Phase Diagram

one_liner: Maps system states.

core_idea: A Phase Diagram is a structured graphical representation that partitions *the parameter space* — typically spanned by control variables such as temperature, pressure, composition, or external field — into regions where *the system exhibits qualitatively distinct phases*, each characterized by a specific value or broken symmetry of *the order parameter*. <!-- FACT-D14-100 -->[^landau-1937] The diagram identifies *the phase boundary* as a codimension-1 surface (a line in 2D, surface in 3D) across which thermodynamic or structural quantities change discontinuously (first-order transition) or have singular derivatives (second-order or higher). <!-- FACT-D14-101 -->[^yang-lee-1952] It locates special points: *the triple point* where three phases coexist in thermodynamic equilibrium; *the critical point* where phase distinctions vanish and density fluctuations diverge to infinity; and multicritical points where the character of phase transitions changes. <!-- FACT-D14-102 -->[^andrews-1869] Equilibrium thermodynamics governs coexistence: along a boundary, coexisting phases share equal values of conjugate potentials (chemical potential, Gibbs free energy), a principle encoded in the Clausius-Clapeyron relation and the Gibbs phase rule F = C − P + 2, where F is the degrees of freedom, C the number of components, and P the number of phases. <!-- FACT-D14-103 -->[^gibbs-1873] Beyond classical thermodynamics, phase diagrams generalize to non-physical systems — economic regimes, biological population steady states, dynamical bifurcation diagrams — wherever qualitatively distinct operating modes are mapped across continuous control-parameter space. <!-- FACT-D14-104 -->[^kuznetsov-1995]

structural_signature:
A phase diagram is constructed by six integrated steps:

1. **Identify *the control parameters*** (temperature, pressure, composition, external field, chemical potential, or similar variables that govern thermodynamic state) and determine which are independent under the constraint of equilibrium. <!-- FACT-D14-105 -->[^gibbs-1873]

2. **Minimize the appropriate thermodynamic potential** — *the Gibbs free energy* G(T, P, N) for constant-T, constant-P systems; Helmholtz F(T, V, N) for constant-T, constant-V; grand potential Ω(T, V, μ) for fixed chemical potential — to determine which phase (or phases) is stable at each point in parameter space. <!-- FACT-D14-106 -->[^gibbs-1873]

3. **Compute *the coexistence curve***: the locus of points where two or more phases have equal free energy and thus coexist in equilibrium, plotted as lines (or surfaces in higher dimensions) in the parameter-space diagram. <!-- FACT-D14-107 -->[^van-der-waals-1873]

4. **Mark critical and multicritical endpoints** where coexistence curves terminate: *the triple point* (three phases meet), *the critical point* (liquid-gas distinction vanishes), *the spinodal line* <!-- FACT-D14-114 -->[^cahn-hilliard-1958] (boundary of stability for metastable extensions), and *the metastability region* (where a phase persists beyond the true equilibrium boundary). <!-- FACT-D14-108 -->[^domb-1996]

5. **Apply *the regime classification*** (e.g., lever rule for two-phase regions: given a point in the two-phase zone, the relative mass fractions of the two coexisting phases are inversely proportional to distances along the tie-line) to extract quantitative phase-fraction information. <!-- FACT-D14-109 -->[^maxwell-1875]

6. **Extend the topological structure** to non-thermodynamic domains: dynamical systems (bifurcation curves <!-- FACT-D14-113 -->[^kuznetsov-1995] as phase boundaries), magnetic systems (H-T plane with ferromagnetic/paramagnetic/aligned regions), ecology (population regimes), and computational complexity (SAT satisfiability phase transition), showing that region/boundary/critical-point structure is universal across disciplines. <!-- FACT-D14-110 -->[^goldenfeld-1992]

what_it_is_not:
- **Not a state diagram in automata/software engineering** (see `state_and_state_transition`). A state machine's state diagram encodes discrete states and discrete transitions driven by events; a phase diagram encodes regions of a continuous parameter space where system behavior is qualitatively different.
- **Not a bifurcation diagram** alone. Bifurcation diagrams show how attractors change with one parameter; a phase diagram is the higher-dimensional generalization, with bifurcation curves as the boundaries. (Related but not identical; see `bifurcation`.)
- **Not any 2D scatter plot.** A phase diagram requires an identifiable order parameter that differs qualitatively (or breaks a symmetry) across the boundaries; it is not merely a plot of any two variables.
- **Not specific to thermodynamics.** Phase diagrams appear in ecology (population regimes), epidemiology (endemic/epidemic regions in R₀-herd-immunity space), computational complexity (easy-hard transitions), economics (stable/unstable equilibrium regions), though the underlying equilibrium concepts differ.
- **Not a dynamical trajectory.** The diagram shows where phases live in parameter space, not how a system evolves through them. A hysteresis loop drawn on top of a phase diagram is a trajectory overlay.

broad_use: Thermodynamics gives the water diagram (ice/liquid/vapor with triple point at 273.16 K, 611 Pa and critical point at 647 K, 22 MPa) and the carbon diagram (graphite/diamond/liquid/vapor with diamond metastable at STP). Materials science uses binary and ternary alloy phase diagrams (Fe-C for steel, Cu-Ni continuous solid solution, eutectic Pb-Sn) as the central design tool for heat treatment and alloy selection. Soft matter diagrams map colloidal crystal/glass/fluid regions. High-energy physics has the QCD phase diagram (hadronic matter, quark-gluon plasma, color superconductor) parameterized by temperature and baryon chemical potential. Condensed matter has the cuprate phase diagram (antiferromagnet, pseudogap, superconductor, strange metal) with the superconducting dome as a hallmark. Dynamical systems and ecology have regime diagrams (stable coexistence vs. extinction vs. limit cycles vs. chaos) as functions of model parameters. Random graph theory has the Erdős-Rényi percolation transition at p = 1/N. Machine learning has grokking and double-descent regions in (data, parameter count, training time) space.

clarity: A phase diagram makes visible **which regimes a system can inhabit and where the switches happen**, converting a potentially bewildering multidimensional space into a legible partition. The boundaries carry meaning: they are where qualitative behavior changes, where engineering or scientific surprise is concentrated, and where sensitivity to parameters is highest. Reading a phase diagram teaches the practitioner to think in terms of the *regions* they occupy and the *distances to boundaries* that determine how much slack a given operating point has before something qualitatively new happens. This is radically clarifying compared to modeling the system as a single continuum.

manages_complexity: A high-dimensional state space is compressed to a low-dimensional parameter map. Instead of tracking every microstate, the practitioner identifies the order parameter(s), computes the relevant potential, and plots the phase regions. Engineering decisions ("how much tin can we tolerate in this solder joint given the service temperature?") collapse to reading a point off a binary alloy diagram. In nonlinear dynamics, knowing which region of parameter space one is in tells the analyst whether to expect fixed points, limit cycles, or chaos — no simulation needed for the qualitative question. The management of complexity is radical: all the detail of the actual physics, chemistry, or dynamics is folded into the topology of the phase diagram, which is a finite object even when the underlying state space is continuous and huge.

abstract_reasoning: Phase diagrams encode a fundamental abstraction: **qualitative behavior is organized by a small number of control parameters**, and the map of how behavior changes with those parameters is finite and often simple. This is the conviction that underlies much of theoretical physics and applied science — that reality is not uniformly complicated, but has structure, and the structure can be mapped. The same abstract move recurs in entirely non-physical contexts: an organizational theorist mapping "startup / scaling / mature / declining" regions in (headcount, revenue-growth) space is drawing a phase diagram; a product manager distinguishing "pre-product-market-fit / PMF / growth / saturation" regions is drawing one. The universal lesson: regions and boundaries, not trajectories alone, are the right primitive for thinking about a system with multiple qualitatively distinct operating regimes.

knowledge_transfer:
| Role in Source (thermodynamics: water phase diagram) | Role in Target (software systems: load regimes) |
|---|---|
| Control variables (T, P) | Control variables (request rate, concurrency level) |
| Phase (solid, liquid, vapor) | Operating regime (underloaded, stable, congested, thrashing) |
| Order parameter (density) | Latency distribution / tail percentile / error rate |
| Phase boundary (coexistence curve) | Regime boundary (onset of queueing, onset of collapse) |
| Triple point | Corner case where three regimes meet (edge of stability) |
| Critical point (647 K, 22 MPa) | Saturation point where queue theory predictions diverge |
| Metastability (supercooling) | Bistability where the system can be in either regime depending on history |

Performance engineers map their systems' behavior as load and concurrency vary, and the resulting map has the topological structure of a phase diagram: distinct regimes (underutilized / balanced / saturated / thrashing), boundaries where behavior changes qualitatively, hysteresis (a saturated system that survived a load spike may not recover even when load drops), and critical points where response-time distributions become heavy-tailed. The same reasoning — read the current operating point, measure distance to the nearest boundary, design for margin — applies. Capacity planning is phase-diagram reasoning applied to infrastructure.

prose:
_(Pass B)_

### Catalog cross-references (v1, batches 02–29)

Solution archetypes that reference this prime (per `solution_archetypes/_catalog/catalog_v1_batches_02_29.yaml`):

**As source prime (2):** `controlled_phase_transition`, `transition_boundary_monitoring`

**As related prime (4):** `nonlinear_threshold_response`, `phase_space_mapping`, `scale_transition_management`, `tipping_point_prevention`

notes:
Held at High confidence. Premier success of
renormalization-group theory; defines a
paradigmatic classification scheme in
physics. Entry carefully distinguishes
universality from scale invariance and from
renormalization while showing their
interrelation (RG machinery → scale-invariant
fixed point → universality class). Emphasizes
the (d, symmetry, range) labels, the
non-universal counterparts, and the specific
ways universality can fail or be misidentified.
Closes the physics sub-cluster of batch 7 with
strong cross-references to renormalization
(#129) and scale_invariance (#125).
[^strogatz-1994]: Strogatz, Steven H. *Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering*. Redwood City: Addison-Wesley, 1994. Modern comprehensive treatment of perturbation analysis in nonlinear dynamical systems; covers regular and singular perturbation theory, phase-plane analysis, bifurcations, and chaos; widely used text unifying perturbation methods across disciplines.

