about integrodynamics

the problem

integrodynamics is an independent research programme concerned with the mathematical modelling of systemic risk, regime change, and institutional failure.

the programme studies complex decision systems — including organisations, regulatory architectures, and governance frameworks — as coupled dynamical systems whose behaviour, stability, and failure modes are structurally constrained. its central focus is not individual error, but the conditions under which formally coherent systems begin to produce persistent, patterned harm while remaining internally justified.

the work sits at the intersection of probability, complex systems, and applied decision theory, and is being developed as a PhD by publication.

the problem

across modern institutions, similar failure patterns recur across sectors: decisions produce harm while remaining procedurally valid; explanations stabilise after the fact; corrective mechanisms weaken; and adverse outcomes repeat with statistical regularity.

existing disciplines capture fragments of this behaviour. ethics evaluates norms but struggles with enforcement. law evaluates compliance but is reactive. economics models incentives but abstracts away institutional coherence. statistics detects anomalies but often stops short of structural explanation.

what is largely missing is a formal framework for analysing whether an institutional system remains coherent with its own stated rationale over time — and, when it does not, whether the resulting regime is benign, adaptive, or structurally harmful.

the central technical contribution of this work is the quantification of contradiction. contradiction is treated not as a logical inconsistency or rhetorical failure, but as a measurable structural event that occurs when a system’s stated rationale and observed behaviour cannot be jointly sustained. this reframing allows contradiction to be detected, accumulated, and analysed quantitatively.

the framework

integrodynamics treats institutions as dynamical systems operating under internal constraints. it models organisational behaviour in terms of stability, drift, regime transition, and collapse, and formalises the conditions under which self-correction gives way to chronic distortion.

at the centre of the framework is an invariant: integrity — coherence between a system’s stated rationale, its declared narrative, and its observed behaviour across time. integrodynamics formalises this coherence and develops it into a measurable diagnostic quantity.

rather than treating bias, contradiction, or institutional failure as primarily interpretive or moral phenomena, integrodynamics formalises them as measurable structural events. this allows breakdown to be detected, accumulated, and analysed quantitatively.

a central technical contribution of the programme is the quantification of contradiction: treating incompatibility between stated constraints and observed behaviour not as rhetorical inconsistency, but as a detectable system-level event that can be modelled, tracked, and subjected to statistical analysis.

programme structure

the integrodynamics series is organised as a unified research programme rather than a collection of standalone essays. it is structured into three primary arcs:

Foundations (parts i–iii)formal definitions of contradiction, symmetry, and bounded drift as system-level objects.

field theory and collapse (parts iv–vi)development of the mathematical machinery: integrity as a conserved quantity, geometries of institutional failure, and quantitative frameworks for regime transition and collapse. part vi constitutes a dedicated collapse block (vi-a to vi-d), addressing collapse detection, institutional inversion, harm propagation, and civilisational regime classes.

axioms and synthesis (parts vii–ix)formalisation of axiomatic structure, origin conditions, and programme-level integration.

each paper is self-contained, but designed to interlock. applied readers may begin with the collapse block; technically oriented readers may prefer the field and axiomatic sections.

intended audiences

this work is intended for researchers and practitioners working with complex risk-bearing systems, including mathematics, statistics, economics, systems theory, governance, regulation, and enterprise risk.

it may also be of interest to technically literate readers seeking formal tools for analysing institutional behaviour, model failure, and regime instability without relying on insider access, normative judgement, or adversarial assumptions.

scope and intent

integrodynamics is not a theory of motives and does not attempt to assign intent or blame. it does not substitute for legal or moral judgement, and it does not rely on insider information.

its sole concern is structural behaviour: what systems declare, what they do, and whether those two can remain compatible over time. where they cannot, integrodynamics treats the resulting incompatibility as evidence — not opinion.

the programme evaluates only whether declared constraints and observed outcomes remain structurally sustainable. interpretation, remediation, and accountability lie outside its scope.

the integrodynamics programme formalises contradiction, proves integrity is a conserved field quantity, and derives a universal constant governing the onset of structural collapse.