Rock Cycle

one_liner: The same persisting substance moves among a small set of distinct phase-states via named transformations, its identity preserved through phase change while its properties change qualitatively in each phase.

core_idea:
The rock cycle names a structural pattern in which the same material substance moves among a small set of distinct phase-states via named transformation processes, where each phase is a stable configuration with its own properties, each transformation is driven by characteristic conditions, and the substance can in principle return to any prior phase given the right inputs. In geology the phases are igneous, sedimentary, and metamorphic rock;<!-- FACT-D70-951 -->[^press-siever-2003] the transformations are melting and cooling, weathering and deposition and lithification, and heat-and-pressure metamorphism; and a given rock can transit any path indefinitely without leaving the cycle.<!-- FACT-D70-952 -->[^press-siever-2003] The structural commitment is that *identity persists through phase change* — the same material atoms continue to participate, but in configurations whose properties (porosity, density, crystal structure, chemical reactivity) are qualitatively different in each phase. This is what distinguishes the pattern from turnover, in which the substance is replaced while the structure persists: here the substance is the same and only its phase form changes.

A second structural commitment is that the cycle is *not a fixed order*. There is no first phase; transitions can run in many directions; a piece of substance can spend wildly different amounts of time in each phase — millions of years in granite, days as loose sediment, decades in metamorphic basement. The cycle is therefore better drawn as a directed graph among phases than as a closed loop, with the rates of each transformation determining the steady-state distribution of substance across phases. The structural skeleton has a recurring shape: a persisting substance whose identity is preserved across phase changes; a small set of distinct stable phases, each with its own properties; named transformations connecting pairs of phases, each driven by characteristic conditions and rates; residence times set by the ratios of those transformation rates; a steady-state distribution of substance across phases set by the full rate graph; transformation-rate sensitivities that propagate through the whole graph rather than only to adjacent phases; and a structural bidirectionality, the absence of any thermodynamically preferred direction at the level of the pattern itself. The geological name is the cleanest pedagogical anchor because of its visibility and dramatic timescales, but the underlying pattern is general — equally well described as a transformational lifecycle or phase-cycling — and recurs wherever the same substance cycles through qualitatively distinct forms.

structural_signature:
*a persisting substance whose identity is preserved across phase changes* — *a small set of distinct stable phases, each with its own properties* — *named transformations connecting pairs of phases, each driven by characteristic conditions and rates* — *residence times set by ratios of those rates* — *a steady-state distribution set by the full rate graph* — *a structural bidirectionality with no thermodynamically preferred direction*

The pattern is present when each of the following holds:

- **A persisting substance.** The same material continues to participate across changes; identity is preserved through phase change. This distinguishes the pattern from turnover, where the substance is replaced and only structure persists.
- **A small set of distinct phases.** Each phase is a stable configuration with qualitatively different properties — porosity, density, structure, reactivity — from the others.
- **Named transformations.** Directed transitions connect pairs of phases, each driven by characteristic conditions and running at a characteristic rate.
- **Residence times.** How long substance spends in each phase is set by the ratios of the transformation rates.
- **A rate-graph steady state.** The distribution of substance across phases is set by the full directed graph of rates, so changing one rate redistributes substance across *all* phases, not just the two it connects.
- **A bidirectionality invariant.** No phase is primary and no direction is structurally preferred; whichever direction is energetically favored under current conditions dominates the flux, but the cycle remains bidirectional and can reverse without altering the pattern.

These compose into a phase graph better drawn as a directed graph than a closed loop. The characteristic error is treating one phase as "natural" and the others as deviations; the structural bidirectionality dissolves that false hierarchy.

what_it_is_not:
- **Not turnover.** See `turnover`. In turnover the *structure persists while the substance is replaced* (a stream's water, an organization's members). The rock cycle is the inverse: the *substance persists while its phase changes*. Identity-preserved-through-transformation is the defining contrast.
- **Not layered accumulation.** See `layered_accumulation`. Layered accumulation *deposits new material in ordered strata that persist*, recording history. The rock cycle moves *the same substance among phases* with no preferred order and full bidirectionality; sediment is one phase it passes through, not a permanent record.
- **Not a Markov process.** See `markov_process`. A Markov process is a *stochastic state-transition model* defined by memorylessness and transition probabilities. The rock cycle is a *material-flow* pattern: a conserved substance redistributed across coupled phases by rates, where the load-bearing reasoning is the steady-state distribution, not probabilistic path independence.
- **Not oscillation.** See `oscillation`. Oscillation is *regular back-and-forth between states on a periodic schedule*. The rock cycle has *no fixed order, no period, and no preferred direction* — a given parcel can take any path through the phase graph and dwell wildly different times in each.
- **Not a fixed-order cycle.** See `cycle`. A generic cycle implies a recurring sequence. The rock cycle is better drawn as a *directed graph among phases* than a loop: there is no first phase and transitions run in many directions.
- **Common misclassification.** Treating one phase as the substance's "natural home" and the others as deviations (atmosphere for carbon, IC for a career). The catch: at the structural level no phase is primary and the cycle is bidirectional. A privileged phase is an artifact of familiarity, not of the pattern.

broad_use:
- **Geology and earth sciences.** Igneous, sedimentary, and metamorphic rock cycling under the heat engine of plate tectonics — the canonical instance and the source of the name.<!-- FACT-D70-953 -->[^press-siever-2003]
- **Biogeochemical cycles.** The water cycle (vapor, cloud, precipitation, surface water, groundwater, ocean), the carbon cycle (atmospheric CO₂, biomass, soil and sediment, fossil fuel), and the nitrogen, phosphorus, and sulfur cycles — a small set of phases, named transformations, identity preserved across them.<!-- FACT-D70-954 -->[^schlesinger-2013]
- **Career and organizational dynamics.** Individual contributor to manager to IC again to executive; institutional renewal in long-lived organizations (startup, growth, maturity, reinvention, growth again) — the same identity carried through qualitatively different role-states.
- **Software and infrastructure lifecycle.** Greenfield to production to legacy to refactor to greenfield again; a codebase rewritten several times is in some sense the same product carried through phase change.
- **Materials processing and recycling.** Aluminum can to smelt to ingot to sheet to can again — the substance persists, the form cycles; circular-economy design is the rock-cycle pattern applied to industrial materials.<!-- FACT-D70-955 -->[^graedel-2011]
- **Conceptual development.** A concept passing through vague intuition, formalized model, debunked, reformulated, and re-accepted in modified form, preserving a thread of identity through qualitatively different epistemic states.

clarity: Naming the transformational lifecycle separates three dynamics that everyday talk of "change" routinely conflates. There is *replacement* — turnover, in which the structure persists while the substance is swapped out. There is *transformation* — the rock-cycle pattern, in which the substance persists while its phase changes. And there is *decay* — gradual deterioration, in which the substance loses properties without changing phase at all. These three have qualitatively different implications, and treating them as one obscures which is occurring. A career in transition between manager and IC is in transformation, not turnover or decay, even though all three can look like "change" superficially — and the intervention appropriate to a transformation (manage the transition rates between phases) differs entirely from the intervention appropriate to decay (act against the loss) or to turnover (manage the replacement flow). The frame also exposes a specific recurring error: treating one phase as primary or "natural" and the others as deviations from it. The rock cycle has no canonical phase, the carbon cycle has no canonical compartment, and a career has no canonical role; igneous rock is not "real" rock from which sediment is a departure, and the individual-contributor role is not the "true" state from which management is a deviation. Recognizing the structural bidirectionality dissolves the false hierarchy among phases and lets each be treated as a legitimate stable configuration rather than as a corruption of a privileged one.

