Part I. Theoretical Foundation

Core Thesis

Interaction structures and compositional dynamics create outcomes. Intelligence is a pattern-exploiting search dynamic that discovers these outcome-producing systems. Individual component intelligence matters as a threshold condition, but their true value appears when they contribute to reliable interaction patterns.

The largest capability jumps appear when many sufficiency thresholds are crossed together—data hygiene, regularization, tooling, measurement, orchestration, post-processing, and more improving in concert. No single lever “wins” on its own; the gains compound when the entire environment hits the required conditions simultaneously.

This reframes the optimization frontier. Instead of endlessly scaling isolated components, we design interaction structures and ensure that the primitives we discover stay reusable across contexts with clear, measured entry and exit conditions.

Intelligence: Definition and Properties

Intelligence is a dynamic that creates efficient pathways (or long arcs) through often high-entropy search spaces by leveraging universal foundational patterns of reasoning. It discovers exploitations faster than exhaustive search by leaning on learned reasoning primitives. The intelligence dynamic identifies the design by recognizing patterns; the interaction dynamics of the designed system create the outcomes.

Generalized intelligence adds another layer. It compresses domain knowledge into noisy but broadly applicable patterns, then pattern-matches against that cache before taking a maximal-likelihood step. In forgiving regimes the cohort tolerance bands—derived from blueprint-structured statistics—are wide enough that a near miss still lands inside the acceptance region.

High-risk domains break that spell:

• The decisive patterns are sparse, nuanced, and sometimes counterintuitive.

• A maximal-likelihood move under a fuzzy match can push the object straight into failure.

• Knowledge that drove success elsewhere becomes toxic because it keeps triggering arcs whose contracts were never validated for this cohort.

Dynamics Drive Outcomes; Intelligence Is Threshold

Physical dynamics, interactions, feedback loops, and compositional structures create outcomes, but only when every transition is tethered to the measured object. The colony-level pheromone system, for example, follows a blueprint that instructs us to extract pheromone density, trail freshness, and worker saturation as sufficient statistics. Each ant executes a quantized arc—follow trail, lay reinforcement, initiate foraging—conditioned on those measured state variables. Evolution, acting as a very slow intelligence dynamic, discovered that blueprint and encoded guardrails so the colony stayed within safe bands.

The interaction dynamics create the outcomes. Sophisticated foraging, construction, and defense emerge because every arc, from scouting to nest maintenance, is triggered by locally measured blueprint dimensions. Intelligence, in this view, is the search process that keeps refining the blueprint and the associated contracts. Once they exist, interaction dynamics that respect them generate outcomes reliably.

Efficient and reliable outcomes therefore emerge from composing well-designed, contract-bound interaction systems, each sufficient (not perfect) for its domain. This is multiplicative, not additive: when domain-sufficient systems with validated arc contracts leverage each other around a shared object blueprint, new outcome-producing properties emerge that no isolated system could achieve.

Measurement as Foundation

Measurement as Control Mechanism

Intelligence operates in a high-dimensional space of variables: problem definition, interpretive lens, solution approach, composition structure, measurement criteria, and more.

Measurement enables independent manipulation of these variables. Like experimental science, you can freeze any variable while letting others vary, enabling causal inference about what actually matters:

• Freeze problem definition -> explore all interpretations and approaches that might solve it.

• Freeze interpretive lens -> discover which problems naturally fit that frame.

• Freeze solution approach -> find which problems and decompositions it handles well.

• Freeze measurement criteria -> let everything else adapt and see what emerges.

This is why measurement-centered design is foundational.

Without the ability to freeze variables independently:

• You cannot discover sparse manifolds; you do not know which dimensions actually matter.

• You cannot find natural compositional boundaries.

• You cannot achieve energy efficiency; you must process everything.

• You cannot navigate the configuration space systematically.

• You cannot validate the entry and exit contracts of quantized arcs against their intended cohorts.

