Systemic Dynamic Trajectory Law (SDTL) A Minimal Axiom for Regulated Systems

Abstract This document proposes a single minimal axiom governing regulated systems and provides explicit scope, methods, and falsification criteria. The claim is intentionally narrow, non-metaphysical, and offered solely for adversarial testing. Agreement or adoption is not requested. 1. The Axiom Primitives (Irreducible) K — Constraint: Limits, rules, values, resources, or boundary conditions that restrict action. A — Action: Behaviors, policies, control signals, or operations performed by the system. F — Feedback: Signals, measurements, or consequences used to evaluate action relative to constraint. T — Time: The accumulation of effects, including update cadence, delay, and historical memory. Axiom (Single Claim) A system is stable only when action remains coherent with constraint under feedback over time. 2. Scope and Scale Qualifier This axiom applies only to: Regulated systems Systems that evolve over time Systems capable of action and feedback This axiom does not apply to: Static systems Non-interacting systems Purely stochastic processes (e.g., radioactive decay) Scale Clarification Coherence may exist locally without existing globally. Stability in a subsystem does not imply stability of the entire system. All analysis must specify scale explicitly. 3. Methods 3.1 System Boundary Definition Define the system in one sentence, explicitly stating what is included and excluded. If the boundary cannot be defined, the system cannot be analyzed. 3.2 Primitive Extraction For the defined system, explicitly identify: K: What constrains action? A: What actions are taken? F: What feedback is used? T: How do effects accumulate or update over time? Hidden or implicit primitives still count as primitives. 3.3 Failure Localization When instability or failure occurs, localize it to one or more of the following: Constraint failure (K) Action failure (A) Feedback failure (F) Time failure (T) No other failure categories are permitted. 3.4 Intervention Rule Any proposed improvement must: Modify only one primitive Specify a measurable outcome Specify a timeframe for verification If an improvement cannot be traced to a primitive edit, it is invalid. 3.5 Observer Invariance Independent observers, given the same system boundary and evidence, must converge on failure localization within ±20% variance. Persistent non-convergence constitutes falsification. 4. Falsification Criteria (Kill Conditions) This axiom is false if any of the following occur: A regulated-system failure cannot be expressed using K/A/F/T. Independent observers cannot converge on localization after boundary clarification. An improvement cannot be causally traced to a single primitive edit. A fifth primitive is required to explain stability or failure. All falsification attempts must be logged. 5. Historical Falsification Table (Summary) A representative historical sweep across ancient, medieval, modern, and contemporary systems was conducted. In all cases examined: Failures localized to K, A, F, or T. No fifth primitive emerged. Local coherence frequently masked global incoherence. Recovery trajectories traced to primitive-level edits. (See accompanying table for cases.) 6. Status of the Claim Internal falsification attempts: completed Historical cross-era stress test: completed External falsification: open This axiom remains provisional and subject to revision or rejection based on external testing. 7. How to Break This Axiom To falsify the axiom, provide any of the following: A regulated system whose failure cannot be localized to K/A/F/T. Persistent observer disagreement after boundary clarification. An improvement that cannot be traced to a primitive edit. Evidence requiring an additional primitive. Credentials, authority, and consensus do not count—only failures do. 8. Ethics and Governance The axiom will not be modified during active falsification. All failures are logged publicly. Updates are rate-limited. No identity, belief system, or application is implied or required. 9. Closing Statement This document presents a single minimal claim and a method to test it. If the axiom survives falsification, it may justify cautious scaling. If it fails, it will be revised or discarded.