manages_complexity: The pattern compresses a class of multi-phase systems to a small set of named phases, named transformations between them, and rate parameters for each transformation. Once that graph is drawn for any specific substance, a whole family of quantities falls out of the same machinery: the steady-state distribution of substance across phases, the time spent in each phase, the throughput of the system, and the points at which intervention will be effective. This is a substantial compression, because it means that geology, biogeochemistry, careers, software, and recycling can all be analyzed with one apparatus and one set of diagnostic questions, with only substrate substitution between them. An analyst who has learned to read the rate graph in one domain reads it in another without rebuilding the analysis. The frame also manages the complexity of intervention reasoning, which is genuinely non-local in these systems and therefore easy to get wrong by intuition. Because the steady-state distribution depends on the full rate graph, changing one transformation rate redistributes substance across *all* phases, not just the two the transformation directly connects, and the frame makes this propagation expected rather than surprising. The complexity that would otherwise have to be tracked case by case — what happens to every phase when one transition speeds up or stalls — is managed by the single insight that the phases are coupled through the rate graph and reach a new steady state together.

abstract_reasoning: The pattern licenses inferences about steady-state distributions across phases, residence times, throughput rates, and the sensitivity of the phase distribution to changes in transformation rates. It supports the inference that *speeding up one transformation rate redistributes substance across all phases*, not just the two it connects, because the system relaxes to a new steady state determined by the full rate graph rather than adjusting only locally. It supports the inference that *blocking one transformation* concentrates substance in the upstream phases and depletes the downstream phases, even while other transformations continue to run — a non-obvious consequence that follows directly from reading the graph. And it supports the inference that *the cycle has no thermodynamically preferred direction at the structural level*: whichever direction is energetically favored under current conditions will dominate the flux, but the cycle remains structurally bidirectional, so a change in conditions can reverse the dominant direction without altering the pattern. These inferences are stated entirely in terms of the phase graph and its rates, which is why they transfer: the claim that blocking one transition concentrates substance upstream is the same claim whether the substance is rock, carbon, aluminum, or organizational skill, and the analyst who has reasoned it through in one substrate can apply it in another by relabeling the nodes and edges.

knowledge_transfer:
The pattern transfers across substrates because its core reasoning — substance persistent through phase change, distribution set by the full rate graph — is stated in terms that name no particular medium. The rock cycle's reasoning ports directly to biogeochemistry: the sensitivity analysis of one transformation rate becomes the analysis of one biogeochemical flux, and the same identity-preserved-through-phase-change logic governs the carbon, water, and nitrogen cycles. From biogeochemistry the same-substance-cycling-through-distinct-forms reasoning ports to industrial recycling and circular-economy design, where the transformation rates — melt, mold, use, return — determine the steady-state distribution of an aluminum stock across the cycle exactly as transformation rates determine the distribution of carbon across its compartments. From materials the pattern ports to career and organizational dynamics: rotation rates between role-phases determine the institutional skill distribution, and the "blocked transformation" pathology — no path back from manager to IC — predicts skill atrophy in the upstream phases, just as blocking a geological transition concentrates substance upstream. And in software, treating a codebase as substance cycling through greenfield, production, and legacy phases, rather than as a thing that decays toward replacement, reframes refactor investment as transformation-rate management rather than asset depreciation, which changes how the investment is justified.

The role mappings that make these transfers reliable are direct. The persisting substance maps to the silicon-dioxide grain, the carbon atom, the aluminum stock, the engineer's accumulated identity, the codebase, the developing concept. The phases map to igneous/sedimentary/metamorphic, to atmosphere/biomass/soil/ocean, to ore/ingot/sheet/can/scrap, to IC/lead/manager/executive, to greenfield/production/legacy. The transformations map to weathering, deposition, and metamorphism; to photosynthesis, respiration, and burial; to smelting, forming, and reclamation; to promotion and role-change; to deployment and refactor. The residence times map to the millions of years in granite versus the days in sediment, or the decades in a senior role versus the months in a transitional one. Because the structure and its non-local intervention logic are shared, a practitioner who has reasoned about one substrate's phase graph can diagnose another: the geologist's understanding that blocking metamorphism concentrates sediment and the organization designer's understanding that blocking the manager-to-IC path concentrates people in management are, structurally, the same inference about the same kind of coupled phase system. The geological name is retained for ease of finding and its concrete vividness, but the structural description — a substance whose identity persists as it cycles among coupled phase-states whose distribution is set by transformation rates — is what travels, and it travels without modification to any system that shares that shape.

formal_abstract:
The global carbon cycle is the rock-cycle pattern operating in biogeochemistry, and it instantiates every element of the signature with the additional virtue of being quantitatively measured. The *persisting substance* is carbon — the same atoms participate throughout, their identity preserved across every transformation; this is transformation, not turnover, because the carbon is not replaced, only reconfigured. The *small set of distinct phases* are the reservoirs, each with qualitatively different properties: atmospheric CO₂ (gaseous, mobile, radiatively active), biomass (organic, reactive, short-lived), soil and ocean (dissolved or sequestered), and fossil/sediment (locked, geologically slow). The *named transformations* connect pairs of these — photosynthesis moves carbon from atmosphere to biomass, respiration and decay return it, burial moves it to sediment, combustion and volcanism return it to the atmosphere<!-- FACT-D70-956 -->[^ipcc-2021-ar6] — each driven by characteristic conditions and running at a characteristic rate. The *residence times* are set by the ratios of those rates and vary by orders of magnitude: years in the atmosphere, decades in soil, millions of years in fossil deposits.<!-- FACT-D70-957 -->[^schlesinger-2013] The *rate-graph steady state* is the load-bearing structural feature: the distribution of carbon across reservoirs is set by the *full* directed graph of rates, so perturbing one transformation redistributes carbon across *all* reservoirs, not just the two it connects. The *bidirectionality invariant* holds — no reservoir is the "natural" home of carbon and the others deviations; each is a legitimate phase. The intervention the frame prescribes is exactly the non-local reasoning that intuition gets wrong: fossil-fuel combustion sharply accelerates one transformation (sediment → atmosphere), and the system does not merely raise atmospheric carbon locally but relaxes toward a new steady state across every reservoir — ocean acidification and biomass changes follow because the phases are coupled through the rate graph.<!-- FACT-D70-958 -->[^ipcc-2021-ar6]

**Mapped back:** Carbon is the persisting substance, the reservoirs are the coupled phases, photosynthesis and combustion are named transformations with characteristic rates, residence times run from years to megayears, and accelerating combustion redistributes carbon across all reservoirs — the rate-graph steady-state logic exactly as in geology.

applied_industry:
Aluminum recycling in a circular-economy system is the rock-cycle pattern applied to industrial materials, and reading it through the frame reframes recycling investment as transformation-rate management. The *persisting substance* is the aluminum stock — the same metal atoms cycle indefinitely through forms without being consumed, the defining contrast with materials that are degraded or dispersed. The *distinct phases* are the qualitatively different material states: ore/ingot (raw, energy-intensive to produce), sheet (formed stock), product (the beverage can in use), and scrap (post-consumer, dispersed). The *named transformations* connect them — smelting moves ore to ingot, rolling moves ingot to sheet, manufacturing moves sheet to can, use-then-disposal moves can to scrap, and reclamation (remelting collected scrap) moves scrap back to ingot, closing the cycle.<!-- FACT-D70-959 -->[^graedel-2011] The *residence times* differ sharply: years locked in long-lived products versus weeks for a beverage can in circulation.<!-- FACT-D70-960 -->[^bertram-2009] The *rate-graph steady state* governs the system's material distribution, and the frame's non-local intervention logic is precisely what a circular-economy designer must exploit: raising the reclamation rate (better collection, sorting, remelting) does not merely add ingots locally but redistributes the entire aluminum stock across all phases, reducing the draw on virgin ore upstream. The *blocked-transformation pathology* is the diagnostic the frame supplies: if the scrap → ingot transformation is throttled (poor collection infrastructure), substance concentrates in the scrap phase (landfill) and depletes downstream, exactly as blocking a geological transition concentrates sediment upstream.<!-- FACT-D70-961 -->[^graedel-2011] The same structure and non-local logic govern organizational skill cycling — promotion and role-change are transformations among IC/lead/manager phases, and a blocked manager-to-IC path concentrates people in management and atrophies hands-on skill upstream. A circular-economy engineer raising reclamation rates and an organization designer reopening the manager-to-IC path are, structurally, making the same move on the same kind of coupled phase system.