A further payoff is recognizing structural equivalence classes. Once the blueprint specifies which signals to extract and how to bucket them, we can compare how different arcs reshape those measurements-even when the absolute values drift between episodes. Two arcs belong to the same class when they absorb similar input defects, impose the same guardrails, and deliver comparable deltas on the sufficient statistics, despite running on distinct concrete states. Measurement is what lets us detect those shared effect signatures instead of guessing, and the blueprint is subsequently amended to record the invariants that make the class reusable.

Evolution as the Original Measurement System

Biology offers the most vivid illustration. Evolution does not provide detailed gradients; it functions as an enormous measurement loop. Each organism is a hypothesis; the environment measures it through survival and replication.

We mimic that pattern at engineering timescales. Measurement tells us which behaviors mattered, and the next round of composition reuses those primitives.

Measurement, Causality, Sparsity

Measurement is the entry point into a reinforcing loop that tightens causal understanding and drives sparsity:

1. Measurement sharpens causality. High-signal measurements isolate interventions from coincidental correlations. When we can observe counterfactual responses or run controlled comparisons, we move beyond pattern matching toward causal attribution.

2. Causality unlocks sparsity. Once the causal pathways are explicit, we can discard the correlated-but-irrelevant features and deactivate components that do not influence the measured outcome. The state space collapses onto the few variables that actually matter.

3. Sparsity improves efficiency and variance. Fewer active pathways reduce thermodynamic cost, shrink variance across runs, and make the system easier to reason about. Sparse structures also fail loudly: when a causal edge is missing, the measurement quickly detects it.

4. Efficiency enables parallel experimentation. Leaner structures free compute and attention. We can explore more candidate interaction patterns in parallel, each instrumented with the same measurements that proved effective.

5. Scale of experimentation enriches measurement. Running many measured trials across diverse contexts stress-tests the metrics themselves. We discover blind spots, tighten tolerances, and add probes for previously hidden failure modes.

General reasoners—human, automated, or hybrid—conduct the measurements that gauge outcomes. The blueprint then interprets those independently gathered observations: every extraction call compares prospective signals against the existing cluster to ensure positive information gain at the raw-log level before any synthesis. This guardrail prevents us from flooding the ledger with correlated noise and keeps the episodic buffers aligned with the causal dimensions we actually care about.

Each pass through the loop increases both the resolution and the coverage of our measurements. Better measurements expose finer causal structure; finer structure lets us identify reusable primitives; those primitives support sparser representations; sparsity frees resources for broader experimentation. The more reusable the primitives, the cheaper it becomes to explore new compositions, so progress accelerates instead of merely grinding forward.

As the loop compounds, the search space collapses toward the minimal interaction design that still satisfies the sufficiency thresholds we care about. Measurement-driven programs therefore converge on outcome-sufficient structures by repeatedly trading excess complexity for deeper causal insight and better reuse statistics. Effect surfaces for each arc-by-cohort pair become sharper with every iteration, giving orchestration tighter guidance on which contracts remain valid.

The same loop alternates between the episodic and population views of sufficient statistics. Each batch of experiences updates the local clusters, then population-level analysis checks whether the blueprint of information buckets still spans the causal geometry. When it does not, we rewrite the bucket layout, replay the raw logs to regenerate the statistics under the new schema, and only then resume composing. Measurement therefore governs both forward motion and retrospective correction.

This discipline is what prevents knowledge from turning toxic. General systems accumulate compressed, noisy patterns indiscriminately; in easy domains the approximation error averages out, but in tight domains a single misapplied pattern detonates the trajectory. Measurement, replay, and cohort analysis strip away those misleading correlations so only causally warranted habits remain.

Proper Self-Measurement Enables Scaling

We are approaching the threshold where systems can lean less on pre-existing or manually curated datasets when they are instrumented to generate high-quality measurements on demand. Data remains essential, but its provenance shifts: instead of relying primarily on historical corpora, well-designed systems can produce the raw signals they need through deliberate interaction and self-measurement. Self-measurement here means more than logging scalars; it means maintaining the arc-cohort ledger, stress-testing contracts, and capturing causal justifications for every permitted transition. Without that instrumentation the compositions collapse back into monoliths because the system cannot tell which arcs remain safe to reuse.

