Research Status

Holistic Data Transformation Theory (HDT²) & Validation Framework

Overview

This page documents the current status of research on HDT² (Holistic Data Transformation Theory) and the development of validation frameworks for question-measurement instruments. Our work establishes falsifiable criteria for distinguishing genuine inquiry structure from surface linguistic artifacts, and develops entropy-based methods for measuring and predicting reasoning stability in large language models.

Important Note on Evidence Status: This page describes frameworks, protocols, and preliminary observations. Where quantified results are reported, we indicate the current status of supporting artifacts (preregistrations, public code, datasets, or reports). Work described as "complete" refers to specification and protocol development, not necessarily to peer-reviewed validation.

Validation Framework for Question-Measurement Instruments

Central Hypothesis

Questions possess measurable internal structure that constrains inference processes prior to answer generation, independently of surface linguistic form.

Three Required Properties

1. Invariance Under Paraphrase Framework Complete

Properties must remain stable when questions are reformulated using transformations that preserve semantic similarity by standard measures (cosine similarity, BERT score, etc.).

Distinguishes inquiry structure from representational artifacts
Requires paraphrase-invariant properties to be measured consistently across meaning-preserving reformulations
Addresses the coordinate-independence requirement: just as physical laws must be coordinate-independent, question measurements must be representation-independent

Evidence Status:

Completed

Formal specification documented in working papers
ICC/variance-based testing protocols specified
Distinction between definitional and empirical invariance formalized

In Progress

Human ground-truth paraphrase annotation protocols prepared but not yet executed
Cross-linguistic testing protocols specified but not yet deployed
Public preregistrations: pending framework paper publication

2. Predictable Inference Effects Protocols Defined

Measured properties must systematically alter downstream inference behavior in large language models in measurable, reproducible ways.

Establishes functional relevance of measured structure
Requires causal demonstration through controlled interventions
Properties must predictably modulate behavior metrics (hedging, uncertainty, calibration, etc.)

Evidence Status:

Completed

Four-phase experimental design specified (discovery → intervention → invariance check → boundary testing)
Behavior metrics operationalized
Falsification criteria established

In Progress

Preliminary behavioral observations recorded but not peer-reviewed
Controlled intervention studies: protocols ready, execution pending
Public datasets and code: pending execution of protocols

3. Independence from Known Variables Framework Complete

Observed effects cannot be reduced to token-level statistics, prompt length, known framing effects, or simple syntactic complexity proxies (e.g., parse depth, clause count).

Rules out reduction to known shallow features
Requires incremental predictive power beyond established confounds
Three-layer evidence structure: matched design + regression controls + adversarial testing

Evidence Status:

Completed

Comprehensive confound set defined (length, syntax, framing, instructional pressure)
Matched stimulus design protocols specified with pre-registration templates
Statistical control frameworks documented
Adversarial testing protocols for boundary verification specified
Distinction formalized between intrinsic correlation and reducibility

In Progress

Empirical testing: protocols ready, execution pending
Public analysis scripts: pending protocol execution

This framework transforms informal claims about "measuring questions" into testable, falsifiable predictions. It establishes what must be demonstrated for claims about measuring inquiry structure to be scientifically credible.

Methodological Innovations

Explicit falsification criteria: Pre-specified thresholds (ICC ≥ 0.80, Δ R² ≥ 0.05, VIF < 5) that create genuine risk of failure
Multi-layer evidence structure: Complementary approaches (matched design, regression, adversarial) that address different validity threats
Epistemic honesty: Clear distinction between what can be proven mathematically vs. what requires empirical demonstration
Reproducibility architecture: Complete pre-registration templates and analysis protocols for independent replication

HDT² (Holistic Data Transformation Theory)

Theoretical Foundation

HDT² treats questions as energetic phenomena with measurable properties that govern how information transforms during inference. The framework uses entropy-based metrics to quantify interrogative structure and predict reasoning stability in computational systems.

Core Components

Ω → Δ → Φ → Ψ Reasoning Cycle

Four-phase transformation process modeling how systems process interrogative demands:

Ω (Omega): Initial state reception and interrogative constraint recognition
Δ (Delta): Transformation space where information reorganizes under constraint
Φ (Phi): Integration phase where coherent response structures emerge
Ψ (Psi): Output generation and closure

Specification Complete

Interrogative Entropy Measurement

Quantification of constraint load and structural complexity in questions through entropy-based metrics. Higher interrogative entropy is hypothesized to indicate greater constraint complexity and predict increased reasoning instability.

Measurement Instruments Implemented

WWWWHW Constraint Framework

Six-dimensional interrogative space (Who, What, When, Where, Why, How) providing geometric representation of question structure and constraint composition.

Framework Specified

Empirical Progress

Internal Validation Studies Exploratory Phase

Evidence Status: The following results are from internal validation experiments conducted during framework development. These have not been peer-reviewed and should be considered preliminary observations pending independent replication.

Non-Interference Testing: Exploratory testing to verify that HDT² measurement and feedback systems do not create artificial stability through intervention artifacts.

Internal testing completed; formal preregistered replication pending
Methods documentation: in preparation
Public data and code: pending formal validation

Entropy Calibration Studies: Preliminary investigations of stability improvements through entropy-based feedback.

