The Dominant Constraint Ordering Theorem
A Derived Structural Theorem Within System Existence Theory
Authors: Jordan Vallejo and the Transformation Management Institute Research Group
Status: Foundational Paper | January 2026
Abstract
Constraint-Governed State Resolution (CGSR) specifies that admissible systems transition from one state to a subsequent state under operative constraints. System Existence Theory (SET) establishes when a proposed unit qualifies as an admissible system object under declared boundary, regime, and time conditions.
This monograph derives a comparative structural theorem within that framework.
The Dominant Constraint Ordering Theorem specifies how, relative to a declared boundary, outcome of interest, operating point, and timescale, operative constraints within an admissible system may be comparatively ordered. It defines the conditions under which one constraint is classified as dominant and formalizes dominance as a local analytic classification rather than a metaphysical property.
This theorem does not replace CGSR, introduce interpretive concepts, or imply legitimacy, meaning, or correctness. It provides a disciplined method for comparative constraint classification within admissible systems.
Dominance classification is undefined for units not established as admissible under SET.
I. Position Within System Existence Theory
This theorem presupposes:
System admissibility under System Existence Theory (SET)
Continuous state propagation under Constraint-Governed State Resolution (CGSR)
It does not modify admissibility conditions, state resolution mechanics, interpretive governance constructs, or authority and legitimacy classifications.
Dominance classification does not alter or influence state resolution. It is an analytic overlay applied to CGSR-governed propagation.
II. Canonical Theorem Statement
Dominant Constraint Ordering Theorem
Within an admissible system governed by CGSR, and relative to a declared boundary, outcome of interest, operating point, and timescale, operative constraints may be comparatively ordered by available margin and marginal sensitivity to the declared outcome.
The constraint with minimal effective margin and maximal first-order sensitivity relative to the declared analytic frame is classified as dominant.
Dominance is local, comparative, operating-point dependent, and relocates upon relief under persistent non-zero constraint.
III. Required Declarations
Dominance classification is invalid without explicit declaration of:
System boundary (SET-compliant)
Interaction regime
Outcome of interest
Operating point
Timescale
Candidate constraint set
Dominance is undefined without these analytic conditions.
IV. Core Terms
IV.a Constraint
A binding limit on admissible state transitions such that violation produces system-defined failure, unacceptable penalty, or loss of integrity relative to declared conditions.
Constraints may be physical, biological, technical, institutional, or structural. Preferences, intentions, and norms qualify only if violation produces binding consequence.
IV.b Outcome of Interest
The declared system-level behavior under evaluation (e.g., throughput, latency, survival, compliance rate, decision finality).
Dominance is always relative to an explicitly declared outcome.
IV.c Operating Point
The system’s current position within its admissible state space relative to declared constraints and outcome conditions.
Dominance classification is operating-point dependent.
IV.d Margin (Slack)
The measurable distance between the system’s operating point and the violation threshold of a constraint relative to the declared outcome and timescale.
IV.e Marginal Sensitivity
The first-order change in the declared outcome resulting from marginal relief of a candidate constraint at the declared operating point, holding other constraints constant.
Marginal sensitivity is evaluated comparatively across candidate constraints.
V. Dominance Classification Criteria
A constraint is classified as dominant relative to the declared analytic frame if and only if all of the following conditions are satisfied:
Bindingness
Violation produces system-defined failure or unacceptable penalty under declared conditions.Minimal Effective Margin
The constraint exhibits the smallest effective slack relative to the operating point and declared timescale.Maximal First-Order Sensitivity
Marginal relief produces the largest first-order change in the declared outcome relative to competing constraints.Relocation Under Relief
Relief of the classified constraint results in a new constraint becoming dominant rather than elimination of constraint-governed behavior under persistent non-zero constraint.
Failure to satisfy any criterion invalidates dominance classification.
VI. Dominance Identification Procedure (DIP-1)
Confirm system admissibility under SET.
Declare boundary and interaction regime.
Declare outcome of interest.
Declare operating point.
Declare timescale.
Enumerate candidate constraints.
Establish bindingness for each candidate.
Estimate effective margin at operating point.
Evaluate marginal sensitivity.
Classify dominance relative to comparative effect.
Assess relocation behavior under constraint relief.
DIP-1 produces one of four classifications: dominant constraint, weak dominance (low separation), distributed constraint regime (no clear separation), or indeterminate (insufficient data or unstable ordering). Indeterminate is a valid scientific result.
VII. Structural Consequences
VII.a Locality
Dominance is local to boundary, outcome, operating point, regime, and timescale. Alteration of any declared parameter may alter dominance ordering.
VII.b Strong and Weak Dominance
Strong dominance occurs when margin and sensitivity separation are clear.
Weak dominance occurs when separation is narrow and small perturbations may change ordering.