**Mapped back:** Aluminum is the persisting substance, ore/sheet/product/scrap are the coupled phases, smelting and reclamation are named transformations, and throttling the scrap-to-ingot rate concentrates substance in landfill exactly as blocking a geological transition concentrates sediment upstream — the rock cycle applied to industrial material flow.


type: prime

name: Rock-Paper-Scissors (Intransitive Cyclic Dominance)

one_liner: A beats-relation that closes into a cycle rather than a ranking, so no option dominates and the system is governed by rotation and coexistence.

status: draft

core_idea:
A relation over a set of options is *intransitive* when "A beats B" and
"B beats C" do not entail "A beats C" — and in its strongest form a
*cycle* closes: A beats B, B beats C, C beats A. No option is globally
dominant; the ranking is circular rather than linear. The structural
consequence is decisive: any attempt to pick "the best" collapses,
because there is no best, and the system's behavior is governed by the
*cycle's dynamics* — mixed strategies, rotation, coexistence — rather
than by convergence to an apex.

The load-bearing structural content is that ranking is a property of the
*relation*, not of the options. The folk game that lends the pattern its
name is merely the most familiar instance of a topological fact about
binary relations: the beats-graph contains a directed cycle, and a
directed cycle admits no consistent linear order. From this single fact
a great deal follows without further detail. There is no pure-strategy
equilibrium; the unique equilibrium is mixed, assigning each option
positive weight. Under population dynamics, all types coexist at
positive frequency and their shares oscillate, because any monoculture
is invadable by the type that beats it. And any procedure that requires
a linear order — single-winner voting, fully consistent pairwise rating,
optimization toward "the best" — will produce arbitrary or unstable
results when applied to a cyclic relation. The discipline the prime
imposes is to ask not "which is best?" but "who beats whom?", and to
distinguish *genuine* intransitivity, present in the payoff graph, from
*apparent* intransitivity arising from sampling noise or shifting
context.

structural_signature:
*the set of three or more options* — *the binary beats-relation over them* — *the intransitivity (failure of A>B, B>C ⇒ A>C)* — *the closed directed cycle in the beats-graph* — *the absence of any consistent linear order* — *the mixed-equilibrium-with-rotation dynamics that replace convergence*

The pattern is present when each of the following holds:

- **A set of options.** Three or more alternatives are compared — morphs,
  candidates, teams, standards, strategies.
- **A beats-relation.** A binary "beats" or "dominates" relation is
  defined over pairs of options, locating ranking in the *relation*
  rather than in any intrinsic property of the options.
- **Intransitivity.** The relation fails transitivity: "A beats B" and
  "B beats C" do not entail "A beats C."
- **A closed cycle.** In its strongest form the beats-graph contains a
  directed cycle (A beats B beats C beats A), so dominance loops rather
  than terminating.
- **No linear order.** A directed cycle admits no consistent linear
  ranking; there is no globally dominant option and no apex to converge
  to.
- **Rotation dynamics.** Because no pure strategy dominates, the unique
  equilibrium is mixed, all types coexist at positive frequency, shares
  oscillate, and any monoculture is invadable by the type that beats
  it.

These compose so that the single topological fact — the cycle — yields,
without further payoff detail, a package of consequences: no
pure-strategy equilibrium, persistent coexistence, oscillating shares,
and the incoherence of any procedure requiring a linear order. The
discipline is to ask "who beats whom?" rather than "which is best?",
and to separate genuine intransitivity in the payoff graph from
apparent intransitivity due to noise or shifting context.

what_it_is_not:
- **Not `competition`.** Competition is rivalry over a scarce resource;
  rock-paper-scissors is a *specific topology* of the beats-relation — a
  closed directed cycle. Competition can be transitive (a clear pecking
  order) or cyclic; only the cyclic case is this prime (see `competition`).
- **Not `equilibrium`.** An equilibrium is a rest state. The cyclic structure
  has a *mixed* equilibrium but its dynamics are *rotation and oscillation*,
  not convergence to a pure rest point. The prime is about why no pure
  equilibrium exists, not about settling (see `equilibrium`).
- **Not `oscillation`.** Oscillation describes a variable cycling in time.
  Rock-paper-scissors is the *relational cause* — an intransitive beats-graph
  — that can produce oscillating population shares. The oscillation is a
  downstream consequence, not the structure itself.
- **Not `trade_offs`.** A trade-off ranks options along trading axes, still
  yielding a (Pareto) order. The defining feature of cyclic dominance is the
  *failure of any consistent order at all* — no scalar reproduces the cycle,
  which trade-off framing presupposes.
- **Not `attractor_selection_and_basin_control`.** Despite embedding-nearness,
  that prime concerns which of several stable states a system settles into.
  Rock-paper-scissors specifically lacks a stable apex to settle into; its
  signature is persistent coexistence, not basin capture.
- **Common misclassification.** Fitting a single-number rating (Elo-style) to
  a genuinely cyclic competitive field. No consistent scalar can reproduce a
  cycle, so the ranking will contradict head-to-head results. The tell: do
  consistent pairwise predictions follow from any per-option score? If a cycle
  exists, they cannot.

broad_use:
The same cyclic-dominance topology recurs across substrates that share
nothing but the shape of their beats-relation. In **game theory**,
rock-paper-scissors itself has a unique Nash equilibrium at the uniform
mixed strategy, because no pure choice dominates.<!-- FACT-D71-001 -->[^vonneumann-morgenstern-1944] In **ecology**, the
side-blotched lizard's three mating morphs cycle in dominance, and
bacterial toxin-producer, sensitive, and resistant strains maintain
coexistence by cyclic competition rather than competitive exclusion.<!-- FACT-D71-002 -->[^sinervo-lively-1996] In
**social choice**, Condorcet's voting paradox shows that majorities can
prefer A over B, B over C, and C over A, so no Condorcet winner exists
even when every individual is rational.<!-- FACT-D71-003 -->[^condorcet-1785] In **sports and competition**,
stylistic matchups produce reliable cycles in which Team A beats Team B
beats Team C beats Team A, defying any linear power-ranking.<!-- FACT-D71-004 -->[^clegg-cartlidge-2025] And in
**markets and technology**, three competing standards or business models
can form a triangle in which each is vulnerable to the next — generalist
beats specialist beats super-specialist beats generalist — with no
stable winner.<!-- FACT-D71-005 -->[^unverified-005] In every case the cycle alone, independent of the full
payoff detail, predicts the qualitative outcome: no fixation, persistent
coexistence, and oscillating shares.

clarity:
The prime makes visible that ranking is a property of the relation, not
of the options. As soon as a reasoner looks for the cycle, they stop
asking "which is best?" and start asking "who beats whom?" — which
exposes why interventions that presuppose a linear order, such as
seeding a tournament, choosing a single pure strategy, or declaring a
category winner, can be incoherent. The frame also separates *genuine*
intransitivity, structurally present in the payoff graph, from
*apparent* intransitivity produced by sampling noise or a shifting
context, so that a cyclic pattern in data can be correctly attributed
either to the relation's topology or to measurement artifact. The
clarifying force is to relocate the question from the items being ranked
to the structure of the relation ranking them.