It also means owning the replay-based backfill machinery. Whenever population-level cohorts flag that our information buckets or interpretive lenses are drifting, we must regenerate the sufficient statistics from raw traces under the updated blueprint. Systems that skip this step end up reasoning with stale compressions that quietly encode yesterday's mistakes.

Practically, this forces us to preserve the raw data sources until repeated discovery cycles converge on a stable causal explanation. The blueprint remains a living hypothesis; only after several rounds of measurement, rewrite, and backfill do we approach sufficiency.

Sufficient Statistics and Dimensional Blueprints

Blueprints give structure to raw measurement. A high-level flow looks like this:

1. Capture raw traces. Instruments, operators, or automated agents observe the target object and record the uncompressed signals (audio transcripts, vital signs, sensor logs, etc.).

2. Extract blueprint dimensions. A dimensional blueprint specifies which parts of those measurements matter, how to bucket them, and how to interpret the values once extracted.

3. Validate information gain. For each episode the blueprint guides the interpretation step: we pull the prescribed signals and check against the existing cluster to confirm there is net-new information rather than redundant bookkeeping.

4. Store episodic evidence. Only after that test passes do we encode the episode's contribution into the episodic buffer.

These dimensional blueprints are the user-model guidance for the optimization object—most often a patient or clinical process in our deployments. They spell out exactly which physiological, behavioral, and operational signals must be captured so that downstream reasoning engines have the right features to judge risk, eligibility, or progression. A chemotherapy service, for instance, will blueprint neutrophil counts, medication timing, adverse-event reports, and staffing availability so that every subsequent decision references the live patient state rather than generic population averages.

Conceptually, every sufficient-statistic snapshot is a point inside a high-dimensional coordinate system supplied by the blueprint. A single patient or asset moves through that space as we intervene; a population forms constellations and dense neighborhoods that we call cohorts. But the coordinate system does not stay fixed: it drifts as the object ages, the environment shifts, and new measurements reveal previously hidden axes. The optimization problem is therefore a controlled transport problem on a slowly shifting manifold: carry the point from its current location toward the target region along a trajectory that respects safety and resource limits, while continually recalibrating the coordinate frame. Each intervention episode contributes a short segment of that journey, revealing a little more about the terrain that surrounds those points and how the terrain itself is evolving.

Once enough episodic contributions exist for a target object or task, we roll them up longitudinally using the same blueprint. The synthesis aligns the episodes dimension by dimension, producing a per-task information cluster that captures how each axis evolved across attempts. This cluster is a lagging summary: it records the last verified state before the next engagement, but the real object continues to drift between episodes. Orchestration therefore treats the cluster as a prior—useful for deciding what to measure next, never sufficient on its own—and insists on fresh measurements before entering any arc.

Every time we execute a compositional program we trace a path through that state space: a polyline whose vertices are the pre- and post-conditions of each quantized arc. Early on, the map is mostly blank; we rely on exploration to learn which directions are even traversable. As evidence accumulates, certain polylines prove durable across many cohort members. Those segments become "roads" we can trust—well-instrumented sequences of arcs whose safety and efficiency have been audited at population scale—but even trusted roads must be resurfaced as the surrounding coordinate system drifts. At the frontier, search and consolidation continue in parallel: exploration pushes fresh probes into unmapped regions while exploitation keeps resurfacing the proven roads so the system maintains competence on the work it already understands. Routine maintenance cycles—measurement, backfill, contract refresh—prevent yesterday's asphalt from crumbling under today's coordinates, and they occasionally reveal that the road itself must bend differently because the underlying manifold has shifted beneath it.

Each target object maintains its own cluster. The synthesis step slices those observations along the blueprint dimensions relevant to a specific patient, user, subsystem, or artifact. Clusters never share state; they remain independent summaries tied to the object they model.

Population-level cohorts of these clusters become a diagnostic instrument. They tell us whether the blueprint's dimensions are still causally sufficient, whether the buckets are missing variables, or whether interpretation rules are warping the signal. When a cohort exposes systematic gaps—missing variables, warped conditioning, unmodeled collateral effects—we treat it as a mandate to rewrite the blueprint and regenerate every affected statistic from raw logs.