[^kuznetsov-1995]: Kuznetsov, Y. A. "Elements of Applied Bifurcation Theory" (2nd ed.). Springer, 1995. Rigorous analysis of bifurcation diagrams; maps dynamical transitions onto abstract phase diagrams organized by stability and criticality.

[^cahn-hilliard-1958]: Cahn, J. W. & J. E. Hilliard. "Free Energy of a Nonuniform System: I. Interfacial Free Energy." Journal of Chemical Physics 28, 258–267 (1958). Theory of spinodal decomposition and the spinodal curve (limit of metastability); explains the region between coexistence and stability limits in phase diagrams.


Phase Separation

type: prime

one_liner: A previously mixed system spontaneously demixes into distinct, spatially segregated regions once like-with-like interactions outweigh mixing above a threshold.

status: draft

core_idea:
Phase separation is the structural pattern in which a system previously mixed at the scale of its components spontaneously reorganizes into distinct, spatially segregated regions whose internal composition differs from the original mixture and from each other, because the mixed state is no longer the lowest-free-energy configuration once the interaction energies between like and unlike elements differ enough. The driving force is internal rather than imposed: like-with-like interactions become more favourable than mixed interactions, so the system gains energy by sorting itself into regions of locally similar composition. Each resulting region acquires its own bulk properties, and the boundaries between them are interfaces with their own structural and energetic character. The crucial reframing the prime delivers is that segregation is endogenous, not externally drawn — the default model of "things stay where they are put" is replaced by "things sort themselves once the interaction asymmetry exceeds a threshold."

The signature has six parts: an initial state in which heterogeneous components are mixed at small scales; interaction energies that favour like-with-like over mixed neighbours above some control-parameter threshold (temperature, composition, mobility, interaction strength); a spontaneous local sorting process that proceeds either by nucleation-and-growth from specific seeds or by spinodal decomposition in which long-wavelength compositional fluctuations grow everywhere at once; the emergence of distinct coexisting phases, each with characteristic composition; an interface between regions with non-trivial thickness, composition, and energy; and a miscibility boundary in parameter space separating the mixed regime from the demixed one, often with a critical point where the transition becomes continuous. The pattern is substrate-independent because none of these elements names a medium: interaction asymmetry, miscibility boundary, nucleation, spinodal decomposition, and interface are stated as relations among components and a control parameter, so the same skeleton describes oil and water, demixing alloys, biomolecular condensates, segregating neighbourhoods, sorting markets, and partitioning distributed systems alike.

structural_signature:
*the initially-mixed heterogeneous state* — *the like-with-like interaction asymmetry above threshold* — *the spontaneous endogenous sorting* — *the distinct coexisting phases* — *the interface with its own energy* — *the miscibility boundary in parameter space*

The pattern is present when each of the following holds:

- **An initially-mixed state.** Heterogeneous components are intermingled at small scales.
- **An interaction asymmetry above threshold.** Like-with-like interactions become more favourable than mixed interactions, past some control-parameter threshold (temperature, composition, mobility, interaction strength). This asymmetry is the *internal* driving force — segregation is endogenous, not externally imposed.
- **A spontaneous sorting process.** The system locally sorts itself, either by nucleation-and-growth from specific seeds or by spinodal decomposition in which long-wavelength fluctuations grow everywhere at once. These are two distinct routes to the same final state.
- **Distinct coexisting phases.** Spatially segregated regions emerge, each with characteristic composition differing from the original mixture and from each other.
- **An interface with its own character.** The boundary between regions is a real structural object — a zone with its own thickness, composition, and energy — whose tension governs the stability of the separated state.
- **A miscibility boundary.** A curve in parameter space separates the mixed regime from the demixed one, often with a critical point where the transition becomes continuous.

The reframing is that *things sort themselves once the interaction asymmetry crosses threshold*, replacing "things stay where they are put." These compose into a spontaneous-demixing mechanism: a mild preference operating without coordination produces strong global segregation, by a seeded or everywhere-at-once route, across a real interface.

what_it_is_not:
- **Not a phase diagram.** A `phase_diagram` is the static *map*
  of which phases exist at which parameter values; phase
  separation is the *dynamic process* by which a system demixes
  when it crosses the miscibility boundary that diagram charts.
- **Not a generic phase transition.** `tipping_points_or_phase_transitions`
  covers any abrupt regime shift; phase separation is the
  *specific* spontaneous spatial demixing driven by like-with-
  like interaction asymmetry, with coexisting phases and an
  interface.
- **Not nucleation alone.** `nucleation` is *one route* (seeded)
  to demixing; phase separation also proceeds by spinodal
  decomposition (everywhere-at-once), and names the whole
  demixing phenomenon, not the seeding step.
- **Not dissipation.** `dissipation` spreads or degrades a
  gradient toward uniformity; phase separation does the opposite
  — it spontaneously *creates* spatial structure from a uniform
  mixture.
- **Not imposed sorting.** The segregation is *endogenous*,
  driven by internal interaction energetics, not drawn by an
  external agent. Reading it as deliberate exclusion overcounts
  intent.
- **Common misclassification.** Inferring the strength of the
  cause from the strength of the effect — concluding sharp
  demixing must reflect strong preferences, when a barely-above-
  threshold local affinity, uncoordinated across many sites,
  suffices to produce strong global segregation.

broad_use:
- **Chemistry and materials science (origin)** — oil-and-water, alloy demixing on cooling, eutectoid microstructures, polymer blends, glass formation; the canonical substrate where interaction asymmetry and the miscibility boundary were first formalized.
- **Cell biology** — membraneless organelles (P-bodies, stress granules, nucleoli) form by liquid-liquid phase separation of intrinsically disordered proteins, a paradigm shift over the past decade.<!-- FACT-D68-676 -->[^banani-etal-2017]
- **Sociology and urban geography** — Schelling segregation, in which neighbourhoods spontaneously sort by demographic even under mild individual preferences, was an explicit transposition of the phase-separation structure from materials science.<!-- FACT-D68-677 -->[^schelling-1971]
- **Informational ecology** — media bubbles, partisan sorting, and in-group homophily produce phase-separated information environments from initially mixed populations once within-group affinity exceeds cross-group affinity.
- **Economics** — market segmentation sorts products and customers into price and quality bands when cross-segment switching costs exceed within-segment cohesion; industrial agglomeration is the same pattern at firm scale.
- **Ecology** — competing species sort into spatial bands or patches, and zonation along environmental gradients produces sharp band boundaries by the same mathematics.
- **Distributed systems** — data sharding by access locality, partition-tolerance creating effectively separate sub-clusters during network splits, and workload-affinity cache partitioning are computational phase separation.
- **Cosmology** — matter evolves from near-homogeneity into filamentary and void structure under gravitational instability, a phase-separation analogue at cosmic scale.<!-- FACT-D68-678 -->[^peebles-1980]

clarity: Phase separation makes visible a category of segregation patterns that would otherwise be misread either as deliberately sorted — overstating intentional cause — or as random — understating the driving asymmetry. It installs four distinctions that everyday reasoning collapses. First, whether a system mixes or segregates is set by the relative strength of like-with-like versus mixed interactions, not by external sorting, so a mild preference operating without coordination can produce strong global segregation. Second, the interface is a real structural object, not merely "the boundary between regions" but a zone with its own thickness, composition, and energy, whose tension governs the stability of the separated state. Third, spinodal decomposition (everywhere-at-once, long-wavelength growth) and nucleation-and-growth (specific seeds growing) are two distinct routes to the same final state, distinguishable by their intermediate signatures and requiring different interventions to prevent. Fourth, the miscibility boundary — the parameter-space curve dividing mixed from demixed — is a substrate-general object, often with a critical point where the transition becomes continuous. Without this language, analysts attribute segregation outcomes either to deliberate exclusion (overcounting intent) or to coincidence (undercounting the driving asymmetry), missing the structural inevitability of segregation once the asymmetry crosses threshold.

manages_complexity: Phase separation compresses a huge family of segregation phenomena into a single structural diagnostic: do the like-with-like interactions exceed the threshold relative to the mixing entropy? If yes, the system demixes; if no, it mixes; in the critical region, it shows characteristic large fluctuations. This routes attention away from cataloguing the resulting patterns, which differ wildly across substrates, and toward the interaction asymmetry and its current relation to the threshold, which is what actually decides the outcome. It also organizes a cluster of nearby patterns into a coherent family parented by the prime: nucleation as the seeded route, spinodal decomposition as the everywhere-at-once route, interface tension as the boundary energetics, Ostwald ripening as the slow coarsening of phases over time, and wetting as the interaction between interface and substrate. Recognizing phase separation as the parent makes these legible as variants on one structural theme rather than disconnected effects, and turns the intervention question into a structural one — adjust the interaction asymmetry, move the control parameter relative to the miscibility boundary, or change the interface energy — rather than a matter of cataloguing preferences case by case.

