaries.

RULE: All failure thresholds are sealed prior to held-out data access. Post-hoc parameter shifting is blocked.

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1. Falsification Principles & Pre-Registered Failure Rules

A scientific theory is defined by the precise conditions under which it fails. The Science of Fabric Reality adheres to pre-registered, non-negotiable failure thresholds:

[PRE-REGISTERED FALSIFICATION DOCTRINE]
├── Mathematical Failure: Inconsistent constraint qualifications or unclosable Dirichlet forms.
├── Numerical Benchmark Failure: Persistent solver drift or ill-conditioned saddle-point operators.
├── Null Model Failure: Inability to outperform degree-preserving randomized graph ensembles.
└── Empirical Exclusion: Observational violation exceeding pre-declared 3-sigma / 5-sigma boundaries.

Pre-Registration Rule

Failure criteria, parameter values, and error models must be sealed in cryptographic artifacts before held-out data access. Post-hoc modification of failure thresholds is strictly prohibited (POST_SEAL_PARAMETER_MUTATION = 0).

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2. Active Falsification Matrix

Subsystem / Sector	Investigated Hypothesis	Pre-Registered Falsification Condition	Status / Diagnostic Route
FQFT-R1 Spectral Generations	3-band structure is a non-trivial graph property ($H_1$)	Null model test: $\mathrm{\Delta }\text{AIC}\le 0$ or $p_{\text{null}}\ge 0.05$ against degree-preserving randomized graphs.	ADVERSARIAL_NULL_TEST_ACTIVE
Lorentz Dispersion (LIV)	Energy-dependent subluminal photon delay $\mathrm{\Delta }t\propto E$	Fermi-LAT GRB constraint $E_{\text{QG},1}>7.6E_{\text{Pl}}$ excludes linear dispersion if ${\xi }_1\ge 1$.	EXCLUSION_CEILING_ENFORCED
Electron Anomaly ($g-2$)	FQFT geometric loop correction $\delta a_e^{\text{FQFT}}$	Observed discrepancy $	a_e^{\text{exp}} - a_e^{\text{theory}}
KP Operator Resolvent	Positive symmetric Green kernel $K_{\lambda }(x,y)\ge 0$	Numerical detection of negative kernel entries on non-negative test vectors ($R_{\lambda }f\ngeqq 0$).	COMPUTATIONALLY_TESTED
FFE Saddle System	Solvability of constrained variational KKT system	Constraint residual $|Cu|>{10}^{-12}$ or singular Schur complement.	VERIFIED_ON_TOY_MODELS

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3. Negative Controls & Null Models

Every numerical claim is paired with explicit negative controls:

1. Regular Graph Null Ensemble: 5-regular graphs compared against random degree-preserving rewired graphs.
2. Spectral Partition Null: Authorial band centroids tested against random three-band partition algorithms ($p_{\text{null}}=0.62$).
3. KP Nonlocal Operator Control: Nonlocal fractional kernel compared against standard combinatorial graph Laplacians.
4. Constrained FFE Control: Constrained solution compared against unconstrained gradient descent to measure constraint penalty.

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4. Canonical Continuations

Domain	Resource	Focus
FQFT Master Node	Fractal Quantum Field Theory	Parent framework and scale-recursive field grammar
Prediction Ledger	FQFT Prediction Ledger	7-tier prediction taxonomy and degrees-of-freedom accounting
Scientific Results	Scientific Results Ledger	35 machine-verified Lean 4 theorems across 11 modules and negative null benchmark ($p_{\text{null}}=0.62$)
Reproducibility	Computational Reproducibility	RFC 8785 JCS verification receipts and reproducible proof environment
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
Mathematical Falsifiability	Mathematical Falsifiability Index	Singular Fisher ranks and statistical obstruction theorems
Formal Mathematics	Mathematics Gateway	35 machine-verified Lean 4 proofs across 11 modules