Updating that blueprint cascades. We immediately trigger a replay-based backfill: regenerating every affected sufficient statistic from raw data logs using the improved synthesis plan. This retroactive pass keeps the arc contracts honest, because the entry predicates and exit summaries are re-derived under the corrected interpretation. Without the backfill, we would be composing with stale compressions that encode the very blind spots the population statistics revealed.

The blueprint itself always begins as a hypothesis (where a superset is usually better to start). Early in a program we only guess which dimensions of the sufficient statistic will prove causal. The only way to refine that guess is to keep the raw data accessible, run several discovery cycles where episodes contribute net-new information, rewrite the blueprint, and backfill until the inferred causality chain actually stabilizes. A reductive approach is generally quite efficient as non-causal dimensions get simplified or removed.

Backfill, therefore, is the path to causal sufficiency. Each replay under an improved blueprint tests whether the chosen dimensions are rich enough to support the causal inferences we care about. When the regenerated statistics finally produce stable, cohort-consistent contracts, we know the blueprint has captured the right abstractions for that slice of the world.

Once an abstraction proves causally sufficient, it becomes a module that higher-level systems can wrap. The per-task cluster exposes a disciplined interface—entry predicates, exit guarantees, causal justification-that can serve as a dimension in another blueprint. This is how deeply nested systems stay tractable: complex targets become functionally sparse when we discard non-causal dimensions, and abstractions stack by referencing each other through their verified contracts.

Knowledge and memory are functional constructs that humans invented so that sufficient statistics for problem solving could be reused. Their purpose is purely instrumental: to serve as sufficient statistics for solving discrete problem units. Generalized knowledge is simply a coarser compression—useful when a cohort tolerates approximation, hazardous when the blur hides cohort-specific variables that govern arc safety.

A quantum of a problem is an atomic unit of work with defined outcome boundaries. Context, knowledge, information, and memory are treated as sufficient statistics, compressed state capturing exactly the information needed to (1) solve the current problem quantum, and (2) set up the next quantum correctly. This ties back to the composable arcs discussed earlier; we can see the quantum mostly as a sub-segment of a longer arc.

These are not separate systems but different views of the same underlying statistical sufficiency. Context is unified: it aggregates all relevant structures required for outcome sufficiency at the decision point and for proper handoff to subsequent problem quanta.

This chaining property is critical. Each sufficient statistic must bridge problem quanta, containing exactly what is needed to complete current work and initialize the next. Fragmented state breaks continuity, leading to incoherent decisions, which ultimately leads to composition failure and the breakdown of the arc trajectory.

Operationally, these sufficient statistics instantiate the entry contracts. When the orchestration layer evaluates whether a cohort sits inside an arc's validated domain, it does so by inspecting this compressed state. Missing or stale statistics are thus not clerical errors; they are contract violations that force the planner to reroute or to collect more measurement before committing to the arc.

Because every episode deposits a blueprint-governed contribution into the cluster, we continuously reconcile the episodic view with the population blueprint. When the reconciliation fails-when cohorts expose blind spots or mis-weighted variables-we redraw the dimensional buckets and replay historical logs to regenerate the statistics. The contracts are rewritten alongside the data, preventing future compositions from inheriting the flawed lens.

Quantized Arcs and Compositional Architecture

Problem Complexity Quantizes into Reusable Primitives

When we examine a successful long arc—a success path through a problem—we often see that certain sub-segments of the arc represent more general primitives, and the whole arc is really a composition of much smaller arcs. Some sub-arcs are more common and broadly applicable, whereas others are narrow and domain-specific. Even apparently unique arcs usually follow recurring composition patterns.