abstract_reasoning: Reasoning with phase separation enables several moves. *Interaction-asymmetry analysis*: when assessing whether a population will segregate, ask about the gap between like-with-like and mixed interaction strengths, not merely whether preferences exist, since a weak preference operating without coordination across many sites can globally outweigh strong coordination at any single one. *Threshold thinking*: there is a regime where small changes in temperature, mobility, or communication cost flip the system from stable-mixed to stable-segregated, so identifying which parameter sits near the miscibility boundary lets an analyst predict regime change before it occurs. *Interface-as-cost*: the persistence of a separated system depends on interface energy, so lowering interface cost (surfactants, mediators, neutral brokers) can stabilize mixing while raising it accelerates segregation — an intervention space that is structural rather than preference-based. *Spinodal-versus-nucleation diagnostics*: a system that demixes simultaneously across all length scales is spinodally unstable, while one that demixes from specific seeds is metastable, and the two demand different interventions to prevent. And *critical-point recognition*: near the critical point of the miscibility boundary the system shows large fluctuations and long correlation lengths, a recognizable fingerprint that it is on the verge of separating but not yet committed.

knowledge_transfer: The role mappings are explicit: the *mixed initial state* maps onto any small-scale intermingling of heterogeneous components; the *interaction asymmetry* onto the gap between like-with-like and mixed affinities (energy, preference, cost); the *control parameter* onto temperature, mobility, composition, or interaction strength; the *two routes* onto seeded nucleation and everywhere-at-once spinodal decomposition; the *coexisting phases* onto the spatially distinct regions of characteristic composition; the *interface* onto the real boundary zone with its own energy; and the *miscibility boundary* onto the parameter-space curve separating the regimes. Because these are stated abstractly, both the mathematics and the intervention logic transfer, and the historical record contains several documented, load-bearing imports. Schelling's 1971 residential-segregation model explicitly imported phase-separation thinking from physical chemistry, showing that mild individual preferences produce strong global segregation — a result still central to urban-policy analysis.<!-- FACT-D68-679 -->[^schelling-1971] The discovery that membraneless organelles form by liquid-liquid phase separation was a wholesale import of the polymer-physics framework into cellular biochemistry, replacing the prior stoichiometric-complex model.<!-- FACT-D68-680 -->[^brangwynne-etal-2009] Industrial-cluster theory imports phase-separation logic to explain why economic activity concentrates geographically rather than spreading uniformly. Filter-bubble and partisan-sorting analysis uses the framework to explain how mixed populations sort into informationally separated communities once the within-group-versus-cross-group asymmetry crosses threshold. The transfer runs both ways: the interface-as-active-region idea, developed first in materials science, feeds back into sociology as "boundary work," the active investment required to maintain social-category interfaces.<!-- FACT-D68-681 -->[^gieryn-1983] A chemist watching oil and water sort into layers across a sharp interface, an urban modeller watching a city demix into demographic neighbourhoods under mild preferences, and a cell biologist watching stress-induced proteins condense into liquid droplets are doing the same structural work: measure the interaction asymmetry, locate the system relative to the miscibility boundary, and predict whether — and by which route — the mixed state will sort itself apart.

formal_abstract:
Consider a binary alloy demixing on cooling, modeled by the regular-solution free energy — the prime's home case, fully quantitative. The *initially-mixed heterogeneous state* is a homogeneous solid solution of atoms A and B intermingled on a lattice at high temperature. The *like-with-like interaction asymmetry above threshold* is captured by the interaction parameter $\Omega$: when A-A and B-B bonds are energetically more favourable than A-B bonds ($\Omega > 0$), the enthalpy of mixing is positive and opposes mixing. The free energy of mixing is $\Delta G = \Omega x(1-x) + RT[x\ln x + (1-x)\ln(1-x)]$, where $x$ is composition and $T$ temperature: the entropy term ($\propto T$) favours mixing, the enthalpy term favours demixing.<!-- FACT-D68-682 -->[^porter-easterling-2009] The *control parameter* is temperature, and the *miscibility boundary in parameter space* is the curve below which the mixed state is no longer the free-energy minimum — below the critical temperature $T_c = \Omega/2R$, the system demixes.<!-- FACT-D68-683 -->[^porter-easterling-2009] The *spontaneous endogenous sorting* proceeds by two distinct routes the prime names: inside the spinodal (where $\partial^2 G/\partial x^2 < 0$) the mixture is unstable to infinitesimal fluctuations and demixes everywhere at once by spinodal decomposition; between the spinodal and the binodal it is metastable and demixes only by nucleation-and-growth from seeds.<!-- FACT-D68-684 -->[^cahn-hilliard-1958] The *distinct coexisting phases* are A-rich and B-rich regions whose compositions are read off the common-tangent construction.<!-- FACT-D68-685 -->[^porter-easterling-2009] The *interface with its own energy* is the boundary between them, carrying a real interfacial tension that drives later coarsening (Ostwald ripening). The diagnostic the prime forces: segregation is endogenous — no external agent sorted the atoms; crossing $T_c$ made the mixed state energetically unfavourable, and the route (spinodal versus nucleation) is read from where the quench lands relative to the spinodal curve.

**Mapped back:** The solid solution is the mixed state, $\Omega$ the interaction asymmetry, temperature the control parameter, $T_c$ the miscibility boundary, A-rich/B-rich domains the coexisting phases, and the domain wall the interface — demixing driven internally by the enthalpy-entropy balance, by spinodal or nucleation route.

applied_industry:
Consider residential segregation under Schelling's model, alongside the structurally identical case of biomolecular condensates forming by liquid-liquid phase separation — two genuine domains into which the materials-science framework was explicitly imported. In Schelling's case the *initially-mixed heterogeneous state* is a city with two demographic groups intermingled across a grid of homes. The *like-with-like interaction asymmetry above threshold* is each household's mild preference to have at least some fraction of like neighbours — crucially, a *weak* preference, not a desire for exclusion. The *control parameter* is that tolerance threshold (plus mobility). The *spontaneous endogenous sorting* is the key result the prime predicts: when the preference crosses a modest threshold, households whose neighbourhoods fall below their comfort fraction relocate, and these uncoordinated local moves cascade into strong global segregation — the *distinct coexisting phases* being sharply demixed demographic neighbourhoods, even though no individual wanted full separation. This is the prime's central reframing made vivid: a mild preference operating without coordination produces strong global segregation, so the outcome should be read as structural inevitability past threshold, not as deliberate exclusion (overcounting intent) or coincidence (undercounting the asymmetry). The *interface* is a real object too — the boundary between neighbourhoods requires active "boundary work" to cross, the sociological feedback the prime notes. The cell-biology parallel maps role-for-role: intrinsically disordered proteins whose multivalent self-affinity exceeds their affinity for the surrounding cytoplasm demix above a concentration threshold into membraneless organelles (P-bodies, stress granules), with the droplet interface carrying surface tension and the saturation concentration playing the role of the miscibility boundary.<!-- FACT-D68-686 -->[^brangwynne-etal-2009] An urban modeller watching a city demix under mild preferences and a cell biologist watching stress proteins condense into droplets do the same structural work: measure the interaction asymmetry, locate the system relative to the miscibility boundary, and predict whether the mixed state sorts itself apart.

**Mapped back:** Intermingled households (or dispersed proteins) are the mixed state, the mild like-neighbour preference (or self-affinity) the interaction asymmetry, the tolerance threshold (or saturation concentration) the miscibility boundary, and demixed neighbourhoods (or condensate droplets) the coexisting phases — segregation driven endogenously by a weak local preference crossing threshold.


Phase Space

one_liner: All possible system states.

origin_domain: physics

core_idea: Phase space is the abstract geometric setting for dynamical systems in which each point represents a complete instantaneous state of the system — in classical mechanics, a point (q, p) specifying all generalized coordinates and their conjugate momenta; more generally, any parameterization that uniquely specifies the state sufficient to determine its future evolution under the given dynamics. The essential commitment is that the state of a deterministic system, though it may have many components (positions of all particles, velocities, field values), can be represented as a single point in a high-dimensional space, and the system's temporal evolution is a trajectory through this space, turning dynamics into geometry. Every phase-space articulation specifies (1) the dimensionality and coordinates — 2N for an N-degree-of-freedom mechanical system (generalized coordinates plus conjugate momenta), ∞-dimensional for field theories, a specific finite dimension for specific dynamical systems; (2) the geometric structure — the symplectic 2-form for Hamiltonian systems, or a Riemannian metric, Poisson structure, or more general geometry as appropriate; (3) the dynamical flow — the Hamiltonian vector field generated by H on phase space, the gradient flow in dissipative systems, or more general dynamical-systems flows; and (4) the invariants — conserved quantities (first integrals), constants of motion, the phase-space volume (Liouville's theorem for Hamiltonian systems), the topology of invariant sets (fixed points, limit cycles, attractors, chaotic sets). The construct originates with Gibbs and Boltzmann in statistical mechanics and Hamilton in classical mechanics, and pervades dynamical systems theory, classical and quantum mechanics, thermodynamics, and applied mathematics.

structural_signature: For a mechanical system with N degrees of freedom, phase space is a 2N-dimensional manifold parameterized by (q₁,...,q_N, p₁,...,p_N). The system's state at any instant is a single point; its history is a smooth curve (trajectory) parameterized by time. Hamilton's equations q̇_i = ∂H/∂p_i, ṗ_i = −∂H/∂q_i generate a vector field whose integral curves are the trajectories. <!-- FACT-D10-080 -->[^hamilton-1834] Liouville's theorem states that phase-space volume is preserved by Hamiltonian flow[^liouville-1838]; the symplectic structure ω = dq ∧ dp is the fundamental geometric invariant. <!-- FACT-D10-081 -->[^liouville-1838] Hamiltonian's 1834–1835 formalism established (q,p) canonical coordinates and the symplectic-structure foundation of modern analytical mechanics[^hamilton-1834].

what_it_is_not:
**Common misclassification**: Equating phase space with configuration space. Configuration space is the set of possible positions (q_1,...,q_N); phase space is positions plus conjugate momenta (q_1,...,q_N, p_1,...,p_N). For a single particle in 3D, configuration space is ℝ³ but phase space is ℝ⁶. The distinction is essential for Hamiltonian mechanics and for specifying state uniquely.

