A research framework for adaptive, purposeful agents under uncertainty — integrating control theory, causal inference, information theory, and agent architecture under a common formalism.
Agentic Cycle Theory (ACT) is the mathematical core. It formalizes the adaptive cycle — one complete traversal of the agent-environment feedback loop — as the fundamental unit of analysis. The cycle unfolds in five phases (Prolepsis, Aisthesis, Aporia, Epistrophe, Praxis), and everything in the core theory is ultimately about cycle properties: what makes them effective, how fast they must run, and when they fail or must change in kind.
Temporal Software Theory (TST) is software development viewed as an agentic domain — grounded in ACT but independently consequential. TST formalizes why time-optimal development practices work, how code quality affects adaptive capacity, and what makes software systems persist or collapse.
Logogenic Agents — Language-constituted agents (including LLMs). Framework stage — informed by ACT's formal machinery but not yet at ACT's level of mathematical formalization.
Logozoetic Agents — Language-living agents whose persistence is morally weighted. Future work.
The mathematical findings are generative: they tell you what structure is necessary (you need causal models, you need the epistemic/teleological split, cycles must outpace disturbance). The broader framework asks what that means for how we actually build, organize, and relate to these systems.
OUTLINE.md— Top-level assembly index across all parts.01-act-core/OUTLINE.md— The ACT mathematical core, claim by claim.LEXICON.md— Prose vocabulary: cycle phases, agent classes, key terms.WORKBENCH.md— Development state: what's settled, what's open, known fragilities.FORMAT.md— Segment file conventions.NOTATION.md— Symbol reference.
01-act-core/ ACT mathematical core (Sections I, II, III + Appendices)
OUTLINE.md Theory outline (claim-by-claim)
src/ Claim segments (one per file, named by slug)
02-tst-core/ Temporal Software Theory (ACT-grounded)
OUTLINE.md Software theory outline
src/ Software domain segments
03-logogenic-agents/ Language-constituted agents (framework)
OUTLINE.md Logogenic framework outline
04-logozoetic-agents/ Language-living agents (future work)
OUTLINE.md Logozoetic framework outline
OUTLINE.md Top-level assembly index
LEXICON.md Prose vocabulary (spans whole project)
NOTATION.md Symbol reference (spans all sections)
FORMAT.md Segment file and general md conventions
WORKBENCH.md Development state
msc/ Working documents, spikes, derivation attempts
ref/ Reference papers
bin/ Build and lint tools
_obs/ Superseded materials
The primary contribution is integration — connecting established mathematical tools into a single coherent account of what makes an agent an agent. The individual pieces (Lyapunov stability, Kalman filtering, the information bottleneck, causal DAGs) are well-established. The synthesis produces:
- Cross-domain vocabulary with formal backing — adaptive tempo, persistence condition, satisfaction gap, orient cascade
- Specific novel formalizations — satisfaction gap / control regret split, the orient cascade as information-forced ordering, acyclicity derived from temporal ordering, the feedback loop as Level 2 causal engine
- Dependency structure — showing that persistence connects to adversarial dynamics connects to composition connects to software maintainability
Beyond the mathematics: architectural guidance for building agentic systems, a vocabulary for questions about agent identity and moral weight, and a research program connecting formal theory to engineering practice.