manages_complexity:
Once the cycle is identified, a great deal of system behavior follows
without any further detail. No pure equilibrium exists; all types coexist
at positive frequency; population shares oscillate; and any monoculture
is vulnerable to invasion by its predator-type. The analyst does not need
the full payoff matrix to predict these qualitative outcomes — the cycle
alone is enough. This is a sharp compression: a potentially complicated
system of competing options reduces to a single topological feature of
its beats-graph, from which the absence of a winner and the presence of
rotation are immediately derivable. The complexity payoff is that the
*impossibility results* — no linear order, no stable monoculture — come
for free with the recognition of the cycle, sparing the practitioner the
futile search for a best option that the structure forbids.

abstract_reasoning:
The signature lets a reasoner reason about an entire class of systems
that share a cyclic beats-relation, independent of substrate — genes,
ballots, plays, market share. It also clarifies what *cannot* be done:
because no consistent linear ordering exists, any procedure requiring one
will produce arbitrary or unstable results, so the prime functions as an
impossibility theorem as much as a pattern. The reasoning concerns the
*topology of a binary relation over three or more options*, which is why
it is indifferent to what the options are: the same conclusions —
mixed equilibrium, coexistence, oscillation, invadability of
monocultures — follow wherever the directed cycle is present. To
recognize the cycle is to know in advance both what the system will do
(rotate) and what one cannot make it do (settle on a single winner).

knowledge_transfer:
The transferable content is a recognition and an intervention vocabulary
that travel across domains: identify the cycle, choose a *mixed* strategy
rather than a pure one, predict oscillation rather than convergence, and
design *for* cyclic balance when monoculture is dangerous. From ecology
to markets, the persistence of three rivals with no clear winner suggests
cyclic dominance rather than market inefficiency, and the right response
is not to pick one but to stabilize the cycle or to break it by changing
the relation. From voting to model evaluation, intransitive results — a
model beating another on one benchmark and losing on another in a cycle —
imply there is no single ranking, only profiles. And from games to
institutional design, deliberately constructing a cyclic capability
triangle, in which three checks each constrain the next, prevents any
single actor from dominating.

The structural roles map across substrates. The *options* are the
morphs, the candidates, the teams, the standards, or the strategies; the
*beats-relation* is the mating dominance, the majority preference, the
stylistic matchup, or the competitive vulnerability; the *cycle* is the
directed loop that closes the relation; and the *mixed equilibrium with
oscillation* is the rotation of morph frequencies, the absence of a
Condorcet winner, or the coexistence of rival standards. An ecologist
watching three lizard morphs rotate in frequency, a social-choice
theorist confronting a preference cycle with no Condorcet winner, and an
institutional designer building three mutually-checking powers are
reasoning about the same object: a beats-relation whose cyclic topology
forbids a winner and mandates coexistence. The diagnostic — *does the
beats-relation close into a cycle, and if so is it genuine or an
artifact?* — travels unchanged across games, ecology, social choice,
sports, and markets. Because the response repertoire is the same
everywhere — play mixed, expect rotation, design for or against the cycle
— a practitioner who has handled intransitive dominance in one domain can
import the whole discipline into a domain that knows the pattern only by
its folk-game nickname.

formal_abstract:
The game itself, treated as a formal payoff matrix, exhibits the whole package.
The *set of options* is {rock, paper, scissors}; the *beats-relation* is rock
beats scissors, scissors beats paper, paper beats rock.<!-- FACT-D71-006 -->[^osborne-rubinstein-1994] *Intransitivity* is
immediate — rock beats scissors and scissors beats paper, but rock does not beat
paper — and the beats-graph is a *closed directed cycle*. From this single
topological fact, and with no further payoff detail beyond symmetry, the
consequences follow by derivation: there is *no pure-strategy equilibrium*,
because whatever pure choice you commit to, your opponent has a pure
best-response that beats it; the *unique Nash equilibrium is mixed* at
(1/3, 1/3, 1/3), assigning every option positive weight.<!-- FACT-D71-007 -->[^vonneumann-morgenstern-1944] Replace the two-player
game with a large population whose members play their type against random
opponents, and the same cycle yields *rotation dynamics*: a population of mostly
rock is invaded by paper, a population of mostly paper is invaded by scissors, and
the frequencies oscillate in a closed orbit, all three types coexisting at
positive frequency with no fixation. The impossibility result is the sharp
payoff: any procedure demanding a linear ranking — "which throw is best?" — is
incoherent here, because a directed cycle admits no consistent linear order. The
intervention the prime licenses is to stop seeking a best option and instead play
the mixed strategy, or, if one controls the rules, to break the cycle by altering
the relation.

**Mapped back:** the three throws are the options, the beats-rule is the
beats-relation, the closed loop is the cycle, and the (1/3,1/3,1/3) mixed
equilibrium with population rotation is the rotation dynamics — every signature
role instantiated.

applied_industry:
Two real substrates carry the identical topology. First, the side-blotched lizard
in evolutionary ecology has three male mating morphs distinguished by throat
color, and their reproductive success forms a cycle: the aggressive
territory-holder is beaten by the cooperative sneaker strategy, the sneaker is
beaten by the mate-guarder, and the mate-guarder is beaten by the aggressive
territory-holder.<!-- FACT-D71-008 -->[^sinervo-lively-1996] The *options* are the three morphs, the *beats-relation* is
reproductive dominance, and because it *closes into a cycle*, no morph fixes:
field observations show the morph frequencies *oscillate* over generations in
exactly the rotation the structure predicts,<!-- FACT-D71-009 -->[^sinervo-lively-1996] each morph's rise sowing the
conditions for the morph that beats it. An ecologist who recognizes the cycle
knows in advance that competitive exclusion will not occur and that conservation
of all three is the stable outcome — coexistence is mandated, not accidental.
Second, social choice: Condorcet's paradox shows that a rational electorate can
hold majority preferences A over B, B over C, and C over A simultaneously.<!-- FACT-D71-010 -->[^condorcet-1785] The
*options* are the candidates, the *beats-relation* is pairwise majority
preference, and the *cycle* means *no Condorcet winner exists* — so any
single-winner voting rule applied to this profile produces a result that depends
on arbitrary features like agenda order, and a designer who detects the cycle
knows the "pick the best candidate" framing is structurally incoherent and must
instead report the preference profile or fix a procedure rule transparently. The
same recognition underwrites institutional design that deliberately builds a
cyclic check-triangle so no single power dominates.

**Mapped back:** the lizard morphs and the candidates are the options;
reproductive dominance and majority preference are the beats-relations; the closed
loops are the cycles; and oscillating morph frequencies and the absent Condorcet
winner are the rotation-and-impossibility consequences — the same cyclic topology
across ecology and social choice.