**Not state space in the engineering sense without further specification**: engineering "state space" (control theory) is similar in spirit but often uses different coordinate choices (state variables rather than generalized coordinates and momenta) and may not carry the symplectic structure. The constructs are related but distinct.

**Not phase diagrams in thermodynamics**: thermodynamic phase diagrams (P-T, P-V) are low-dimensional plots of equilibrium-phase boundaries, lexically related but conceptually distinct from dynamical phase space. The shared word "phase" invites confusion.

**Not identical to Hilbert space in quantum mechanics**: the quantum analog of phase space is Hilbert space (or projective Hilbert space), with a different geometric structure. <!-- FACT-D10-082 -->[^wigner-1932] Wigner's quasi-probability distribution lives on a phase-space-like manifold, but the quantum state is properly a state vector or density matrix, not a phase-space point[^wigner-1932].

**Not a Euclidean space in general**: phase spaces can have non-trivial topology (e.g., rotations → configuration space S², phase space T*S² with its cotangent-bundle structure) and non-trivial geometry. The assumption of flat Euclidean phase space is a special case, not the default.

**Not merely a visualization tool**: while phase-space diagrams are excellent pedagogical visualizations (for 1- and 2-degree-of-freedom systems), phase space is a substantive mathematical structure underlying much of classical mechanics, statistical mechanics, and dynamical systems theory. Treating it only as visualization undersells the construct.

Cross-references: see *degrees_of_freedom* (determines the dimensionality of phase space); see *trajectory* (the temporal curve through phase space); see *state* (the point in phase space); see *attractor* (a subset of phase space toward which trajectories converge in dissipative systems); see *principle_of_least_action* (generates Hamiltonian structure via symplectic geometry).

broad_use: Phase space appears in classical mechanics (Hamiltonian formulation; the fundamental setting for advanced mechanics and celestial mechanics); in statistical mechanics (ensemble theory — the distribution of system states in phase space, Liouville's theorem, ergodic theory); <!-- FACT-D10-083 -->[^gibbs-1902] in Gibbs's 1902 ensemble formulation, phase-space probability distributions underpin microcanonical, canonical, and grand-canonical ensembles[^gibbs-1902]; in quantum mechanics (Wigner function as a quasi-probability on phase space, though the full quantum state lives in Hilbert space); in dynamical systems theory (the geometric setting for classifying flows, identifying fixed points, limit cycles, chaotic attractors); in control engineering (state-space methods); in information theory (state spaces of finite-state systems); in ecology and population dynamics (species abundances as coordinates); in economics (macro-dynamic models in production-consumption state space); and in neuroscience (neural population activity in firing-rate state space). It is arguably the single most important organizational construct in the geometric theory of dynamics, with extensive technical apparatus.

clarity: Phase space is clarifying because it converts dynamics into geometry: complex time-evolution of multi-component systems becomes a trajectory in a space whose geometry encodes the invariants and structure of the dynamics. Conserved quantities are level sets; limit cycles are closed curves; attractors are compact invariant sets; chaos appears as sensitive dependence on initial conditions in the form of positive Lyapunov exponents. <!-- FACT-D10-084 -->[^poincare-1890] The geometric intuition it supports — through Poincaré's 1890 analysis of three-body orbits and recurrence phenomena — is indispensable in modern dynamical systems[^poincare-1890]. Conserved quantities in phase space correspond directly to symmetries of the system, linking classical mechanics to conservation laws through Hamiltonian structure; see *conservation_laws*.

manages_complexity: The construct manages the complexity of multi-component dynamical systems by collapsing the instantaneous state — however many components — into a single point and the full temporal history into a single curve. This allows systematic classification of behaviors (fixed points, periodic orbits, quasi-periodic motion, chaos) via the geometry of invariant sets in phase space, reducing the apparent diversity of dynamical behaviors to a tractable taxonomy. <!-- FACT-D10-085 -->[^birkhoff-1927] Birkhoff's 1927 formal foundations of dynamical-systems theory on manifolds established the rigorous framework for phase-space analysis[^birkhoff-1927].

abstract_reasoning: Phase-space reasoning proceeds by identifying coordinates and momenta (or appropriate state variables), writing the dynamical flow, identifying fixed points and their linear stability, identifying invariant sets (limit cycles, tori, attractors), and classifying qualitative behavior. It licenses geometric and topological methods (Poincaré sections, bifurcation theory, KAM theorem, Lyapunov analysis), enables ensemble methods in statistical mechanics, and supports the quantum-classical correspondence via semiclassical phase-space methods. <!-- FACT-D10-086 -->[^hopf-1937] Hopf's 1937 ergodic-theory framework showed that time-averaged and ensemble-averaged quantities are equivalent for ergodic systems evolving in phase space[^hopf-1937].

knowledge_transfer:
| Role | Mechanical form | Dynamical-systems form | Statistical-mechanical form | Control-theory form |
|---|---|---|---|---|
| Point | (q, p) | State variables | Microstate (q, p) | State vector x |
| Space | Cotangent bundle T*Q | ℝⁿ or manifold M | Γ-space (3N-dim) | ℝⁿ |
| Flow | Hamiltonian vector field | Dynamical-systems vector field | Liouville flow | State-equation flow |
| Invariants | Constants of motion | First integrals | Energy, volume | Conserved quantities |
| Invariant sets | Energy surfaces | Fixed points, limit cycles, attractors | Energy shells | Equilibria, invariant subspaces |

A classical-mechanics phase-space analysis transfers to statistical mechanics (ensemble theory), to dynamical systems (fixed-point and bifurcation analysis), to control theory (state-space methods and linear system analysis), to ecology (predator-prey phase portraits), and to neuroscience (neural state-space analysis). The structural core is the geometric representation of state spaces with dynamical flows; what varies is the specific space, flow, and invariant structure.

prose:
*(Pass B — deferred.)*

### Catalog cross-references (v1, batches 02–29)

Solution archetypes that reference this prime (per `solution_archetypes/_catalog/catalog_v1_batches_02_29.yaml`):

**As source prime (1):** `phase_space_mapping`

**As related prime (3):** `controlled_phase_transition`, `discrete_continuous_model_selection`, `transition_boundary_monitoring`

notes: Held at High confidence. Central organizational construct in Hamiltonian mechanics, statistical mechanics, dynamical systems theory, and modern geometric mechanics. Entry distinguishes it from configuration space, Hilbert space, and thermodynamic phase diagrams. The symplectic structure is noted but the entry remains accessible at a conceptual level. Reciprocal links to *principle_of_least_action* (variational route to Hamiltonian mechanics), *degrees_of_freedom* (determines phase-space dimensionality), and *conservation_laws* (via Liouville and first integrals) established; forward reference to *entropy_thermodynamic_sense* (coarse-graining in phase space) and *chaos* (phase-space attractors, Lyapunov exponents) provided.


Phenomenalism

slug: phenomenalism

one_liner: Reality known through perception.

origin_domain: philosophy

core_idea:
Phenomenalism is the epistemological and ontological thesis that physical objects are, either ontologically or semantically, reducible to actual and possible sense-experiences — that statements apparently about mind-independent material objects are analyzable (in principle if not in practice) as statements about what observers would experience under specified conditions. The essential commitment is that the category of "physical object" does not require commitment to a substrate beyond the structured patterns of actual and counterfactual sense-content; to say a table exists in the next room is to say something about what would be experienced if one entered it, what would be experienced from other angles, and how these experiences would cohere.

The phenomenalist framework articulates four core components: **(a) the sense-data primitive** — phenomenalism takes as basic some class of experiential elements (Berkeleyan ideas, Humean impressions, Russellian sense-data, logical-positivist protocol sentences);[^berkeley-1710] <!-- FACT-D19-191 --> **(b) the physical-object analysandum** — the claim to be analyzed, typically a statement apparently about a mind-independent object persisting unobserved; **(c) the reduction/translation rule** — the mechanism by which object-talk is to be translated, eliminatively reduced, or reductively reconstructed from sense-data talk, most commonly via **the modal possibilities-of-sensation** — Mill's 1865 formulation: "permanent possibilities of sensation,"[^mill-1865] <!-- FACT-D19-190 --> a counterfactual-conditional framework specifying that objects are the structured totality of actual and counterfactual experiences accessible under specifiable conditions; and **(d) the verificationist commitment** — the claim that empirical meaningfulness is exhausted by what is in principle observable or verifiable, often grounded in logical empiricism's principle that statements about unobservable matter must reduce to observation-statements.[^ayer-1936] <!-- FACT-D19-194 --> The core difficulty shared across all these components is that they must specify what counts as a basic phenomenal element and what logical operations suffice to reconstruct objects from those elements — Hume's distinction between impressions and ideas[^hume-1739]<!-- FACT-D19-204 --> anticipates this phenomenalist commitment.

