Temporal Software Theory: The Mathematical Foundation

These theorems aren't heuristics or best practices - they are some of the notable mathematical necessities that emerge from first principles. They are applied most appropriately not as rules or simplifications but rather through the pattern of thinking through software development decisions with this temporal lens (modified by other salient real-world needs and ambiguities), with a working hypothesis (whether analytical or grounded in these first principles).

Table of Contents

#	Name	Type
T-01	Temporal Optimality	First Principle
D-01	Feature	Definition
T-02	Implementation Time Lower Bound	First Principle
C-02.1	Communication as Limiting Factor	Corollary
T-03	Evolving Systems Scope	Scope Definition
T-04	Change Expectation Baseline	Fundamental
C-04.1	Investment Scaling with Observed History	Corollary
C-04.2	Bayesian Updating from Baseline	Corollary
D-02	Comprehension Time	Definition
D-03	Implementation Time	Definition
T-05	Dual Optimization	Derived
T-06	Change Investment	Derived
T-07	Conceptual Alignment	Hypothesis
C-07.1	Evolution Justifies Realignment	Corollary
D-04	Atomic Change-Set	Definition
T-08	Change-Set Size Principle	Empirical
C-08.1	Comprehension Follows Change-Set Size	Corollary
D-05	Change Distance	Definition
T-09	Change Proximity Principle	Derived
H-09.1	Exponential Cognitive Load	Hypothesis
Der-09.1	How T-06 and T-09 Interact	Derivation
D-06	System Coupling	Definition
D-07	System Coherence	Definition
T-10	Coherence-Coupling Measurement	Measurement
T-11	Principled Decision Integration	Integration
D-08	System Availability	Definition
T-12	Continuous Operation Under Perturbation	Scope Narrowing

---

The Synthesis

These twelve theorems establish:

1. T-01: Time is the fundamental metric after all constraints are satisfied
2. T-02: Specification time bounds implementation speed
3. T-03: We optimize for evolving systems, not static artifacts
4. T-04: Past change predicts future change absent other information
5. T-05: Comprehension and implementation must both be optimized, especially with high turnover
6. T-06: Small time investments now compound into massive future savings or costs
7. T-07: Code-domain alignment reduces comprehension time, justifying realignment as features evolve
8. T-08: Implementation time is proportional to change-set size, making architecture measurable
9. T-09: Proximity of changes within change-sets affects implementation time, possibly exponentially
10. T-10: Coherence and coupling become measurable through historical change patterns
11. T-11: Principled decisions integrate multiple temporal factors despite imperfect information
12. T-12: Operational systems must optimize recovery time alongside implementation time

Together they transform software engineering from aesthetic judgment to mathematical optimization. Every decision becomes measurable against temporal reality. The theory doesn't prescribe specific practices but reveals which practices minimize $\int P(\text{future}) \times \text{time}(\text{future}) , d(\text{future})$.

When you internalize these as mathematical necessities rather than helpful guidelines, you stop following "best practices" and start optimizing for the only metric that remains after all other constraints are satisfied: time.

The cognitive shift we seek: Even in task-execution mode, when you're deep in implementation, these mathematical truths should surface at decision points. The moment you type function, the moment you name a variable, the moment you structure a module - these are optimization opportunities measured in minutes saved or lost, compounded over every future interaction. Feel the mathematics, don't just know it.