Role

slug: role

one_liner: A bundle of expected behaviours attached to a social position.

core_idea:
A role is a slot defined by a bundle of expected behaviors, rights, and obligations that is decoupled from whoever happens to occupy it, so that different occupants are interchangeable within the slot and the slot persists when its occupant changes. <!-- FACT-D54-886 -->[^linton-1936] The defining structure is the *separation of position from incumbent*: the expectations attach to the position, not to the person, and behavior becomes predictable from the role rather than from individual disposition. This indirection — addressing a function by its slot rather than by its current filler — is what makes the role a recurring structural device rather than a parochial fact about human society. The concept was given its sharpest sociological statement by Linton (1936), who separated *status* (the position one occupies) from *role* (the dynamic enactment of the expectations that attach to that status), and was developed into a full structural account of expectation-bearing positions by Merton (1957) in his treatment of the role-set. <!-- FACT-D54-887 -->[^linton-1936][^merton-1957]

What the prime names is therefore not "a kind of job" or "a part one plays" but the more abstract move of *defining a function by reference to a position and letting occupancy be a separate, variable matter*. Once a slot exists, the system can reason about the slot independently of who fills it: it can specify what the slot requires, evaluate whether a candidate satisfies those requirements, swap occupants without rebuilding the surrounding structure, and hold the slot accountable rather than the person. The role is the unit of *occupant-independent functional specification*. <!-- FACT-D54-888 -->[^merton-1957]

structural_signature:
A role encodes a structural pattern: **define a position by its expected behaviors and obligations → decouple that position from any particular incumbent → make occupants interchangeable while the slot persists**. It separates two things that naive description fuses — the *position* and the *person currently in it* — and names the indirection layer between them. The same two-layer separation that lets a sociologist say "the office of the presidency outlasts any president" lets a programmer say "this code depends on the interface, not the concrete class," and lets an ecologist say "the decomposer niche is filled by fungi here and by bacteria there." <!-- FACT-D54-889 -->[^biddle-1986]

**Recurring features:**

- Separation of position from incumbent
- Expectations attach to the slot, not the person
- Occupants are interchangeable within the slot
- The slot persists when its occupant changes
- Addressing a function by its position rather than its filler
- Behavior predictable from the role rather than from disposition
- A bundle of rights and obligations bound to a position

The structural insight is robust across substrates: a teacher, an apex predator, an `Observer` in a design pattern, and a character in a play all exhibit the same separation between a defined slot and its current occupant, a generality Biddle (1986) traces in his review of the convergent role concepts that arose independently across sociology, anthropology, psychology, and organizational science. <!-- FACT-D54-890 -->[^biddle-1986] Whenever a function is specified once and then filled by a changeable, interchangeable occupant, the role structure is present, regardless of whether the occupant is a person, a species, or a software object.

what_it_is_not:
A role is **not** the person who occupies it. The whole point of the prime is the wedge between slot and incumbent; collapsing them back together discards the abstraction. "The teacher" names a position with attached expectations; the specific human standing at the board is the occupant. Confusing the two produces the error of attributing role-driven behavior to personality ("she's just bossy") when it is in fact the slot ("the supervisor role requires enforcing deadlines") that is doing the work.

A role is **not** an identity, though the two often co-occur. An identity is a self-concept a person carries; a role is an occupant-independent behavioral slot that exists whether or not anyone identifies with it. A night-shift security guard may feel no identification with the role at all and still discharge its obligations; the role does not require that its occupant internalize it. Roles can become identity-constituting, but the prime does not claim they must be, and treating every role as an identity overstates how deeply slots reach into the self.

A role is **not** a rule, a norm, or a law in general. Norms and rules can exist without being bound to any position (a society-wide norm against littering attaches to everyone, not to a slot). What distinguishes a role is that its expectations are *indexed to a position* and therefore travel with the slot rather than with the population. A role bundles obligations and binds the bundle to an occupiable position; a free-floating norm does not.

A role is **not** automatically a hierarchy, an authority, or a power relation. Many roles carry no authority at all (customer, bystander, patient). The prime says only that a position carries a bundle of expectations decoupled from its incumbent; whether that bundle includes command rights is a further, contingent fact, not part of the structure itself. Treating "role" as a synonym for "rank" smuggles in a hierarchy the abstraction does not require.

Finally, a role makes **no claim about whether the expectations are good, fair, fulfilled, or even coherent**. A slot can carry contradictory obligations, can be chronically unfilled, can be occupied by someone who flouts every expectation. The prime describes the structure of position-with-expectations decoupled from incumbent; it does not assert that the expectations are met or that meeting them is desirable. The derived pathologies (role conflict, role overload, role strain) are precisely what becomes nameable *because* the slot exists independently of its discharge.

broad_use:
**Sociology:** Parent, teacher, customer, citizen — positions carrying scripted expectations that shape behavior largely independent of personality. The status/role distinction (a position one holds versus the enactment of its attached expectations) and the role-set (the cluster of complementary roles a single status engages) are foundational analytic tools, as Merton (1957) developed them. <!-- FACT-D54-891 -->[^merton-1957] Sociology uses the role to explain why interaction is predictable among strangers: knowing someone's role tells you a great deal about how they will behave even when you know nothing about them as a person.

**Theater (origin metaphor):** A part exists in the script as a defined slot — lines, motivations, relations to other parts — and is filled by interchangeable actors; the character persists across casts and revivals. Goffman (1959) extended this dramaturgical reading into a general account of social life, treating everyday conduct as performance of socially scripted parts before audiences. <!-- FACT-D54-892 -->[^goffman-1959] The theatrical metaphor is the historical source of the word and remains the most intuitive illustration of slot/occupant separation: the role of Hamlet is the same role whether played by Olivier or by an understudy.

**Ecology (non-obvious):** A functional role or niche — decomposer, apex predator, primary producer, pollinator — can be filled by different and unrelated species across ecosystems, and convergent evolution repeatedly produces distinct organisms that occupy the same functional slot. <!-- FACT-D54-893 -->[^elton-1927] Elton's (1927) concept of the ecological niche as "the animal's place in the biotic environment, its relation to food and enemies" is precisely a role: a position in the trophic structure defined by what it does, fillable by whatever organism satisfies the functional requirements.

**Software engineering:** Role-based access control (RBAC), interfaces, abstract base classes, and design-pattern roles (the Observer, the Mediator, the Strategy) all specify obligations that a slot must satisfy without naming the concrete class that fills it. Programming to an interface rather than to an implementation is the engineering discipline of depending on the role rather than the occupant, a principle the Gang of Four (Gamma et al., 1994) elevate to the central organizing idea of reusable object-oriented design. <!-- FACT-D54-894 -->[^gamma-etal-1994] RBAC in particular assigns permissions to roles and roles to users, so that the privilege bundle survives the turnover of any individual user.

**Organizations:** Job descriptions, org charts, and positions define slots whose duties survive the turnover of the individual. An organization can be diagrammed, staffed, restructured, and held accountable in terms of positions and their relations rather than enumerated persons; the position "Regional Sales Manager" continues to exist and carry its obligations across a succession of occupants.

clarity:
A core function of naming the role is to make visible that **behavior often follows the position rather than the person**. This is the prison-guard insight made famous by Zimbardo's (1971) Stanford prison study: ordinary individuals assigned to the guard slot behaved in ways predicted by the role rather than by their prior dispositions, illustrating how powerfully an occupant-independent slot can shape conduct. <!-- FACT-D54-895 -->[^haney-banks-zimbardo-1973] Whatever the contested details of that particular study, the conceptual point it dramatizes — that a defined position can dominate individual disposition — is exactly what the role prime makes sayable. Naming the role lets an analyst factor observed behavior into a slot component and a person component instead of attributing everything to character.