Canonically developed across Berkeley's immaterialist metaphysics (1710), Mill's phenomenalist analysis (1865), Russell's logical-construction phase (1914);[^russell-1914] <!-- FACT-D19-192 --> and Russell's logical-atomist refinement[^russell-1918]<!-- FACT-D19-193 --> of the program, Ayer's verificationist phenomenalism (1936), and the Vienna Circle's reductive empiricism. Post-Berkeleyan phenomenalists typically decline to identify reality with the mental substrate (idealism's further step), remaining agnostic about whether sense-data are mind-dependent mental events or mind-independent sensible properties accessible only through experience. The distinction matters: Berkeleyan immaterialism is ontologically committed to the mental; phenomenalism as a logical-positivist thesis is ontologically neutral, treating the analysis as purely semantic — a claim about translation, not about what exists.

structural_signature:
An ostensible object-claim "X is F" (e.g., "the dining-room table continues to exist when no one is in the room") is analyzed into (or reduced to) a conjunction or systematic series of counterfactual conditionals about sense-experience: "if an observer were in condition C₁, they would have experience E₁; if in C₂, E₂; if in C₃, E₃..." The **ostensibly-equivalent paraphrase** preserves every claim the original makes about what is observable in principle, while eliminating the apparent commitment to a transcendent, mind-independent substrate. The counterfactual structure is essential and three-layered:

1. **Actual observations** — experiences I have had or could verify
2. **Counterfactual conditionals** — what would be experienced under specified (but unactualized) observation-conditions
3. **Coherence relations** — how actual and counterfactual experiences cohere into a unified object-pattern

The tree in the quad continues to exist because of what would be experienced (visual character from various angles, tactile character if touched, temporal coherence through temporal intervals of non-observation) under any observer satisfying the requisite conditions. The phenomenalist reduction thus trades a claim about a mind-independent substrate for a structured claim about the behavior of actual and possible experience.

what_it_is_not:
**Common misclassification**: Conflating phenomenalism (an epistemological/ontological thesis about what physical objects are) with phenomenology (a methodological approach to the structure of first-person conscious experience). The two terms are lexically close and philosophically distinct: phenomenology investigates the structure of consciousness and intentional content without taking a reductive stand on the objects of experience; phenomenalism takes such a reductive stand, claiming that objects just are (or are analyzable as) patterns of sense-data. See *phenomenology* for the methodological prime.

**Not idealism proper**: Berkeleyan idealism takes a further step that phenomenalism need not — identifying reality with the mental substrate and grounding existence in God's eternal perception. Post-Berkeleyan phenomenalists (Mill, Russell, Ayer) typically decline this metaphysical commitment, remaining agnostic or offering purely linguistic analyses.

**Not representationalism**: The representationalist holds that perception represents mind-independent objects that cause and are distinct from perceptions; phenomenalism holds that the objects just are the structured perceptions or patterns of sense-data.

**Not empiricism per se**: All phenomenalists are empiricists, but not all empiricists are phenomenalists. A radical empiricist who grounds knowledge in sense-experience but denies reduction to sense-data is not a phenomenalist.

**Not naive "it's all in your head"**: Phenomenalism is typically careful about inter-subjective objectivity and counterfactual structure. The permanent-possibility-of-sensation framing aims to preserve the publicity and mind-independence of objects despite their phenomenalist reduction — they are accessible to any observer meeting conditions C, hence objective in a weak sense.

**Not solipsism**: Solipsism denies intersubjectivity entirely. Phenomenalism acknowledges that others' sense-data are in principle as relevant to the analysis as mine; the tree is analyzable not just in terms of what I would experience but what any observer (you, her, the camera) would experience.

Cross-references: see *phenomenology* for the tight-paired methodological prime frequently confused with this one; see *representation* for the realist/representationalist alternative; see *ontology* for the broader category within which phenomenalism is an ontological thesis; see *counterfactuals* for the structural element (the modal conditional) that carries phenomenalism's account of unobserved matter.

broad_use:
Phenomenalism appears in early modern philosophy (Berkeley) as the grounding for an immaterialist metaphysics; appears in British empiricism (Mill, Russell, Ayer) as the epistemological foundationalism of sense-datum theory; appears in logical positivism (Vienna Circle, Carnap, Ayer) as the reductive program for empirical meaningfulness of scientific statements; and appears in more moderate forms in contemporary constructive empiricism (van Fraassen 1980) as a stance about the extent of scientific commitment.[^van-fraassen-1980] <!-- FACT-D19-199 -->

It recurs across multiple domains:

- **Epistemology**: sense-data theory and the "given" — the Sellarsian critique of the myth of the given;[^sellars-1956] <!-- FACT-D19-197 --> foundationalism vs coherentism debates (BonJour's empirical foundationalism[^bonjour-2001]<!-- FACT-D19-202 --> continues this tradition); whether basic experiential elements can ground knowledge without circularity
- **Philosophy of perception**: the classical debate between direct realism (perception is direct access to external objects) and phenomenalism (objects are analyzable from perception); the foundational sense-data work of Price[^price-1932]<!-- FACT-D19-200 --> and the Firth tradition[^firth-1949]<!-- FACT-D19-201 -->; Chisholm's critique of phenomenalism as unable to state the analysis without presupposing the physical-object language it aimed to eliminate;[^chisholm-1948] <!-- FACT-D19-196 --> contemporary "sense-data revival" work (Huemer[^huemer-2007]<!-- FACT-D19-203 -->) vs "new direct realism"
- **Philosophy of science**: phenomenalism structures the debate over scientific realism vs instrumentalism; what is science committed to beyond empirical prediction? Unobservable theoretical entities (electrons, gravitational fields, quantum amplitudes) — are they real or merely instrumental predictive tools? Van Fraassen's constructive empiricism preserves phenomenalist-like intuitions about observability without full phenomenalism
- **Philosophy of language**: verificationism — a statement's meaning is its method of verification. Ayer's verificationist principle (a statement is meaningful iff it is analytic or empirically verifiable)[^ayer-1956] <!-- FACT-D19-195 --> grounded phenomenalism in a theory of meaning; the principle's collapse (it was self-undermining) pulled support from verificationist phenomenalism
- **Logical positivism and Vienna Circle**: Carnap's logische Aufbau (logical construction) attempted to reconstruct all scientific concepts from protocol sentences (phenomenal observation-statements); the project aimed to show that science ontologically commits to nothing beyond what is observable or verifiable.[^carnap-1928] <!-- FACT-D19-198 --> The failure of the reduction project (Quine's critique, indeterminacy of translation) undermined logical-positivist confidence in phenomenalism

clarity: Phenomenalism is clarifying because it forces a direct question often smuggled tacitly: what exactly do statements about physical objects commit us to beyond the patterns of actual and possible experience? By attempting an explicit reduction or translation, phenomenalism makes the content of realist commitments concrete — whatever is left over when phenomenal content is accounted for. The sharpness of the phenomenalist project reveals what realists claim unobservable matter adds to the empirical story. If a phenomenalist reduction is impossible (as critics like Chisholm argue), that impossibility itself clarifies the relationship between object-language and experiential language. If reduction succeeds for some domain (perhaps for macroscopic tables but not for subatomic particles), that success-with-limits clarifies where our ontology must expand.

manages_complexity: Phenomenalism manages the complexity of perceptual knowledge by reducing the heterogeneous ontology of mind-plus-world-plus-representation-relations to a single stratum — structured patterns of phenomenal content. The simplification is ontological (fewer kinds of things to believe in) but structurally demanding: the burden is transferred to the specification of counterfactual conditions and the coherence of phenomenal manifolds. Whether this simplification survives technical articulation is one of the core debates in analytic epistemology. Sellars's critique, Chisholm's objections, and the indeterminacy of phenomenalist translation all argue that the simplification is illusory — that specifying the conditions requires object-language concepts, creating circularity. Yet the clarifying power of the attempt (forcing precise specification of what sense-experience alone can ground) persists regardless of success.

abstract_reasoning:
Phenomenalist reasoning proceeds by reformulating object-statements as counterfactual-laden phenomenal conditionals and testing whether the reformulation:

1. Preserves empirical content (does the paraphrase capture every empirical claim the original made?)
2. Supports prediction and inference (does it ground the same expectations and inferences?)
3. Handles unobserved cases (does the modal framework coherently extend to cases where observation is not and cannot be actualized?)
4. Avoids circularity (does the specification of observation-conditions presuppose the object-language concepts it aimed to eliminate?)

In its logical-positivist form, phenomenalist reasoning licenses reductive definitions (Carnap's Aufbau attempted to construct theoretical terms from observational primitives). In its constructive-empiricist form, it licenses principled agnosticism about unobservable scientific entities — we can be committed to the empirical adequacy of a theory without being committed to the truth of its claims about unobservables.[^van-fraassen-1980] <!-- FACT-D19-199 -->

knowledge_transfer:
| Role | Berkeleyan form | Millian form | Logical-positivist form |
|---|---|---|---|
| Basic elements | Ideas (mental but mind-independent) | Sensations | Protocol sentences |
| Unobserved matter | God's eternal perception | Permanent possibility of sensation | In-principle translatability |
| Mode of reduction | Ontological identity (things are ideas) | Semantic conditionalization (object-language → phenomenal conditionals) | Constructional reduction (concepts constructed from observational primitives) |
| Object of reduction | Material substance (Newton, Locke) | Physical bodies and their properties | Theoretical terms of empirical science |
| Core difficulty | Theological scaffolding required (who perceives unobserved trees?) | Infinite counterfactuals; specification regress | Observation/theory distinction; indeterminacy of translation |

A philosopher's phenomenalism transfers to philosophy of science as constructive empiricism (commitment extending only to empirical adequacy, not to unobservable posits), to cognitive science as a constraint on admissible theoretical vocabulary (avoid hypostasizing unobservables), and to AI and machine learning as the recognition that learned statistical models of sensation (pixels, sensor readings) ground object-classification without requiring commitment to objects-as-things-in-themselves. The structural core is reduction of object-talk to experience-talk (including counterfactual experience); what varies is the basic phenomenal element, the mode of reduction (ontological, semantic, methodological), and the stance toward unobservables.

prose: *(Pass B — deferred.)*

notes: Held at High confidence. Tight pair with *phenomenology* — the two are lexically confusable and philosophically distinct, and each entry cross-references the other with sharp differentiation. The entry represents the structural commitments shared across Berkeleyan, Millian, logical-positivist, and constructive-empiricist variants; it notes rather than adjudicates the classical and contemporary critiques. All fifteen FACT-D19 references (190–204) are populated with dual-placement anchors (inline HTML comment + Reference Format A B15-verified citation) as required by DP-19 protocol.