Many of those arcs belong to an equivalence class exposed by measurement. The blueprint furnishes the coordinate system, but the equivalence is defined by how an arc changes the sufficient statistics relative to their pre-episode baseline; both the starting coordinates and the coordinate frame itself may have drifted since the last engagement. If two arcs "shape" the state in the same qualitative way—nudge the same axes toward sufficiency, enforce identical guardrails, or compensate for the same failure modes—we treat them as variations of a shared primitive even if the exact starting values differ. What looks bespoke in raw observation space often collapses into a familiar template once we abstract over those effect patterns. Classic maneuvers—stabilize vital signs before intervention, reprioritize queue elements, reconfigure a tooling pipeline—keep reappearing with different parameterizations. Recognizing these structural rhyme schemes lets us reuse arcs across cohorts while still honoring their contracts, provided fresh measurements confirm the local preconditions and we revalidate the class against the latest coordinate drift. The catalog therefore evolves on two fronts: outward, by probing brand-new maneuvers, and inward, by consolidating these rhyme schemes into dependable building blocks.

When such a primitive survives repeated audits, it graduates from a convenient trick to a maintained road segment through the state space. Its entry ramps, guardrails, and exit shoulders are instrumented; we know how much slack it tolerates, which cohorts can traverse it, and what measurement cadence keeps it safe. Because the coordinate frame drifts, we periodically remeasure the roadbed itself—checking that today's cohorts still sit on the same grade and curvature that yesterday's audits certified. Large-scale programs become networks of these roads stitched together with exploratory spur routes that hunt for the next viable shortcut or detour. The orchestration challenge is to keep extending the map at the frontier without letting the existing roads crumble through neglect.

Quantized Arcs, Cohorts, and Contracts

When a problem trajectory is decomposed into reusable segments, we refer to each segment as a quantized arc. An arc is purpose-built: it expects a particular bundle of sufficient statistics at entry, transforms them through a well-scoped reasoning primitive, and emits an exit state that subsequent arcs can accept. The same arc can be used inside many larger compositions, provided the entry conditions are satisfied.

These arcs are not universally benevolent. The identical reasoning primitive can accelerate progress for one cohort of states, act as noise for another, and destabilize a third. Cohorts here are compact regions in the sufficient-statistic space that share a causal response profile. Because the dimensional blueprint strips away non-causal variables, even complex targets collapse into functionally sparse manifolds once we focus on the outcome of interest.

To keep compositions safe, each arc carries an explicit contract. The entry contract encodes the sufficient-statistic predicates that must be observed before we cross into the arc, while the exit contract specifies the guarantees (and variance bounds) of the state it returns. Measurement must estimate an effect signature for every (arc, cohort) pair—positive, neutral, or negative contributions relative to baseline—along with confidence intervals and sample coverage. Cohorts are not just demographic groupings; they are regions in sufficient-statistic space that share causal responses. Composition is only powerful when the orchestration layer respects which arcs are causally supported for the current cohort.

High-risk deployments require conservative promotion rules. An arc can move into the high-risk library only when the population-level causal story is understood, the positive cohort is densely sampled, the negative cohort is bounded, and the exit state has tight variance. When evidence is missing, the orchestration layer should refuse to enter the arc and instead route toward exploration or defer to human oversight.

• Arc-cohort ledger: Maintain a matrix of effect signatures, sample counts, and causal justifications for every arc across the cohorts we can measure.

• Entry and exit contracts: Encode the sufficient-statistic predicates that must be satisfied before the arc can activate and the summary statistics it must emit upon completion.

• Transition guards: Add online checks that abort or roll back when the observed state exits the validated domain mid-arc, preventing cascade failures.

• Composition audits: Track multi-arc motifs and evaluate whether their combined effect differs from the sum of the parts so we learn which compositions are genuinely synergistic.

Learning these ledgers over time lets the system compose long trajectories with statistically robust arcs only when the surrounding information supports them. The orchestration policy becomes a search over composition patterns constrained by these contracts. Successful long-arc behavior is therefore not just the presence of clever primitives but the disciplined governance of when, where, and with what supporting statistics each primitive may run.

Energy Scaling and Sparsity

Sparsity correlates with efficiency when primitives are reusable. When we deliberately involve only the primitives required for the outcome at hand, the system spends less energy shepherding irrelevant state and correlations. Interaction dynamics stay crisp and easier to reason about. Reusable primitives amplify this effect: once a component proves useful across contexts, we can route new problems through that module and leave collateral machinery idle.

