## Mouth as Execution Log: Abductive ABM Rule Discovery from a Time-lapse of Craig Douglas (Patient)

> This is a research-method section written in the style of the “Landscapes as Execution Logs” workflow, applied to an intraoral time-lapse. 

### Empirical Observation
We collected a multi-week time-lapse of Craig Douglas’s mouth as a patient, focused on a single tooth and its surrounding soft tissue. The sensing stack emphasized repeatable viewpoint and illumination so that subtle changes (swelling, color shift, gingival contour change, occlusal micro-motions) could be treated as comparable frames rather than anecdotal snapshots. The time-lapse is treated as an *execution log* of an underlying, coupled dynamical system.

### Phase Space Mapping
We reframed each frame as a state vector in a low-dimensional “mouth phase space,” where axes are measurable proxies rather than unobservable physiology. Example axes:

- **Tooth Color / Translucency Index** (normalized per session lighting)
- **Gingival Margin Height + Contour Curvature** (per-tooth neighborhood)
- **Edema Proxy** (local volumetric change inferred from surface motion)
- **Thermal Proxy (if available)** (relative temperature around the tooth)
- **Behavioral Load Proxy** (time-aligned biting/chewing events if instrumented)
- **Pain Signal Proxy** (patient-logged ordinal value, aligned to frames)
- **Interdental Contact / Occlusal Micro-Shift Proxy** (if measurable)

We then identified “surprising transitions” in this phase space—rapid reorganizations that look like discrete regime changes (e.g., quiescent → flare; flare → partial remission; remission → recurrence).

### ABM Primitive Abduction (Fields, Particles, Links)
Working backwards from the observed transitions, we abducted the minimal ABM primitives capable of generating the time-lapse signatures:

**Fields (rasters / patch layers; spatially local intensities)**
- **Inflammatory Field** (soft tissue region surrounding the tooth; drives swelling proxy)
- **Pressure / Confinement Field** (within hard boundaries; drives pain proxy and contour shifts)
- **Diffusion/Access Field** (how quickly “interventions” penetrate; approximates hidden pockets)
- **Nutrient/Leak Field** (couples coronal seal state to microbial resurgence potential)

**Particles (mobile entities)**
- **Microbial Load Packets** (coarse-grained colonies that can persist, migrate, and reseed)
- **Immune Response Packets** (recruited activity that reduces microbial load but increases inflammation)

**Links (topology / boundaries / conduits)**
- **Canal-to-Apex Link** (1D conduit with segment-wise “accessibility” weights)
- **Side-Pocket Links** (dentinal tubule / lateral canal reservoirs: slow exchange, high persistence)
- **Coronal Interface Link** (seal/leak boundary controlling nutrient influx and reseeding)

### Intensive Asymmetries as Control Parameters
We treated gradients and constraints as *intensive asymmetries* that steer the system, rather than as detailed physiology:

- **Access Asymmetry**: main canal accessible vs side pockets poorly accessible
- **Kill Asymmetry**: planktonic kill rate vs biofilm kill rate (biofilm advantage)
- **Seal Asymmetry**: tight coronal seal vs microleak nutrient inflow
- **Load Asymmetry**: episodic chewing/occlusal stress concentrating at one tooth
- **Time-step Asymmetry**: slow background change punctuated by discrete intervention impulses

These asymmetries are the knobs we tuned until the ABM could reproduce the observed regime changes.

### Rule Discovery (Abductive Hypotheses)
From the execution log, we inferred the simplest local interaction rules that could plausibly generate the time-lapse patterns:

1. **Reservoir Rule (Hidden Volume):** side-pocket reservoirs exchange slowly with the main canal; they can reseed after an apparent “clear.”
2. **Biofilm Robustness Rule:** microbial persistence is nonlinearly resistant to clearance; reductions are fast in open conduits and slow in pockets.
3. **Immune Tradeoff Rule:** immune recruitment reduces microbial load but increases inflammation (swelling proxy rises even as microbial packets fall).
4. **Confinement → Pain Rule:** pain proxy increases sharply when inflammation occurs inside constrained geometry (pressure field threshold behavior).
5. **Intervention Impulse Rule:** treatment events act as impulses that temporarily increase access (diffusion) and spike antimicrobial field, followed by relaxation.
6. **Leak-Driven Recurrence Rule:** coronal interface leak increases nutrient field and makes recurrence more likely even after successful impulse events.

Each rule was adopted only when needed to explain a specific “surprise” in the time-lapse phase space.

### Simulation: Replaying Craig’s Time-lapse as a Generative Mechanism
We ran ensembles of abducted ABMs whose outputs were not images but *predicted trajectories* through the same phase space used to encode the time-lapse. The ABM is considered successful when it reproduces:

- timing of regime shifts (flare onsets)
- hysteresis (system not returning by the same path)
- recurrence intervals (apparent clearing followed by delayed relapse)
- sensitivity to impulses (intervention strength/duration effects)
- locality (changes confined to the tooth neighborhood unless rules imply spread)

### Iteration: Closing the Abductive Loop
We iterated the cycle:
time-lapse → phase space → abduct primitives → propose asymmetry knobs → simulate → compare to observed phase trajectory → revise rules.

The outcome is not “the truth” of Craig’s mouth, but a compact computational explanation: a minimal set of interacting local rules that makes the observed time-lapse unsurprising.

### Deliverable
The final artifact is an interactive ABM “story of the tooth” that treats Craig’s mouth as a site whose observed forms are an execution log—allowing clinicians/designers to test counterfactual impulses (better seal, longer medicament duration, altered access) as changes to asymmetry parameters and link topology.