01-theory.md

01 — Theory

Intelligence Flow studies harnesses as networks: how useful signal moves, where it degrades, and which boundaries limit accepted output.

A harness is a flow network

A harness is not a wrapper around an agent. A harness is an inspectable flow network for routing, measuring, constraining, and improving useful intelligence through a system. The model is only one node. The real system is the graph around it.

Definition

H = (S, N, E, T, Σ, R, V, F)

Symbol	Name	Meaning
S	source	The origin of the flow: task, question, objective, failing test, research goal, user intent.
N	nodes	Transformation boundaries. A node receives input and produces output. A node is defined by the boundary it exposes, not by a domain label (model/tool/memory/evaluator are not hardcoded).
E	edges	Measured flow between nodes. An edge carries something — context, state, evidence, plan, code diff, decision, error signal, observation — from one boundary to another.
T	trace	The observed execution record: what happened at each node and edge during a run.
Σ	signals	Measurements attached to nodes, edges, paths, or full runs: cost, latency, error, retry count, relevance, confidence, scope error, relation preservation, output quality.
R	relations	Expected relations that should be preserved through the graph. Public language: relation checks. Example: if an input changes in a known way, the output should change in a predictable way.
V	verifier / sink	The acceptance rule for useful output: tests pass, answer is supported, PR approved, state valid, relation preserved, human accepts.
F	feedback	Paths that route observation or error back into the system. Feedback can trigger retry, re-routing, new context, memory update, graph update, or human input.

Simplified:

H = (nodes, edges, traces, signals, relations, verifier, feedback)

Shape:

source → nodes → edges → sink
         ↓       ↓
       trace   signals
         ↓       ↓
      relation checks
         ↓
      feedback

Useful intelligence flow

Useful intelligence flow is not raw output. It is the amount of useful signal that reaches an accepted sink under constraints:

Φ(H) = useful signal reaching the accepted sink

A simple, practical per-path score:

Φ(path) = Q(path) / C(path)

• Q(path) = accepted quality / usefulness of the path
• C(path) = total cost of the path (tokens, latency, money, retries, human input, complexity, risk)

A more detailed cost and quality decomposition:

C(path) = α·tokens + β·latency + γ·money + δ·retries + ε·human_input + ζ·complexity

Q(path) = w1·correctness + w2·relation_preservation + w3·scope_control
        + w4·confidence  + w5·completeness

This is a practical scoring lens, not a mathematically complete theorem. It exists to make harnesses comparable, not to prove optimality.

First principles

1. A harness is a graph, not a wrapper.
2. Nodes are transformation boundaries, not fixed categories.
3. Edges are measured flow, not just connections.
4. Traces make behavior inspectable.
5. Signals quantify quality, cost, error, and degradation.
6. Relations define what must be preserved.
7. Verifiers define accepted output.
8. Feedback turns error into a new path.
9. Bottlenecks reveal where to improve.
10. Better harnesses route more useful signal to the sink under constraints.

See 02-primitives.md for how each symbol maps to code.