Exploratory studies conducted; formal validation pending
Sample sizes and conditions: to be documented in methods paper
Reproducibility artifacts: pending formal study execution

Validation Against Three-Property Framework Protocols Ready

Property 1: Paraphrase Invariance

Measurement protocols defined
Human ground-truth annotation protocols prepared
ICC/variance analysis ready for execution upon ground truth completion

Property 2: Behavioral Effects

Preliminary correlational observations between interrogative entropy and behavior metrics (hedging, uncertainty)
Controlled intervention studies ready for execution
Cross-model replication protocols prepared

Property 3: Independence from Known Variables

Confound set comprehensively defined
Three-layer testing protocols prepared
Matched design experiments ready for execution
Adversarial confound manipulation protocols prepared

Related Developments

Φ-Seal GPT Prototype Operational

Middleware component implementing HDT² principles for interrogative structure analysis. Functions as a prototype for reasoning governance applications.

Working prototype; public release pending validation completion and documentation.

Recursive Personality Index (RPI) Framework Developed

Proposed metric for computational personality treating personality as recursion patterns. Extends HDT² principles beyond question measurement to general cognitive architecture characterization.

Theoretical framework specified
Potential applications mapped (including clinical psychology as exploratory domain)
Empirical validation in early exploratory phase

Publications

In Preparation

"Representational Validity for Question Measurement: A Falsifiable Three-Property Framework"

Type: Methodological contribution
Focus: Establishes validation standard for question-measurement instruments through three necessary properties (paraphrase invariance, predictable inference effects, independence from known variables)
Target Venues: Philosophy of Science, Cognitive Science, Measurement Theory journals
Status: Manuscript in preparation

"HDT²: Entropy-Based Measurement of Interrogative Structure - Empirical Validation"

Type: Empirical validation study
Focus: Tests whether HDT² satisfies the three-property framework through comprehensive empirical protocols
Target Venues: Computational Linguistics conferences, AI venues, Cognitive Science
Status: Validation protocols defined; execution in progress

Licensing Strategy

Open-source release under AGPL v3 license following non-provisional filing. This "seatbelt philosophy" approach establishes baseline standards while enabling broad adoption and independent verification.

Research Accomplishments

Framework Development

Three-property validation framework for question measurement specified
Phased validation protocols with pre-registration templates developed
Falsification criteria and decision thresholds formally specified
Cross-linguistic testing framework designed
Distinction between definitional and empirical invariance formalized

Theoretical Specifications

HDT² Ω→Δ→Φ→Ψ reasoning cycle specified
Interrogative entropy measurement framework developed
WWWWHW constraint space geometrically defined
Recursive Personality Index (RPI) framework specified
Intrinsic correlation vs. reducibility framework for confound analysis
Behavioral validity operationalized through predictable inference effects

Implementation & Prototyping

Measurement instruments for interrogative entropy implemented
Φ-Seal GPT prototype operational
Validation protocol templates and pre-registration frameworks prepared
Cloud infrastructure established for validation experiments

Exploratory Studies

Internal validation testing conducted (formal replication pending)
Preliminary behavioral observations documented
Exploratory entropy calibration studies completed

Note: Empirical validation through peer-reviewed studies is ongoing. Quantified results from exploratory studies are preliminary and subject to formal validation.

Collaboration Opportunities

We welcome collaboration on:

Validation Studies

Applying the three-property framework to other question-measurement systems
Cross-linguistic testing for non-English language pairs
Domain-specific validation (scientific questions, legal interrogatives, educational assessment)
Independent replication of HDT² validation protocols

Available Documentation

Methods Memo: Human Ground-Truth Paraphrase Annotation Protocol (PDF)

Complete specification for establishing independent paraphrase equivalence classes including annotator selection criteria, task structure, quality control procedures, and inter-rater reliability analysis. This protocol is ready for deployment by independent researchers.

Version 1.0 | January 2025

Theoretical Extensions

Connections to quantum cognition frameworks
Integration with formal epistemology and philosophy of inquiry
Links to measurement theory in psychometrics and other domains
Extensions of RPI framework to biological cognition

Methodological Applications

AI safety and reasoning governance systems
Question quality assessment for educational contexts
Interrogative design for human-AI interaction
Measurement instrument validation in other domains

Collaboration Expectations: We seek collaborators with relevant expertise in measurement theory, computational linguistics, cognitive science, or related domains who are committed to rigorous methodology and open science practices.

Technical Resources

Validation Protocols (Specified)

Human Ground-Truth Paraphrase Annotation: Complete protocol for establishing independent paraphrase equivalence classes
ICC/Variance-Based Invariance Testing: Quantitative methods for measuring property stability within and across question classes
Cross-Linguistic Validation: Framework for testing universality vs. language-relativity of measured properties
Behavioral Effects Testing: Four-phase experimental design for establishing causal relationships
Independence Testing: Three-layer evidence structure (matched design, regression controls, adversarial testing)

Pre-Registration Templates (In Development)

Complete pre-registration frameworks for each validation protocol
Falsification criteria and decision thresholds specified
Analysis plans with statistical tests and reporting standards

Public Release: Detailed protocols, templates, and analysis scripts will be made publicly available upon framework paper publication to enable independent replication and community evaluation. Empirical artifacts (data, code) will be released as validation studies are completed and peer-reviewed.

Open Science

Open Science Commitment

Following completion of patent process and peer review:

Validation frameworks and protocols released under open licenses
Code and measurement tools released under AGPL v3
Pre-registration templates and analysis scripts made publicly available
Data shared via open repositories (where ethically permissible)

This approach balances intellectual property considerations with the scientific community's need for transparent, replicable research infrastructure.