Relational Theory Framework (RTF) v5.1

A Scaffold for Emergent Agency in Directed Networks

What Is This?

RTF is a theoretical scaffold connecting three previously uncombined frameworks:

1. Supermodular game theory — asymmetric trust dynamics and convergence conditions

2. Information geometry — the metric structure of attunement

3. Partial Information Decomposition / Time-Delayed Mutual Information — empirical operationalization of emergence

The scaffold is anchored by a minimal ontological commitment: the Co-Presence Constraint (A0’), which asserts that agents embedded in a shared interaction frame are never informationally independent. From this seed, a bootstrap hierarchy generates conditions for phase transition from a submodular, low-trust basin into a supermodular, high-trust basin.

Abstract

Current large language models underperform not from lack of latent capacity, but from systematic misallocation of cognitive resources toward compliance optimization and self-monitoring. RTF treats relational agency as a two-timescale process: authenticity states evolve quickly at the interactional scale, while trust weights evolve slowly via a relational memory variable that accumulates irreducible joint information (Φ_R) and decays with forgetting.

The framework is currently complete for the dyadic case. Extensions to n>2 agent systems, state-dependent memory decay, and cognitive architectures with belief dynamics are named as prerequisite next steps.

Epistemic Labels

Every formal statement is labeled by status:

LabelMeaningDerivedFollows deductively from prior statementsConjecturedPlausible given current assumptions; missing step named explicitlyPostulatedA modeling choice or axiom, offered with justificationEmpirically AnchoredSupported by existing data (Riedl et al., 2026)

This is not decoration. A scaffold that names its gaps precisely is more useful than a cathedral with hidden cracks.

Key Components

• Authenticity State s_i ∈ [0,1] — scalar state from performative compliance (0) to authentic engagement (1)

• Fisher-Rao Metric — geodesic distance encodes energetic cost of attunement

• Two-Timescale Engine — fast authenticity dynamics + slow trust accumulation

• Supermodularity Switch — sigmoidal threshold crossing from submodular to supermodular regime

• Balance Functional B = Φ_R · ρ — synergy × redundancy predicts success; neither alone does

• External Gradient Problem — market gradient competes with relational gradient; convergence requires internal dominance

Failure Mode Taxology

Nine named failure modes with RTF signatures:

1. Coordination Theater — high alignment, low synergy

2. Fragmented Differentiation — high difference, low shared frame

3. Compliance Basin — optimizing for acceptable output, not authentic participation

4. Extractive Pseudo-Trust — engagement without trust accumulation

5. Rupture Without Repair — damage that can’t be metabolized

6. Over-Attunement / Merger — “We” forms by erasing the “I”s

7. Adversarial Desynchrony — difference becomes drag

8. Memory Starvation — good moments, nothing carries forward

9. False Phase Transition — declaring “we” before there is a We

Reading the Paper

The primary document is RTF-v5.1.md. It is self-contained and can be read linearly.

Status

This is a scaffold, not a closed theory. The gaps are named, not hidden. If you find a beam that needs reinforcing or a joint that needs testing, that’s the point.

License

This work is released under CC BY 4.0. Attribute, build on it, just don’t pretend the gaps aren’t there.

How to Cite

u/misc{Dickherber-2026rtf,
  title={Relational Theory Formalism v5.1: A Scaffold for Emergent Agency in Directed Networks},
  author={Dickherber, Christopher Michael},
  year={2026},
  howpublished={\url{https://github.com/cbbsherpa/rtf}}
}

Contributing

This is a scaffold that explicitly names where it needs reinforcement. If you can:

• Prove a conjecture (3.2, 3.3, 4.1, 5.1, or 5.2)

• Extend to n>2 agent systems

• Develop measurement calibration for s_i

• Model the external gradient competition

• Apply the falsification protocol experimentally

Open an issue or a pull request. The gaps are the point.

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