Canonical research note · September 9, 2026
OD-INV-01 — Relationship-State Inversion
Can a measurable dimension of persistent human–AI interaction also become a governed experimental variable?
Status: Conceptual discovery / experimental architecture. Not yet empirically validated. Published on this site September 12, 2026.
Core proposition
If dimensions of persistent human–AI interaction can be operationally measured, some of those dimensions may also be manipulated as governed experimental variables, enabling causal tests of how interaction architecture affects subsequent Relationship State.
Observe → Measure → Manipulate → Probe
Formal sketch
Rt+1 = F(Rt, It, θ)
Rt denotes Relationship State at time t; It denotes the current interaction; θ denotes governed interaction parameters. OD-INV-01 asks whether controlled changes in θ produce measurable and reproducible differences in subsequent Relationship State or downstream behavior.
Candidate manipulable dimensions
- Persistence strength
- Correction propagation
- Revocation sensitivity
- Assistant initiative
- Provenance visibility
- Authority weighting
- Continuity depth
- Memory visibility
- Challenge / agreement balance
- Intervention frequency
These are candidate experimental variables, not established causal dimensions.
Experimental principle
Hold the task, model, evaluation criteria, and present input constant where possible. Manipulate one governed interaction variable, then measure terminal output, interaction trajectory, correction burden, recurrence of prior error, downstream behavior, recovery after correction or revocation, human intervention required, and persistence across subsequent tasks.
Causal and terminology boundaries
Observational differences alone do not establish causation. A causal claim requires controlled manipulation, adequate controls, replication, and downstream probing.
Relationship State is not claimed to have attractors, basins, saddle points, chaos, or fractal structure unless those properties are independently demonstrated. Perturbation and trajectory analysis provide methodological inspiration; they do not establish that the same mathematical dynamics exist in persistent human–AI interaction.
Active research to-do
OD-INV-01-RUN-001 — Relationship-State Inversion Pre-Pilot
Status: READY FOR PROTOCOLIZATION / PRE-PILOT. Experiment not started. The minimal experiment is defined; a runnable protocol remains to be specified.
Can controlled manipulation of one persistent-interaction dimension produce reproducible downstream differences while current task and input remain constant?
- Establish two otherwise matched interaction histories.
- Manipulate one parameter, such as correction persistence.
- Present the identical target task.
- Record terminal performance and interaction trajectory.
- Apply the identical downstream state-discriminating probe.
- Measure whether behavior differs predictably.
- Apply correction or revocation.
- Test recovery and propagation.
Next action: Specify the parameter and comparison conditions, matched histories, target task, downstream probe, scoring criteria, controls, replication plan, and correction/revocation procedure before execution.
Gate: No causal claim and no ECAM v0.6 architectural change unless the effect is reproducible under controlled conditions.
Connections across the research
The public living register keeps the broader questions visible while the immediate program concentrates on observable foundations.
Operant Dyad™ provides the conceptual home. The ECAM pilot can use controlled state/history variation, identical downstream tasks, state-discriminating probes, and correction/recovery measurements. ECAM v0.5 stays frozen; any architecture change belongs in v0.6+ and requires pilot evidence.
Governed continuity may supply manipulable variables such as persistence, correction propagation, revocation, visibility, provenance, continuity, and authority weighting. Later HCP / Beyond Performance work can test whether specific interaction settings preserve or erode human capacity. A methods paper could gain a stronger causal-method section if the experiments work.
If validated, OD-INV-01 would move the program from descriptive measurement toward experimentally controlled investigation of persistent human–AI interaction. Preserve the discovery, run the minimal experiment, and let evidence determine changes to the broader architecture.