VII.c Relocation Under Persistent Constraint
Under persistent non-zero constraint, relief of a dominant constraint results in reclassification rather than elimination of boundedness.
Under persistent non-zero constraint, admissible state space remains bounded relative to declared boundary, regime, and timescale conditions.
VII.d Leverage Asymmetry
Interventions targeting non-dominant constraints do not produce first-order outcome change while dominance separation exceeds analytic tolerance.
This is a structural result of comparative ordering.
VII.e Nonlinear Regimes
In nonlinear systems, dominance ordering may change discontinuously under small perturbations of the operating point or constraint margins.
VIII. Cross-Substrate Illustrations
Each illustration declares analytic frame explicitly.
VIII.a Fluid Network
Boundary: pipe system
Outcome: volumetric throughput
Operating point: steady-state pressure
Timescale: continuous flow
Candidate constraints: pipe diameters
Dominant constraint: minimal-diameter segment under declared operating conditions.
Relief shifts dominance to the next minimal segment.
VIII.b Cellular Metabolism
Boundary: defined metabolic pathway
Outcome: reaction throughput
Operating point: substrate saturation state
Timescale: reaction cycle
Candidate constraints: enzymatic capacities
Dominant constraint: enzyme exhibiting maximal control coefficient relative to throughput under declared conditions.
Relief relocates dominance to the next limiting step.
VIII.c Distributed Software System
Boundary: defined service pipeline
Outcome: request completion rate
Operating point: declared load and concurrency
Timescale: request cycle
Candidate constraints: CPU capacity, network latency, write-lock contention
Dominant constraint: write-lock contention under declared load profile.
Relief may relocate dominance to network latency or compute capacity.
VIII.d AI Governance System
Boundary: model + enforcement layer + policy interface
Outcome: policy-compliant action rate
Operating point: live inference environment
Timescale: enforcement cycle
Candidate constraints: model capacity, enforcement throughput, compliance-threshold bindingness
Dominant constraint: enforcement throughput under declared policy load.
Relief may relocate dominance to latency, model accuracy thresholds, or compliance binding conditions.
IX. Falsifiability Conditions
The theorem is disconfirmed if, under declared boundary, outcome, operating point, and timescale:
No constraint exhibits greater marginal sensitivity than others within analytic tolerance.
Relief of a non-dominant constraint produces larger first-order outcome change while the classified dominant constraint remains binding.
Dominance fails to relocate under persistent non-zero constraint.
All disconfirmation claims require explicit declaration of analytic frame.
X. Relationship to Other Canon Constructs
X.a Physics of Becoming (PoB)
Physics of Becoming articulates the universal conditions under which systems propagate, destabilize, and reconstitute across time. CGSR is specified within PoB as the substrate mechanism of state transition under constraint. The Dominant Constraint Ordering Theorem operates within this substrate, providing comparative classification of operative constraints at a declared operating point. It does not model transformation, destabilization, or regime transition.
X.b Constraint-Governed State Resolution (CGSR)
CGSR specifies state transition under constraint. The Dominant Constraint Ordering Theorem classifies comparative constraint structure within that transition.
CGSR resolves state; dominance classification does not alter or influence resolution mechanics.
X.c System Existence Theory (SET)
SET determines admissibility of system objects. Dominance ordering applies only to admissible systems and is undefined outside SET-compliant boundary declarations.
X.d Interpretive Constraint Dominance
Interpretive Constraint Dominance operates event-internal within candidate-meaning competition and presupposes interpretive events.
The Dominant Constraint Ordering Theorem operates at the existence layer and does not require interpretation.
The two constructs are formally distinct.
XI. Alignment With Established Disciplines
The dominance concept is structurally analogous to active constraint sets in constrained optimization, Lagrange multiplier sensitivity analysis, control coefficients in metabolic control analysis, and bottleneck classification in throughput systems. This theorem generalizes comparative constraint ordering across admissible systems under CGSR without introducing interpretive constructs.
XII. Exclusions
This theorem does not define meaning, determine legitimacy, imply moral priority, assign correctness, suspend CGSR, eliminate constraint, or replace interpretive governance. It remains a comparative structural classification discipline operating strictly within admissible systems.
XIII. Conclusion
Within admissible systems governed by CGSR, operative constraints may be comparatively ordered relative to declared analytic conditions.
The Dominant Constraint Ordering Theorem formalizes how such ordering is performed and how dominance is classified.
Dominance is local, analytic, operating-point dependent, and relocates under persistent non-zero constraint; it is not a global property independent of the declared analytic frame.
Constraint ordering clarifies which bound presently governs outcome sensitivity under the declared analytic frame.
Citation
Vallejo, J. (2026). The Law of Constraint Dominance. System Existence Theory Foundational Paper. Transformation Management Institute.