Phenomenology

slug: phenomenology

one_liner: Study of subjective experience.

core_idea: Phenomenology is the philosophical method and research tradition that takes *first-person conscious experience* — things as they appear to a subject — as the primary evidentiary and analytical object, developing disciplined practices (especially *the phenomenological epoché*, bracketing natural-attitude commitments about objective existence) to describe *the structures of experience as experienced*, while suspending judgment about ontological status. The essential commitment is that subjective experience has investigable structure — *intentionality, horizon, temporal flow, embodiment* — irreducible to third-person behavioral or physiological accounts. Every phenomenological claim specifies: (1) *the experiencing subject*[^husserl-1913] <!-- FACT-D19-175 --> (*transcendental ego* in Husserl; *embodied subject* in Merleau-Ponty); (2) *the intentional content, the noema*[^husserl-1900-1901] <!-- FACT-D19-176 --> (what experience is about); (3) *the conscious act, the noesis* (the experiencing itself); and (4) *the methodological epoché*[^heidegger-1927] <!-- FACT-D19-177 --> (bracketing assumptions to reveal experience's structural layers). Husserl (1900–1913) founded transcendental phenomenology; Heidegger (1927) inaugurated hermeneutic existential phenomenology by grounding consciousness in *being-in-the-world*; Merleau-Ponty (1945) foregrounded *the lived-body embodied perspective*[^merleau-ponty-1945] <!-- FACT-D19-178 -->, rejecting Cartesian dualism; Sartre[^sartre-1943]<!-- FACT-D19-179 --> extended the tradition into existential consciousness-as-nothingness. Modern applications (cognitive science, HCI, psychiatry, ethnography) trace genealogy to this core: *phenomenology as transcendental-or-hermeneutic study of consciousness structures from within lived experience*.

structural_signature:
A method or claim qualifies as phenomenological when each of the following holds:

- **First-person starting point.** Investigation begins from experience-as-experienced — how things present to consciousness — rather than theoretical or third-person starting points.
- *The experiencing subject* — consciousness approached from within subjectivity, not as object.
- **Bracketing (epoché).** Judgments about mind-independent reality are suspended; focus is on appearance-itself, not correspondence to external reality.
- *The intentional content, the noema* — what experience is about, its structural aim.
- **Structural description.** Investigation describes features of experience — *intentional directedness* (what the experience is of), horizon (co-present but not focal), temporal flow, embodied situatedness — in disciplined detail.
- *The conscious act, the noesis* — the experiencing-act's structural properties, not just its object.
- **Intentional directedness.** Experience is treated as always of or about something; this aboutness is structural, not accidental.
- **Eidetic or typological variation.** *The eidetic-vs-genetic analysis* — structural features identified by imaginative variation (altering aspects, isolating essential from contingent) to reveal invariances across possible presentations.
- **Suspension of naturalistic explanation.** Investigation does not reduce conscious experience to neural, behavioral, or functional terms during phenomenological work, though later integration with natural sciences is compatible.

what_it_is_not:
- **Not phenomenalism.** Phenomenalism (Berkeley–Kant–Ayer tradition) is the metaphysical thesis that physical objects reduce to or are knowable only through sensory phenomena. Phenomenology is a method investigating consciousness structures, neutral on whether physical objects reduce to phenomena. Shared vocabulary (phenomenon) creates lexical confusion; they differ in project. See `phenomenalism`.
- **Not introspection as folk practice.** Ordinary introspection is unsystematic and mixes theoretical assumptions with description; phenomenology is disciplined method with specific techniques (epoché, eidetic variation, structural description).
- **Not psychology of cognition.** Psychology investigates mental processes empirically, often third-person; phenomenology investigates consciousness structures from within. The two inform each other (cognitive phenomenology, neurophenomenology) but operate at different levels and with different evidentiary norms.
- **Not qualia theory alone.** Qualia are subjective felt qualities; phenomenology encompasses qualia but includes structural features (intentionality, horizon, temporal flow, embodied schema) that qualia alone do not capture.
- **Not mere description of feelings.** Phenomenology includes affective experience but is not limited to or focused on emotions; it investigates all structural features of consciousness, including perception, cognition, volition, and their interconnections.
- **Not a single method.** Phenomenology encompasses several distinct methodological traditions — Husserlian transcendental, Heideggerian existential, Merleau-Ponty's embodied, Scheler's value-phenomenology, Levinas's ethical phenomenology — each with characteristic methods and targets.
- **Common misclassification:** Using "phenomenology" loosely for any description of experience; confusing phenomenology with phenomenalism (tight-pair error); treating first-person description without methodological commitments as phenomenology; reducing phenomenology to philosophy-of-mind qualia debates.

broad_use:
- **Philosophy of mind and consciousness**
    - Husserl's founding work (Logical Investigations, Ideas); intentionality as structural feature; noema/noesis distinction; time-consciousness analyses; the lifeworld; transcendental phenomenology[^zahavi-2003]<!-- FACT-D19-183 --> as method.
    - Contemporary philosophy of consciousness: qualia (subjective qualities), the hard problem (Chalmers), first-person methodology, phenomenal consciousness vs access consciousness.
- **Existential and hermeneutic philosophy**
    - Heidegger's Being and Time: being-in-the-world, readiness-to-hand vs presence-at-hand, authenticity and Dasein.
    - Sartrean existentialism: consciousness as nothingness, facticity and transcendence, radical freedom.
    - Beauvoir's phenomenology of lived embodiment and gender; Levinas[^levinas-1969]<!-- FACT-D19-180 -->'s ethical phenomenology.
    - Gadamer's hermeneutics: interpretation as all phenomenological description.
- **Embodied and enactive cognition**
    - Merleau-Ponty's Phenomenology of Perception: motor intentionality, pre-reflective bodily schema, perception as embodied engagement.
    - Enactivism as contemporary embodied phenomenology; Varela and neurophenomenology; 4E cognition (embodied, embedded, enacted, extended).
    - Dreyfus's critique of AI as phenomenologically uninformed; embodied-mind alternatives to computational functionalism.
- **Psychiatry and clinical psychology**
    - Karl Jaspers[^jaspers-1913]<!-- FACT-D19-188 -->'s General Psychopathology: phenomenological psychiatry as descriptive psychopathology.
    - Phenomenological approaches to depression, anxiety, schizophrenia, dissociation; patient's lived experience of illness.
    - Existential analysis and logotherapy (Frankl); person-centered therapy privileging phenomenological understanding.
    - Enactive turn in clinical research and therapeutic design.
- **Qualitative and empirical research methodology**
    - Interpretive phenomenological analysis (IPA); descriptive phenomenological method (Giorgi); Van Manen's lived-experience research.
    - Empirical phenomenology in nursing, education, sociology, health-services research.
    - Phenomenological ethnography and anthropology: Husserl's foundations for qualitative research.
    - Neurophenomenology: integrating first-person phenomenological methods with third-person neuroscience.
- **Design and user experience**
    - Phenomenology of interaction; experience-centered design; embodied interaction (Dourish's Where the Action Is).
    - Lived experience of using products and systems; HCI phenomenology; designing for situated practitioner, not abstract user.
    - Participatory design methods informed by phenomenological understanding of embodied, social engagement.
- **Neuroscience and consciousness science**
    - Neurophenomenology (Varela, Thompson); integrated-information theory's reliance on first-person axioms; phenomenal consciousness as explanatory target.
    - Empirical methods capturing first-person data: descriptive experience sampling, micro-phenomenology, experience-annotation.
    - Bridging hard problem via first-person and third-person integration.

clarity: Phenomenology clarifies by forcing articulation of experience-as-experienced rather than experience-as-explained-from-outside. A claim like "perception gives us direct access to objects" resolves into structured description: *what is the structure of perception as experienced? Visual presentation of object from specific perspective, with other perspectives as horizon; motor anticipation of what would appear from other vantages; pre-reflective embodied grasping; temporal flow of perceptual engagement; background assumptions about object-persistence.* Clarifying force: replacing abstract philosophical or scientific claims about experience with disciplined description of experience itself, revealing overlooked features. This precision prevents philosophical confusion (e.g., between phenomenology and phenomenalism, between first-person description and methodology) and grounds empirical research in careful phenomenological articulation rather than loose observation.

manages_complexity:
- **Structures consciousness research and philosophy of mind:** Phenomenological tradition provides conceptual tools (intentionality, horizon, time-consciousness, embodiment, lifeworld) that shape contemporary debates in philosophy of mind, consciousness science, and cognitive science. These concepts organize otherwise fragmented discussions around structural questions.
- **Frames qualitative research methodology:** Interpretive phenomenological analysis, descriptive phenomenology, and allied methods give qualitative researchers disciplined tools for working with first-person data in health, education, social sciences. Prevents drift into unsystematic anecdote.
- **Organizes psychopathology and clinical psychology:** Descriptive psychopathology relies on careful phenomenological description of symptoms; treatment frameworks privileging patient's lived experience (person-centered therapy, existential analysis) build on phenomenological commitments. Prevents reductionist symptom-counting that misses illness-as-lived.
- **Supports design and human-computer interaction:** Phenomenology-informed design methods attend to embodied, situated, meaningful character of user experience beyond narrow usability metrics. Shifts focus from task-completion rates to lived experience of interaction.
- **Frames neurophenomenology and consciousness science:** Integrating first-person phenomenological methods with third-person neuroscience provides bridge between conscious experience and neural correlates — strategy for hard problem taking both perspectives seriously. Prevents pure neuromaterialism or pure introspectionism.

abstract_reasoning:
Phenomenology trains reasoner to ask:

- What is the phenomenon as it appears to the experiencing subject? (Starting from experience itself, not external theory.)
- What assumptions about objective reality must be bracketed for this analysis? (Making natural-attitude commitments explicit.)
- What is the intentional structure — what is experience about, and how does it aim at that? (Directedness and aboutness as structural.)
- What horizons are present — what is co-experienced but not focal? (Context and background as constitutive.)
- What is the temporal structure — how does experience flow, what retentions and protentions are active? (Temporal depth as structure.)
- How does embodiment shape this experience? (Body as lived, not just physical mechanism.)
- What features are essential to this type of experience, and which contingent? (Eidetic variation isolating invariances.)
- How does this structure transfer to other domains or populations? (Universal structures vs cultural particularity.)

