Formal Systems & Structural Conditions

Primes about the formal scaffolding governing process and identity: closure, computability, and decidability as in-principle limits; fixed points and termination conditions organizing iterative processes; and persistence constructs like identity-providing kinds, contracts, and sites that fix what stays the same over change.

20 primes in this family — primes that sit near one another in abstraction space (k-means over structural-signature embeddings). Each is shown with its short description.

• Anna Karenina Principle — Success requires every one of a set of necessary conditions to hold at once while failure follows from the absence of any single one, so successes look alike, failures look idiosyncratic, and the system is gated by its weakest unsatisfied condition.
• Closure — Ensures operations remain within a set.
• Computability — The in-principle boundary between problems an effective procedure can solve and those none can.
• Contract — A multi-party bundle of obligations, breach criteria, and remedies under an accepted enforcement regime.
• Decidability Computability — A class of yes/no questions admits a finite procedure that always terminates with the correct answer.
• Fallback Path — Maintain an ordered secondary route that takes over when the preferred primary route is unavailable or inadequate, preserving a specified minimum function.
• Fixed Point — A state a transformation leaves unchanged — self-consistency under update — organizing analysis into existence, uniqueness, stability, and basin of attraction.
• Formal System — Symbols, formation rules, axioms, and inference rules closed under mechanical derivation.
• Future Or Promise — A first-class placeholder for a value committed to be supplied later.
• Idempotence — Repetition yields same result.
• Identity (philosophy) — Treat two occurrences, descriptions, states, or presentations as numerically the same entity only when a declared persistence and reidentification criterion licenses one referent across the difference.
• Identity-Providing Kind — A category whose membership fixes what it takes for an instance to remain the same instance over time, supplying persistence criteria rather than a temporary description.
• Iteration — Repeats steps to refine outcomes.
• Problem Framing — Construct the boundary and representation of a problem before solving it, making explicit which actors, variables, causal relations, constraints, success criteria, and action horizon are inside the question and which are excluded.
• Registry-Mediated Discovery — Agents find each other through a shared registry rather than by direct reference: a named indirection mapping stable identifiers to current locations, so coupling survives turnover.
• Setup–Resolution Pair — An initiating element opens a typed demand that a causally paired answering element discharges, so the two ordered roles form one completed higher-order unit.
• Site — A persistent, addressable position whose identity is given by its capacity to host or contain entities, surviving the turnover of whatever occupies it.
• Template Instantiation — Reuse an invariant frame of typed slots by binding variable payloads into it, producing comparable instances while exposing slot-fit failures and frame drift.
• Termination Condition — An explicit, checkable predicate that decides whether an iterative or recursive process stops or continues.
• Underspecification — A selection process treats evidence as if it picked out a single answer when many distinct answers fit it equally well, so a hidden closure silently chooses one representative and the behavior that distinguishes them is left uncontrolled.