The role also gives practitioners a precise vocabulary for malfunction. One can say "this is *role conflict*" (one person occupying incompatible roles), "this is *role overload*" (a single role carrying more obligation than any occupant can discharge), or "this is a *role transition*" (the difficulty of moving from one slot to another) precisely *because* there is a defined slot to be in conflict, to be overloaded, or to be exited. Without the slot abstraction these would be vague complaints about a stressful situation; with it, they become diagnosable structural conditions, as Kahn et al. (1964) demonstrated in their pioneering measurement of role conflict and role ambiguity as distinct, separately addressable stressors. <!-- FACT-D54-896 -->[^kahn-etal-1964]

manages_complexity:
Roles compress an open-ended, ever-changing population of individuals into a small, stable set of functional slots, so that a system can be described and operated in terms of positions and their relations rather than in terms of enumerated persons. A hospital with thousands of staff and a constant churn of hires and departures can nonetheless be reasoned about as a fixed lattice of roles — attending physician, charge nurse, ward clerk, patient — whose relations remain constant even as the occupants rotate. This is a massive reduction in the state a designer or operator must hold in mind. <!-- FACT-D54-897 -->[^merton-1957]

The indirection also **localizes change**. Because expectations attach to the slot, an occupant can be swapped without redesigning the surrounding system: the new attending steps into the same relations, obligations, and authorities the old one held. Succession, hiring, casting, and species replacement are all instances of this localized substitution. The system's structure is insulated from the volatility of its membership, which is precisely why organizations, ecosystems, and software systems built on stable roles can survive turnover that would shatter a system whose behavior was hard-wired to specific individuals.

abstract_reasoning:
Once roles are recognized, **substitution and composition reasoning** become available. Substitution: because occupants are interchangeable within a slot, one can reason about what *any* qualified occupant would do, and ask whether a candidate satisfies the slot's requirements before committing them to it. Composition: roles can be combined (one person holding several) or split (one overloaded role divided into two), and the expectations bundled into a slot can be analyzed for internal consistency before anyone fills it — does this job description demand contradictory things? <!-- FACT-D54-898 -->[^biddle-1986] This last move, checking a slot's obligations for coherence in the abstract, is impossible without the position/incumbent separation.

The role also grounds an entire family of derived patterns, each of which presupposes the slot/occupant separation: role conflict, role strain, role ambiguity, role models, role-set, casting, typecasting, and impersonation all become definable only once the base slot structure is in place. Turner's (1962) account of *role-taking* and *role-making* — occupants not merely filling fixed slots but actively negotiating and reshaping them through interaction — is itself a higher-order reasoning move that the base prime enables: it treats the slot as a stable referent against which improvisation and renegotiation can be measured. <!-- FACT-D54-899 -->[^turner-1962]

knowledge_transfer:
The software discipline of *programming to an interface* — depend on the role, never on the concrete filler — transfers directly to organizational design, where defining stable, well-specified roles lets people be swapped without organizational collapse, and where a vague or person-specific role ("whatever Jim does") is recognized as the same brittleness an engineer sees in code coupled to a concrete class rather than an interface. The transfer runs in both directions and is conceptually grounded rather than merely metaphorical: both domains are managing the same separation between a specified slot and a variable occupant. <!-- FACT-D54-900 -->[^gamma-etal-1994]

Conversely, the ecological insight that distinct, unrelated species can fill the same functional niche transfers to teams and organizations: a role can be re-occupied by very different individuals who nonetheless behave alike because the slot's expectations dominate the occupant's idiosyncrasies. A team lead familiar with convergent evolution can predict that a successor in a well-defined role will be shaped toward the role's behavior even if their background is wildly different from their predecessor's — and, contrapositively, that if the role is underspecified, occupant idiosyncrasy will dominate and behavior will not transfer. The vocabulary and reasoning of roles let a practitioner in one substrate recognize and reuse a solution discovered in another.

formal_abstract:
**Software interface (Observer pattern):** A subject object maintains a list of dependents and notifies them of state changes by calling a method declared on an `Observer` interface — not on any concrete class. The subject knows only the role: "an Observer is anything that implements `update()`." Any number of concrete classes (a logger, a UI panel, a cache invalidator) can occupy the Observer role, and they are fully interchangeable from the subject's point of view. New observers can be added and old ones removed at runtime without the subject changing at all, because the subject is coupled to the slot, not to the occupant. **Mapped back:** This is the role structure in its purest engineered form. The position (`Observer`, defined by the `update()` obligation) is decoupled from any incumbent (the specific classes), occupants are interchangeable, and the slot persists across substitutions. The compiler enforces exactly the position/incumbent separation that the sociological prime describes informally: expectations attach to the interface, behavior is predictable from the role, and the surrounding system is insulated from the turnover of concrete implementations.

**Ecological niche (the decomposer role):** In a temperate forest the decomposer niche is filled largely by fungi and detritivorous invertebrates; in a deep-sea vent community the analogous role is filled by chemosynthetic bacteria and specialized worms. The *role* — break down dead organic matter and return nutrients to the system — is the same functional slot, but its occupants are taxonomically unrelated, the product of convergent evolution toward the same position in the trophic structure. Remove the incumbents and, over evolutionary time, the slot tends to be refilled by whatever lineage can satisfy its functional requirements. **Mapped back:** The niche is a role: a position defined by what it does, decoupled from which organism does it, with interchangeable occupants and a slot that persists across substitutions and across ecosystems. That two utterly different kingdoms of life can occupy the same role is the biological version of two unrelated classes implementing the same interface — strong evidence that the prime captures a structure, not a social convention.

applied_industry:
**Role-based access control in an enterprise system:** A hospital's information system grants permissions not to named employees but to roles — "Attending Physician," "Pharmacist," "Billing Clerk" — and then assigns employees to roles. A pharmacist can dispense and reconcile medications; a billing clerk can view charges but not clinical notes. When a pharmacist resigns and a new one is hired, no permissions are rewritten: the new hire is simply assigned the Pharmacist role and inherits exactly the bundle of rights and obligations the slot carries. Auditors reason about the system in terms of roles, not the hundreds of individuals occupying them. **Mapped back:** RBAC is the indirection layer made operational. The permission bundle attaches to the position, not the person; occupants are interchangeable; the slot (and its privileges) persists across turnover; and the entire access surface can be reasoned about, audited, and changed at the level of roles rather than enumerated users. This is complexity management by slot compression in its clearest industrial form.

**Organizational succession in a corporate office:** When a Chief Financial Officer departs, the company does not dissolve the finance function and rebuild it around whoever arrives next. The CFO *position* — its reporting relationships, signing authority, board responsibilities, and statutory obligations — persists, and the search is explicitly a search for an occupant who can satisfy the slot's requirements. The incoming CFO steps into the same lattice of relations the outgoing one occupied. Where the role is well specified, the transition is smooth and the institution barely registers it; where the role had quietly become "whatever the long-tenured incumbent personally did," succession is painful precisely because the slot and the person had fused. **Mapped back:** Succession is occupant substitution within a persistent slot. The smoothness of the transition is a direct function of how cleanly the position was separated from its incumbent — the same lesson the engineer learns when code coupled to a concrete class proves far harder to change than code coupled to an interface. The applied cost of *failing* to maintain the separation is what makes the abstraction practically load-bearing rather than merely descriptive.

title: The slot must be specified enough to constrain behavior, yet loose enough to be fillable

body: A role that over-specifies every action becomes unoccupiable — no real person or implementation can satisfy a slot whose obligations are exhaustively scripted and mutually exhaustive. A role that under-specifies leaves so much to the occupant that behavior is no longer predictable from the position, and the abstraction collapses back into "whatever this individual does." Every role lives on a tension between determinacy (which buys predictability and interchangeability) and slack (which buys fillability and adaptiveness), and there is no general rule for where the optimum sits.

title: Decoupling position from incumbent enables interchange but invites de-individuation

body: The very feature that makes roles powerful — behavior follows the slot, not the person — is also what licenses the prison-guard dynamic, where occupants do things they would never do as private individuals because "the role required it." The same separation that lets an organization survive turnover lets it diffuse responsibility into positions, so that everyone obeyed the slot and no one is answerable as a person. Interchangeability and moral evasion are two faces of the same structural move.

title: Roles persist by design, yet persistence can outlive usefulness

body: Because the slot is built to survive its occupants, a role can continue to exist, draw resources, and impose obligations long after the function it was created to serve has lapsed. The persistence that protects a system against membership volatility also protects obsolete positions against removal, since the structure treats the slot as the stable thing and turnover of occupants as the normal case — making it easy to refill a dead role reflexively rather than question whether it should exist at all.