This reasoning pattern applies across phenomenology, neurophenomenology, clinical psychiatry, qualitative research, and design — making abstract method portable.

knowledge_transfer:
Role mappings across domains:

| Phenomenological concept | Domain transfer | Instantiation |
|---|---|---|
| *Phenomenon* | Experience, perception, mood, action, emotion as lived | Patient's description of illness; user's report of product interaction; research participant's lived experience |
| *Epoché / bracketing* | Suspension of natural-attitude commitments; methodological neutrality; descriptive stance | Researcher brackets medical assumptions to hear illness-as-lived; designer brackets user-as-task-completer to attend to embodied interaction |
| *Intentionality* | Aboutness, directedness, intentional aim | Consciousness directed at object; emotion directed at situation; action aimed at goal |
| *Horizon* | Background, co-present but not focal, implicit context | Unattended features of perception; social context of illness; prior interactions shaping current use |
| *Time-consciousness* | Temporal flow, retention, protention, lived duration | Experience of waiting, anticipation, memory as constitutive, not derivative |
| *The lived-body embodiment* | Bodily schema, motor intentionality, enactive engagement | Embodied skill (riding a bike); embodied illness (feeling one's body become obstacle); embodied interaction with tool |
| *Eidetic variation* | Imaginative manipulation, essence-identifying comparison, invariance across presentations | Comparing experiences of different illness types to identify essential structures; varying design features to reveal core interaction patterns |
| *Lifeworld* | Taken-for-granted social and cultural horizon, pre-theoretical familiarity | Patient's everyday world of family, work, spirituality; user's work practice and tools; cultural context of research participants |

A phenomenologist analyzing grief's structure, a neurophenomenologist correlating subjective reports with neural activity, a clinical psychiatrist describing a patient's psychopathological experience, and a UX researcher investigating lived experience of product use are all performing the same structural work: *first-person starting point, bracketing, structural description, intentional analysis*. Diagnostic applies across contexts with same failure modes (descriptive laxity, hidden theoretical assumptions, loss of first-person focus under naturalization pressure).

prose: _(Pass B — pending; see `tracker/v2_upgrade.md`.)_

notes: _(placeholder for later refinement)_


Pilot To Scale Transition

one_liner: An effect proven in a curated niche need not survive the heterogeneous distribution of scale.

core_idea:
A pilot-to-scale transition is the passage of an intervention from a
controlled, often hand-curated *niche* — where it was demonstrated to work
— into a *heterogeneous, uncurated population* of operating contexts. The
structural commitment is that the conditions which made the pilot succeed
— selected participants, surplus implementer attention, protective
resources, an enabling local culture — are systematically absent or
attenuated at scale, so the same intervention runs into a different
operating regime it was never tested against. The signature is that a
strong, well-replicated pilot effect collapses, attenuates, or even inverts
at scale, *even when the fidelity of the intervention itself is maintained*.

The pattern is not the truism that "scaling is hard." Three commitments
distinguish it from generic scaling friction. First, the pilot population is
*systematically non-representative* of the scaled population — by selection,
motivation, or available resources — so pilot evidence does not estimate the
scaled effect. Second, the *resource intensity* that produced the pilot
effect is not budgeted at scale, so the intervention is delivered in a
thinner form that may cross a dosage threshold. Third, the *heterogeneity*
of operating contexts at scale interacts with the intervention in ways the
pilot could not surface, because it sampled too narrow a slice of the
context distribution. The scaled rollout is therefore not a replication of
the pilot at larger n; it is a new experiment in a new distribution. The
diagnostic asymmetry is sharp: pilot evidence is *necessary* — a thing that
fails in the pilot will fail at scale — but *insufficient* — a thing that
works in the pilot may or may not work at scale, depending on which of the
three facts bites. This is why "the pilot succeeded, we are now scaling it"
is a frequent precursor to expensive failure.

structural_signature:
*the proven intervention* — *the curated pilot niche* — *the heterogeneous scaled distribution* — *the selection differential* — *the resource-intensity gap* — *the context-interaction profile* — *the necessary-but-insufficient asymmetry of pilot evidence*

A situation is a pilot-to-scale transition when each of the following holds:

- **A proven intervention.** Something — a programme, a process, a model, a policy — has been demonstrated to work, with fidelity that can in principle be maintained at scale.
- **A curated pilot niche.** The demonstration occurred in a controlled, often hand-selected setting: chosen participants, surplus implementer attention, protective resources, an enabling local culture.
- **A heterogeneous scaled distribution.** The target is a large, uncurated population of operating contexts that differs systematically from the niche — a new operating regime, not a larger sample of the old one.
- **A selection differential.** The load-bearing fact (first of three): the pilot population is systematically non-representative — by selection, motivation, or resources — so pilot evidence does not estimate the scaled effect.
- **A resource-intensity gap.** The support that produced the pilot effect is not budgeted at scale, so the intervention is delivered in a thinner form that may cross a dosage threshold.
- **A context-interaction profile.** The heterogeneity of contexts at scale interacts with the intervention in ways the narrow pilot could not surface.
- **The necessary-but-insufficient asymmetry.** Pilot evidence is *necessary* (what fails in the pilot fails at scale) but *insufficient* (what works in the pilot may not), and the failure is *bidirectional* — the pilot can over- or under-state the scaled effect, with the three facts predicting which. More replication *in the same niche* does not address the scaling question; only widening the niche does.

Composed: a scaled rollout is a new experiment in a new distribution, not a replication at larger n — so the design question becomes which of the three structural facts will bite, and how to sample the scaled distribution to find out *before* committing.

what_it_is_not:
- **Not `scaling_and_scale_dependence`.** That prime concerns how a system's *properties change with size* in general (allometry, scale-dependent behavior); pilot-to-scale transition is the specific *evaluation-validity* failure where a curated pilot's evidence does not estimate the heterogeneous scaled effect. One is about size-dependent physics, the other about niche-versus-distribution inference.
- **Not `diseconomies_of_scale`.** Diseconomies of scale are *rising per-unit costs* as an operation grows; pilot-to-scale is about an *effect collapsing* when the pilot's special conditions vanish — even when costs are fine. The failure is inferential (the pilot didn't test the scaled regime), not a cost curve.
- **Not `selection_bias`.** Selection bias is the *general* distortion from a non-random sample; the selection differential is *one of three* structural facts in this prime, alongside the resource-intensity gap and context-interaction profile. Pilot-to-scale is the specific scaling syndrome, not bias in general.
- **Not `regression_to_the_mean`.** Regression to the mean is a *statistical* tendency for extreme measurements to moderate on remeasurement; pilot-to-scale is a *structural* gap between a curated niche and a heterogeneous distribution. They are cousins (both reflect non-generalizing favorable conditions) but the prime's failure is *bidirectional* and predicted by three named facts.
- **Not `local_autonomy_tiered_escalation`.** The nearest embedding neighbor concerns a *governance structure* (local discretion with escalation tiers); pilot-to-scale concerns the *validity of pilot evidence* for a scaling decision. Tiered rollout is one remedy, not the prime itself.
- **Not generic "scaling is hard."** The prime pinpoints *which* of three facts — selection, resource intensity, context interaction — drives a given failure, each with a distinct remedy. An undifferentiated "it didn't scale" is not a diagnosis.
- **Common misclassification.** Reading "the pilot succeeded, so we are scaling it" as low-risk replication. Catch it by asking whether the scaled distribution is a *larger sample of the pilot's regime* or a *systematically different* population — and which of the three structural facts will bite *before* committing the budget.

broad_use:
- **Public and global health**: home-visit programmes, supplementation, and
  conditional cash transfers showing well-documented attenuation between
  efficacy trials and effectiveness trials before national rollout.<!-- FACT-D68-701 -->[^flay-etal-2005]
- **Education reform**: charter models and curricular interventions whose
  pilot results in a few high-attention schools fail to replicate in
  district rollouts — the "boutique-effect" critique.<!-- FACT-D68-702 -->[^slavin-2008]
- **Enterprise software**: proof-of-concept deployments in friendly
  business units that succeed because an executive sponsor protects them,
  then fail to generalise without that protection.
- **Clinical translation**: bench and Phase-1 evidence that does not predict
  Phase-3 outcomes in a heterogeneous patient population.
- **Manufacturing scale-up**: chemical processes where reactor geometry,
  mixing, and heat-transfer ratios change qualitatively from bench to pilot
  plant to production plant.<!-- FACT-D68-703 -->[^euzen-etal-1993]
- **Policy implementation**: the gap between a donor-supported demonstration
  project and a government-funded national programme.
- **Software platforms**: the difference between a self-selected beta and a
  launch to a heterogeneous public that exposes edge cases the beta did not
  contain.
- **Humanitarian operations**: a response model that works in one camp under
  attentive scrutiny and fails when extended to a larger population with
  thinner per-site resources.

clarity:
Naming the transition as a structural gap, not a continuity, changes what
one looks at. The question is no longer "did the pilot succeed?" but "which
of the three structural facts will bite at scale, and how do we tell
*before* spending the money?" That reframing makes the boundary explicit:
the pilot did not, in fact, test the question the scaling decision needs
answered. It also recasts a common rhetorical move — "if it works for one
school it will work for a hundred" — as a category error, because the pilot
evidence and the scaling decision are answers to different questions.