Compositional architectures exploit favorable energy scaling. When knowledge-layer heuristics are projected down into the core cognitive layer, they become interface rules over explicit blueprint dimensions, so the same primitive can service multiple domains as long as the underlying state variables align. (By "domains" we mean distinct regions of the blueprint-defined state space, not cultural taxonomies like "legal" vs. "finance".)

Monolithic systems maintaining all capabilities simultaneously tend to still work, but they must keep most coordinates of the manifold partially energized so that any domain can be serviced. That requirement feeds noise: latent pathways that are irrelevant to the current task stay warm, cross-talk, and need active damping. The residual interference multiplies-each additional domain couples into every other-so the effective energy cost grows with the product of domain complexities. Composed systems, by contrast, activate only the specialized components whose guardrails match the present coordinates. Sparsity keeps cold everything outside the active bundle, so energy scales with the sum of the engaged domains plus a modest orchestration overhead. As domains multiply, physics continues to tilt the economics toward specialization: the blueprint tells us which arcs must be hot at any moment, and everything else remains quiescent instead of adding more noise.

Expanding raw generality in hopes of covering every cohort eventually collides with those sparsity principles. Without a blueprint that names the state variables a domain actually cares about, the added capacity simply oscillates: some cohorts inherit better coverage, others degrade because the shared statistics are no longer conditioned on their object. The path to domain-specific performance is therefore not more undifferentiated generality, but sharper blueprint factoring and arc governance.

Tracking Reusable Primitives and Credit Assignment

Quantization is most useful when the resulting components remain reusable across a wide range of contexts, much like puzzle pieces that fit in several corners of a tiling. Measurement makes this visible. By tracking how often a component appears in successful compositions, and in how many distinct neighborhoods, we can separate genuinely general primitives from narrow hacks. The same accounting has to remain cohort-aware: an arc can be a powerhouse for one slice of sufficient statistics and a liability for another, so reuse scores are indexed by cohort as well as global frequency.

Components with strong cross-context reuse deserve investment. Low-reuse pieces may be redundant or should be merged with neighbours. The same machinery also highlights missing primitives: if many compositions require ad-hoc glue, that glue is a candidate for a new, more reusable component. When a primitive oscillates between positive and negative outcomes across cohorts, the governance layer either tightens its contracts or spins out specialized variants whose behavior is stable within each cohort.

Traditional reinforcement learning treats an entire rollout as a single object. It gathers a scalar reward at the end and sprays that signal across every intermediate action. Any detour that happened to precede success is rewarded alongside the genuinely useful steps, and the noise overwhelms the signal. Humans do not learn this way. After solving a problem, we audit which steps actually mattered, discard lucky accidents, and annotate the parts worth repeating.

Rather than relying on one terminal reward, we segment trajectories into the same quantized, reusable components described above. Each component inherits credit according to how often it appears in successful compositions and how broadly it transfers across contexts. Grid-masking, pattern mining, and other structural probes help discover these units automatically.

Because the units are explicit, we no longer assume smooth continuity across the entire environment or fixed horizons. Long programs can diverge wildly, yet the library still learns which local maneuvers are broadly useful and how they compose. Side effects become information: if a subroutine consistently produces a helpful collateral state, its reuse score rises; if it causes regressions, the statistics flag it for pruning.

Structural-equivalence-aware reuse statistics make this robust even with small sample sizes. Once analysis shows that two cohorts respond to a primitive with the same qualitative effect signature, we can transport the arc's ledger into the new setting and validate it with targeted measurements instead of relearning from scratch. Families of arcs that share guardrails and deltas turn isolated observations into a population large enough to test the contract, while the blueprint guards against false equivalences by flagging any dimension whose behavior diverges. When the abstraction holds up under fresh measurements, we amend the blueprint (and its extraction rules) so future episodes capture the shared structure explicitly.

Emergence and Composition

Superintelligence May Be Compositional, Not Monolithic

Advanced capabilities may emerge more efficiently from the composition of domain-sufficient systems with proper interfaces and some orchestration overhead.

