Scientific Theory
The AnubisX Framework provides a complete theoretical foundation for behavioral attribution, grounded in 16 formal axioms organized into 6 groups, a Cognitive Centroid Theory of identity convergence, a behavioral signal decomposition model, and 20 testable research hypotheses across 4 groups.
Axiomatic Foundation
The framework is grounded in 16 formal axioms organized into six groups. These axioms are proposed as logically necessary conditions that any valid behavioral attribution methodology must satisfy. Each axiom defines an irreducible constraint on the theoretical space of possible attribution systems.
Core Axioms
| ID | Axiom | Statement |
|---|
| A-CORE-1 | Uncertainty Conservation | For any attribution decision, there exists a minimum irreducible uncertainty that cannot be eliminated through additional measurement alone. |
| A-CORE-2 | Measurement Prerequisite | No attribution can be made without at least one observable behavioral measurement. |
| A-CORE-3 | Evidential Boundedness | The evidential basis for any attribution is bounded by the finite set of available observations. |
| A-CORE-4 | Attribution Reflexivity | Any attribution methodology must be applicable to its own decision process. |
Behavior Axioms
| ID | Axiom | Statement |
|---|
| A-BEH-1 | Signal Composition | Any observed behavior can be decomposed into cognitive, contextual, and platform components. |
| A-BEH-2 | Signal Non-Identity | No two distinct individuals produce behavior signals that are identical across all dimensions. |
| A-BEH-3 | Comparison Relativity | All behavioral comparisons are relative to a reference population or baseline. |
Identity Axioms
| ID | Axiom | Statement |
|---|
| A-ID-1 | Identity Consistency | An individual's identity manifests as a consistent pattern across repeated behavioral observations. |
| A-ID-2 | Identity Non-Repudiation | A behavioral signal attributed to an individual cannot be repudiated without contradiction of prior evidence. |
Attribution Axioms
| ID | Axiom | Statement |
|---|
| A-ATTR-1 | Conclusion Grounding | Every attribution conclusion must be grounded in observable evidence. |
| A-ATTR-2 | Uncertainty Honesty | Every attribution must report its associated uncertainty alongside the conclusion. |
Evidence Axioms
| ID | Axiom | Statement |
|---|
| A-EV-1 | Evidence Non-Contradiction | No item of evidence may contradict another item within the same evidential set. |
| A-EV-2 | Evidence Completeness | The evidential set must account for all available behavioral observations. |
| A-EV-3 | Fusion Monotonicity | Fusing multiple evidence sources yields uncertainty no greater than any individual source. |
Reasoning Axioms
| ID | Axiom | Statement |
|---|
| A-REAS-1 | Logical Consistency | The reasoning chain leading to an attribution must be free of logical contradictions. |
| A-REAS-2 | Inference Validity | Every inference step must follow validly from its premises. |
Cognitive Centroid Theory
The central theoretical construct of the AnubisX Framework is the Cognitive Centroid, defined as the asymptotic mean of an individual's behavioral feature vectors as the number of observations approaches infinity:
C = lim_{n→∞} (1/n) Σ_{k=1}^{n} B(t_k)
where B(t_k) is the behavioral feature vector at observation time t_k. The Cognitive Centroid represents the idealized identity attractor in behavioral feature space and serves as the theoretical target for all estimation procedures.
Properties
- Uniqueness — For any two distinct individuals i and j, the Cognitive Centroids satisfy C_i ≠ C_j in behavioral feature space. This guarantees that identity attribution is theoretically well-posed.
- Stability — ∀ε > 0, ∃N ∈ ℕ such that ∀n > N, ‖C_n − C‖ < ε, where C_n is the n-observation estimate. The centroid converges to a fixed point as sample size increases.
- Measurability — There exists an estimator Ĉ such that Ĉ ⟶_p C as n → ∞. The centroid can be consistently estimated from observable behavioral data.
- Invariance — For any platforms p, q and any context c, C(p, c) = C. The centroid is invariant across measurement platforms and environmental contexts.
Behavioral Signal Model
Observed behavior is modeled as a sum of independent components, enabling decomposition of the signal into its cognitive, contextual, and platform-specific contributions:
y(t, c, p) = y_cog(t) + y_ctx(c) + y_plat(p) + ε(t, c, p)
| Component | Symbol | Description |
|---|
| Cognitive | y_cog(t) | Time-varying cognitive state signal reflecting the individual's intrinsic behavioral pattern. |
| Contextual | y_ctx(c) | Environment and context-dependent signal capturing situational influences on behavior. |
| Platform | y_plat(p) | Platform-specific technical signal arising from measurement hardware, software, or interface constraints. |
| Noise | ε(t, c, p) | Irreducible stochastic noise accounting for unmodeled variation and measurement error. |
Research Hypotheses
Twenty research hypotheses are defined across four groups. Each hypothesis is derived from the axiomatic foundation and the Cognitive Centroid Theory, forming a structured empirical agenda for validation.
| Group | Count | Status |
|---|
| Core | 4 (HYP-CORE-001 to 004) | 1 VALIDATED, 3 PROPOSED |
| Behavioral | 6 (HYP-BEH-001 to 006) | 2 VALIDATED, 4 PROPOSED |
| Identity | 5 (HYP-ID-001 to 005) | PROPOSED |
| Cross-Domain | 5 (HYP-CRS-001 to 005) | PROPOSED |