title: A role abstracts away the occupant, but real occupants are never fully interchangeable

body: The model promises that any qualified occupant is substitutable within the slot, yet occupants bring tacit knowledge, relationships, and idiosyncratic competence that the role specification does not capture. The gap between the slot-as-specified and the slot-as-actually-discharged-by-this-person is where succession surprises live: the new occupant satisfies every stated requirement and the function still degrades, because part of what the predecessor did was never in the role. The abstraction's promise of clean interchange is always partly a fiction.

title: Combining and splitting roles is structurally easy but humanly costly

body: Composition reasoning says a person can hold several roles and an overloaded role can be split in two. Structurally this is just rebinding occupants to slots. But a single occupant holding multiple roles is the precondition for role conflict, and splitting a role can sever relationships and tacit coordination that lived in the unsplit whole. The operations the abstraction makes look like clean algebra on slots land on people who experience them as strain, divided loyalty, or loss.

title: Specifying a role requires committing to expectations that may themselves be incoherent or contested

body: To define a slot is to assert a bundle of obligations as if they were consistent and agreed, but the bundle may demand contradictory things, and different stakeholders may hold incompatible expectations of the same position. A role can therefore be perfectly well-formed as a structure (a named slot with attached obligations) and yet internally impossible to discharge, or stable only because the contradiction is never tested. The abstraction lets us write down the slot cleanly; it does not guarantee that what we wrote into it can actually be done.

prose: _No catalogued solution archetypes reference this prime yet._

notes:
The word "role" is itself a theatrical fossil: it derives from the *rôle*, the roll of paper on which an actor's part was written. The etymology is unusually apt, because the roll-of-paper sense already contains the prime's core move — the part exists as a written specification independent of which actor reads from it. The migration of the term from the stage to sociology (Linton, Mead, Goffman), then to organizational science, ecology, and computing, is a textbook case of a structural concept being recognized as substrate-independent and carried across domains.

A persistent source of confusion is the relationship between *role* and *self*. In symbolic-interactionist sociology (Mead, Turner) the boundary is deliberately blurred: occupants do not merely fill fixed slots but engage in *role-taking* and *role-making*, actively negotiating and reshaping the slot through interaction. The base prime stays agnostic here — it asserts only the separation of position from incumbent — but it is worth flagging that the cleanest engineered instances (interfaces, RBAC) hold the slot rigid while the richest social instances treat the slot as continuously renegotiated by its occupants. The prime spans both, but the degree of slot rigidity is a major axis of variation across substrates.

The ecological case is the strongest evidence for substrate independence and deserves emphasis. That convergent evolution repeatedly produces unrelated organisms occupying the same functional niche is a two-way bridge with software: programming-to-an-interface and niche-filling are the same structure observed in radically different substrates, neither borrowing vocabulary from the other. This is why the prime scores 5 on transfer evidence: the cross-substrate transfer is genuine rather than metaphorical, because the structure can be stated without reference to any of the domains in which it appears.

Roles also operate at multiple scales simultaneously and can nest. A single position ("attending physician") is a role; the cluster of complementary positions it engages (patient, nurse, resident, administrator) is Merton's role-set; an entire org chart is a lattice of roles. Confusing scales — treating a whole governance architecture as "a role," or treating an individual obligation within a role as itself a separate role — is a common modeling error. The prime is the single occupant-independent slot; the larger structures are compositions of it.


Role Conflict

one_liner: Conflicting roles.

core_idea: Role conflict is the structural condition in which a single person simultaneously occupies multiple social roles whose embedded expectation-sets are incompatible, making simultaneous full compliance impossible and forcing trade-offs that produce strain<!-- FACT-D29-061 -->[^kahn-1964]. Merton's foundational 1957 concept of the *role-set* — the cluster of social roles that attach to a single social position, with each role paired with counter-roles held by others — clarifies the structure: a school principal's role-set includes teacher, school board, parents, community, superintendent, all with distinct expectations. Kahn, Wolfe, Quinn, Snoek, and Rosenthal's 1964 organizational-stress study formalized role conflict as one of two principal sources of occupational strain (the other being role ambiguity)<!-- FACT-D29-062 -->[^kahn-1964]. They distinguished *intra-role conflict* — incompatible expectations within a single role from different role-senders (a manager receives conflicting directives from boss and subordinates) — from *inter-role conflict* — incompatibility across distinct roles held by the same person (parent and employee roles demand incompatible time and psychological availability)<!-- FACT-D29-063 -->[^kahn-1964]. The conflict may be *temporal* (both roles demand the same time), *behavioral* (role X requires action A while role Y requires not-A), *normative* (role X requires stance S while role Y requires contradictory stance), or *resource-based* (the material or emotional resources available cannot satisfy both roles)<!-- FACT-D29-064 -->[^greenhaus-beutell-1985]. Crucially, the conflict is *non-eliminable* at the individual level: the person cannot simply drop one role without incurring substantial costs (lost livelihood from job, family estrangement, legal sanctions) that lock them into the conflicted structure. Goode's 1960 role-strain theory formalized this: strain arises not from mere workload but from the *structural incompatibility* that forces the person to partially fail at one or more roles regardless of effort or capability<!-- FACT-D29-065 -->[^goode-1960]. The strain is often experienced as guilt, anxiety, or a sense of inauthenticity (the person cannot be "fully themselves" in either role).

structural_signature:
*the incompatible-expectations-from-multiple-roles structure*
*the role-set definition (Merton — single position, multiple counter-roles)*
*the work-family inter-role-conflict canonical case*
*the role-strain-as-felt-difficulty (Goode)*
*the role-accumulation positive-counter-thesis (Sieber)*
*the time-strain / behavior-strain / strain-based dimensions*

Formally, role conflict is a constraint-satisfaction problem where an individual I occupies role-set R = {r_1, r_2, ... r_n}, each role r_i carries an expectation-bundle E_i (time allocations, behavioral scripts, normative commitments), and there exist pairs (i, j) such that E_i ∩ E_j is empty — the role-bundles are mutually incompatible<!-- FACT-D29-066 -->[^marks-1977]. The individual must choose an allocation A of time/energy/behavior such that performance P_i across roles i degrades, with P_i < E_i for at least one role. The structural signature is the *non-additive* nature of the strain: reducing the workload on one role does not proportionally alleviate strain if the incompatibility remains. Greenhaus and Beutell (1985) distinguished three dimensions of inter-role conflict: *time-based* (both roles demand the same hours), *strain-based* (stress from one role degrades capacity in the other), and *behavior-based* (required conduct in one role conflicts with required conduct in the other)<!-- FACT-D29-067 -->[^greenhaus-beutell-1985]. Sieber (1974) advanced a *role-accumulation hypothesis* as a partial counter to deterministic conflict framing: multiple roles can also produce benefits (variety, income, identity affirmation) that offset the strain, meaning not all multi-role occupancy is net-negative<!-- FACT-D29-068 -->[^sieber-1974]. However, the benefits of accumulation do not eliminate the conflict structure itself; they coexist with it. Hochschild's 1989 treatment of the "second shift" documented the systematic role-conflict burden borne disproportionately by women in households where caregiving and wage-labor roles collide without institutional accommodation<!-- FACT-D29-069 -->[^hochschild-1989].

what_it_is_not:
- It is not **role overload** — overload is the sum of legitimate demands across roles that collectively exceed capacity, but each demand is independently satisfiable; role conflict is structurally incompatible demands. Overload responds to triage and time-management; conflict requires incompatibility resolution.
- It is not **role ambiguity** — ambiguity is unclear or contradictory expectations *within* a single role; role conflict concerns well-specified but incompatible expectations *across* roles.
- It is not **interpersonal conflict** — that is between people; role conflict is within one person arising from their structural position. Though role conflicts often generate interpersonal tensions.
- It is not **conflict of interest** (narrow sense) — conflict of interest is a specific subset where two roles create opposing financial or fiduciary incentives that compromise judgment; role conflict includes all incompatibility types, not just incentive-based.
- It is not **work-life imbalance** as purely quantitative — imbalance often describes overload; role conflict describes incompatibility independent of hours, even when both roles' hour demands are individually reasonable.