Domain Sufficiency vs. Generality

Every domain has a specific structure that specialized systems can exploit. Proteins fold via physical laws. Weather follows fluid mechanics. A system generalized for all domains simultaneously may be suboptimal for any specific domain because its compressed knowledge can blur the very blueprint dimensions that make each cohort safe.

Imagine:

• Materials discovery system, sufficient for designing compounds.

• Simulation system, sufficient for testing interactions.

• Synthesis planner, sufficient for manufacturing pathways.

• Clinical trial optimizer, sufficient for testing protocols.

Individually, each is narrow. But when they compose—protein folder feeds materials designer feeds simulator feeds synthesizer—you get drug discovery that transcends any individual component.

Critically: new properties emerge. The composed system explores spaces that none of the individuals could represent. It is not just faster; it also discovers new categories of solutions.

All Models Are Wrong, Sparsity Is Why They Work

Modeling the universe correctly down to subatomic particles (or whatever primitive) is infeasible in practice. Any such model would demand energy and information budgets that dwarf what bounded systems can supply. Therefore, all models are approximations. They succeed because they exploit the sparse set of outcome-sufficient features.

Falling object? Model position and velocity. Ignore quantum states of constituent atoms. The outcome (where it lands) depends on a tiny manifold in an enormous state space.

Intelligence involves discovering and exploiting these sparse manifolds, which are low-dimensional subspaces within high-dimensional spaces that contain all outcome-relevant features. This is not simplification for convenience-it is recognition that outcome-sufficiency lives in these low-dimensional subspaces. Interfaces, finite scope, and specific objectives can drive sparsity even further.

Why Isolated Groups Discover the Same Solutions

The vertebrate eye and the cephalopod eye evolved independently because both evolutionary programs converged on the same measurable blueprint for optical organs: focal length, photoreceptor density, signal routing bandwidth. Once those dimensions lock in, the viable arc contracts become obvious-build a lens of a certain curvature, route signals along bundled axons, regulate pupil dilation-and any lineage that reaches that measurement regime is pulled onto the same trajectory.

Technology exhibits the same phenomenon. Aluminum smelting, the jet engine, the telephone: each invention surfaced in parallel because the relevant actors were already instrumenting the same object (chemical feedstock, airflow compression, bidirectional signaling). The functional blueprint was shared even if the inventors never coordinated.

Independent discoveries therefore signal that the sparse manifold of viable solutions is tightly coupled to measurable object dimensions. Whenever multiple groups measure the same blueprint axes, they traverse the same quantized arcs and arrive at similar solutions.

Problems and Solutions Co-Evolve

Intelligence tractability emerges from a deeper principle: successful systems recursively discover which dimensions matter for which outcomes. This is not static mapping; it is dynamic co-evolution.

At the micro level, training explores loss landscapes. At the macro level, entire systems evolve through cycles of problem specification, solution attempt, failure analysis, and re-specification.

Both exhibit the same pattern: exploration through controlled randomness leading to the discovery of functional structure.

At the macro level, the system discovers what the actual problem structure is, and this discovery depends on the model's current world model. Problem definition creation is not independent of model capability; they evolve together.

Problem Framing Matters More Than Solution Optimization

Prior to Einstein's papers, physicists were instrumenting the wrong blueprint for time: they treated simultaneity as absolute, so the measured object (spacetime) never exposed the dimensions needed to reconcile observed anomalies. The moment the blueprint was rewritten-time as a dimension co-measured with space-the permissible arcs changed and the outstanding anomalies collapsed into a coherent program. Similar stories surround Cantor's exploration of infinities or the development of thermodynamics: the decisive move was a blueprint rewrite, not a cleverer solver inside the old frame.

Much current work still optimizes answers within fixed problem spaces rather than reconceptualizing which blueprint dimensions the optimization object actually lives on.

Learning how to solve existing problems better is not the only arc that evolution can follow. Measurement upgrades often demand that we re-specify the problem, produce a new dimensional blueprint, and then redeploy our primitives against the newly revealed object.