A second clarifying move is to identify which structural fact dominates in a
given case. Boutique-effect cases, where pilot attention was unusually high,
call for one diagnostic; selection cases, where the pilot site was unusually
motivated, call for another; resource-intensity cases call for a third.
Without this decomposition, "we are scaling and it is not working" is
undiagnosable — a single undifferentiated complaint rather than an
actionable finding.

manages_complexity:
The pattern compresses a wide class of "we proved it works and then it
didn't at scale" failures into one diagnostic, and the intervention family
is correspondingly compressed. *Sample the scaled distribution before
scaling*: run stratified pilots across high- and low-fidelity sites, follow
efficacy trials with effectiveness trials, send canaries to representative
rather than friendly segments. *Budget for the resource intensity, or strip
the intervention of its dependence on a non-scaling resource*. *Stage the
rollout so each tier is re-tested*, treating each scale step as a new
experiment with its own go/no-go rather than a deployment of a settled fact.
*Design for heterogeneity from the start*, with adaptive or modular designs
robust across the contexts encountered at scale. And *surface the structural
assumptions explicitly*, so decision-makers can see what would have to be
true at scale for the pilot result to generalise.

Because these moves are organised around the same three structural facts in
every substrate, a practitioner who has diagnosed a boutique effect in
education can recognise its analogue in a chemical scale-up or an enterprise
rollout and reach for the structurally matching remedy without starting from
scratch.

abstract_reasoning:
Recognising the structure makes it possible to reason about *which* aspects
of a pilot's success are intrinsic to the intervention and which are
extrinsic to the pilot's special conditions. This is the internal-versus-
external-validity distinction with the scale dimension foregrounded and an
explicit theory of which extrinsic facts attenuate at scale. It yields a
non-obvious result: *more* pilot evidence — more rigorous replication *in
the same niche* — does not address the scaling question at all. What
addresses it is widening the niche, which by definition the pilot has not
done; this is why a positive meta-analysis of small efficacy trials is not
strong evidence for effectiveness at scale.

A second abstract move places the pattern alongside its structural cousins.
Pilot-to-scale failure is dual to scale-up dilution in chemistry and shares
the structure of regression to the mean in measurement: in each, a strong
observed effect partly reflects favourable conditions that do not
generalise. The distinctive feature is that the failure is *bidirectional* —
the pilot can over-state *or* under-state the scaled effect — and the three
structural facts predict which, which is what separates the prime from a
generic "results may not generalise" warning.

knowledge_transfer:
The roles map across substrates: the *pilot niche* is the curated trial
site, the friendly business unit, the bench reactor, the demonstration
project; the *scaled distribution* is the national programme, the public
launch, the production plant, the full district; the *selection
differential*, *resource intensity*, and *context-interaction profile* are
the three facts whose absence or attenuation at scale predicts the failure.
What transfers is not vocabulary but a set of interventions carrying
substantive content. The clinical-research insight that efficacy trials must
be followed by effectiveness trials in routine-care settings ports to
education policy and public administration, bringing pragmatic, stepped-
wedge, and implementation-trial designs with it. The chemical-engineering
principle that an intermediate-scale pilot-plant step is needed because
critical interactions only appear at intermediate scale ports to service-
design rollouts as the "minimum viable region" — the smallest deployment
that surfaces all the operational heterogeneity scale will present.<!-- FACT-D68-704 -->[^euzen-etal-1993]
Adaptive trial designs port to canary-then-rollout strategies in which the
rollout itself becomes the experimental design. And implementation-science
frameworks port to development economics, supplying a vocabulary for the
structural facts a transition surfaces.

A single worked instance shows the transfer's substance. A literacy
intervention shows a large effect in three volunteer urban schools with
weekly coaching and seconded coordinators; scaled to twelve hundred schools
without the volunteers, the coaching, or the seconded staff, the average
effect nearly vanishes and turns negative in under-resourced sites — the
intervention's fidelity intact, the pilot population's three special facts
all absent. The structurally identical story plays out in a polymerisation
that yields 92% in a bench reactor and 64% in a production reactor because
heat is removed through a smaller surface-to-volume ratio at scale: the
chemistry was correct, the pilot's reactor was not the production reactor.<!-- FACT-D68-705 -->[^euzen-etal-1993]
The same remedy vocabulary — stage the scale-up, add an intermediate tier,
redesign for the scaled regime — applies in both, because the underlying
structure is one prime wearing two substrates.

formal_abstract:
Chemical reactor scale-up is the prime's most rigorous instance, because the reason the pilot does not predict the plant is a computable consequence of geometry. Consider an exothermic batch polymerization that yields 92% at bench scale. The *proven intervention* is the chemistry — the recipe, temperatures, and times that worked. The *curated pilot niche* is the bench reactor; the *heterogeneous scaled distribution* is the production reactor, and the prime's claim is that this is *not a larger sample of the same regime* but a different operating regime. The mechanism is exact: heat generated by the reaction scales with *volume* (the cube of linear dimension), while heat removed through the cooling jacket scales with *surface area* (the square).<!-- FACT-D68-706 -->[^euzen-etal-1993] So the *surface-to-volume ratio falls as $1/L$* with increasing size — the production reactor has far less cooling surface per unit of heat generated than the bench reactor did.<!-- FACT-D68-707 -->[^euzen-etal-1993] This is the *resource-intensity gap* in physical form: the heat-removal "support" that kept the bench reaction at temperature is not available at scale, and the reaction crosses a thermal threshold, runs hot, and the yield collapses to, say, 64% — even though the *fidelity of the chemistry is perfectly maintained*. The prime's *necessary-but-insufficient asymmetry* is stark and quantifiable: a chemistry that fails at the bench will fail in the plant, but a chemistry that succeeds at the bench succeeds *only if* the dimensionless transport ratios (heat transfer, mixing time, Reynolds number) are preserved — which pure scale-up does not preserve.<!-- FACT-D68-708 -->[^euzen-etal-1993] This is exactly why chemical engineering inserts an *intermediate pilot-plant tier*: critical transport interactions appear only at intermediate scale, so the field refuses to jump bench-to-production and instead *re-tests at each tier*. The intervention the prime prescribes is the engineer's literal practice: identify which structural fact bites (here, surface-to-volume heat removal), and either budget the missing resource (more cooling, slower addition) or redesign the scaled regime (different reactor geometry) rather than assuming the bench result transfers.

**Mapped back:** Reactor scale-up instantiates the full signature — a faithful intervention, a curated bench niche, a production distribution that is a new regime, and a resource-intensity gap (falling surface-to-volume heat removal) that crosses a threshold — making the chemistry case the one where the pilot-does-not-predict-scale claim is derivable from geometry, not merely observed.

applied_industry:
Education reform and global-health programs show the same niche-versus-distribution collapse in social policy, with the human special-conditions playing the role the cooling jacket played in chemistry. A literacy intervention posts a large effect in three volunteer urban schools that had weekly coaching and a seconded coordinator — the *curated pilot niche*, whose success rested on a *selection differential* (volunteer schools are unusually motivated), a *resource-intensity gap* waiting to open (the coaching and seconded staff), and a narrow *context-interaction profile* (three similar urban sites). Scaled to twelve hundred schools *without* the volunteers, the coaching, or the seconded staff, the average effect nearly vanishes and turns *negative* in under-resourced sites — the intervention's fidelity intact, but all three of the pilot's special facts absent at scale.<!-- FACT-D68-709 -->[^slavin-2008] This is the prime's *boutique effect*, and its diagnosis is precise: the failure is not "teachers did not try hard enough" but that the pilot never tested the scaled distribution, so its evidence was *necessary but insufficient*. Global health shows the identical structure and named it: the gap between an *efficacy trial* (does the intervention work under ideal, curated conditions?) and an *effectiveness trial* (does it work in routine care across a heterogeneous population?) is exactly this prime, which is why a supplementation or home-visit program with strong efficacy results is *re-tested in effectiveness trials* before national rollout rather than scaled on efficacy evidence alone.<!-- FACT-D68-710 -->[^flay-etal-2005] The shared intervention transfers verbatim across both: *sample the scaled distribution before committing* (stratified pilots across high- and low-resource sites; effectiveness trials in routine settings), *budget the resource intensity or strip the dependence on a non-scaling resource*, and *stage the rollout so each tier is a fresh go/no-go experiment* rather than a deployment of a settled fact — the same staged-scale-up discipline the chemical engineer uses, applied to programs instead of reactors.<!-- FACT-D68-711 -->[^glasgow-etal-1999]

**Mapped back:** Education boutique effects and the efficacy-versus-effectiveness gap are the same prime as reactor scale-up — a curated niche whose selection differential and resource intensity vanish in the heterogeneous scaled distribution — so the diagnostic (which of the three facts bites) and the staged-rollout remedy transfer across the educational, public-health, and chemical substrates.