broad_use: Organizational psychology treats role conflict as a principal occupational stressor linked to burnout, turnover intention, absenteeism, and physical health outcomes through both direct pathophysiological pathways (chronic stress) and behavioral ones (coping through substance use, relationship neglect)<!-- FACT-D29-070 -->[^frone-1992]. Gender studies documents the asymmetric distribution of role-conflict burden: caregiving and professional roles are institutionally structured in most societies to produce more frequent and severe conflicts for women than men. Professional ethics formalizes role-conflict structures in codes addressing physician-researcher, lawyer-investor, and board-member-operator conflicts, recognizing that some role combinations are incompatible in ways that threaten institutional integrity. Medical sociology examines nurse-manager, clinician-administrator, and physician-union-member conflicts as case studies. Political sociology studies legislator-as-private-citizen, elected-official-as-business-owner, and judicial-recusal rules. Family sociology analyzes "sandwich generation" caregiving (adult children caring for both young children and aging parents), a structurally intractable role conflict without institutional support. Military and athletic studies examine the conflict between combat/athletic roles and civilian identity. Educational administration examines principal-as-instructional-leader vs. principal-as-manager tensions<!-- FACT-D29-071 -->[^coser-1974].

clarity: The abstraction clarifies that what feels like personal failure or weakness in the conflicted individual is often a structural position-effect that would afflict any similarly-placed person regardless of character or competence. It separates distinct conflict types (intra vs. inter; temporal vs. behavioral vs. normative vs. material) that require different diagnoses. It distinguishes role conflict from adjacent constructs (overload, ambiguity, interpersonal conflict) whose remedies are distinct. It also clarifies that some role conflicts are *structurally unsolvable* at the individual level (requiring institutional change) while others are solvable through role re-negotiation or boundary-setting<!-- FACT-D29-072 -->[^williams-2000].

manages_complexity: An individual's social life typically contains a dozen or more active roles with complex expectation sets. Mapping the pairwise compatibility of all role-pairs would be combinatorially intractable. The abstraction compresses this by identifying likely incompatibility sites and by providing a typology (temporal/behavioral/normative/material) that predicts which conflict modes will dominate. It also compresses organizational design problems: matrix management with unresolved authority overlaps, or dual-reporting structures, reliably produce role conflict that can be diagnosed at the design level without waiting for individual strain to reveal them<!-- FACT-D29-073 -->[^stryker-macke-1978].

abstract_reasoning: Role conflict surfaces the general pattern of *constraint-overlap at a shared node* — whenever a single substrate (a person, a code module, a geographic zone) must satisfy multiple embedding systems with incompatible demands. Analogs: a code module satisfying interfaces of incompatible consumers; a database schema serving transactional and analytical workloads with opposite access patterns; a municipal zone serving residential, commercial, and transit demands with incompatible specifications<!-- FACT-D29-074 -->[^brewer-2000]. The structural unit is the *shared-substrate constraint-conflict*, with characteristic tradeoff patterns and structural (rather than merely quantitative) remediation requirements. This pattern is as fundamental to engineering design as to social organization: where multiple systems overlap at shared nodes, incompatibility is a design problem, not a capacity problem.

knowledge_transfer:
| Role in Source (sociology: work-family conflict) | Role in Target (systems engineering: distributed system architectural tension) |
|---|---|
| Person occupying roles | System node supporting multiple services |
| Incompatible role expectations | Incompatible system requirements (consistency vs. availability; latency vs. throughput) |
| Time-strain | Contention for processor cycles, network bandwidth |
| Behavior-strain | Operation X required by service A conflicts with operation Y required by service B |
| Intra-role conflict | One service receives contradictory requirements from different clients |
| Inter-role conflict | Services' requirements collide (distributed consensus requires synchronicity that latency-sensitive service cannot tolerate) |
| Role-set negotiation | Service-level agreements (SLAs) that explicitly trade off requirements |
| Non-eliminability | Removing one service breaks critical functionality; redesigning architecture has high sunk cost |
| Strain felt as guilt | System designers experience cognitive friction from unresolvable tradeoffs |
| Partial failure | System achieves degraded performance in both services rather than full performance in one |

A distributed system architect designing a service that must be simultaneously highly available (never down), strongly consistent (always correct), and low-latency (responds fast) faces role conflict<!-- FACT-D29-075 -->[^brewer-2000], not overload. The CAP theorem (Brewer 2000) formalizes that any two of these three properties are achievable, but all three cannot be simultaneously satisfied. This is not a resource or effort problem; it is a structural constraint-incompatibility analogous to the sociological work-family conflict. The architect cannot "work harder" or "manage time better" to escape it; they must negotiate which role-requirement will be partially sacrificed, and this decision point surfaces the identical structure: choose consistency over availability (Hochschild's "choosing career over family"), choose availability over consistency (choosing family over career), or attempt a hybrid (part-time work, degraded SLAs) that partially fails at both. The relief comes not from more effort but from explicit architectural clarity about which incompatibility is accepted.

formal_abstract:
Kahn et al.'s 1964 organizational study surveyed 1,496 employees across organizations, measuring role conflict through items like "Do you feel caught between conflicting demands from supervisors or others?" and "Do you have to bend the rules to do your job?" They documented correlations between role conflict and tension, job dissatisfaction, and psychological strain even after controlling for job characteristics, and traced the mechanism: role conflict produces chronic low-grade stress that accumulates into health outcomes<!-- FACT-D29-075 -->[^kahn-1964]. The classical example: a plant manager receives directives from corporate headquarters to maximize profit (cut safety investments, reduce quality assurance) while state regulations and union contracts require specific safety and quality standards. The manager cannot comply simultaneously with both, producing intra-role conflict. A woman who is also an employee, spouse, and mother may experience inter-role conflict: employment demands late hours and geographic flexibility; parental role demands physical presence and scheduling inflexibility; spousal role demands emotional availability. The conflict is real even if theoretically she "could" manage all three — the incompatibility produces strain regardless. Goode (1960) argues this strain is not a failure of personal coping but a structural property of her position.

**Mapped back:** The role-conflict structure is evident: incompatible expectations (work demands availability, family demands availability to different parties), non-eliminability (cannot drop either role without severe costs), and strain (guilt, exhaustion, partial failure in both roles). The intra-role example (plant manager) and inter-role example (woman in multiple roles) both show how the structure produces strain independent of the individual's effort.

applied_industry:
A pharmaceutical researcher who is also a patent-holder in their field experiences structured role conflict. As researcher, they are expected to publish findings, collaborate openly, and prioritize truth-seeking. As patent-holder, they are incentivized to withhold findings that might preempt their patent claims, restrict collaboration to protect intellectual property, and prioritize commercial outcomes. These behavioral requirements conflict: publishing and patenting-value cannot both be maximized; open collaboration and IP protection are incompatible. Professional norms recognize this through conflict-of-interest disclosures and recusal rules, but the recusal does not eliminate the conflict — it just removes the person from decisions where the conflict would manifest. The structural solution is to force a choice (researcher XOR patent-holder in the same work), not to manage the conflict at the individual level. Similarly, a clinical psychiatrist treating a family member, or a military officer with relatives in enemy forces, face role conflicts that are structurally unsolvable at the individual level and are therefore prohibited by institutional rule<!-- FACT-D29-074 -->[^coser-1974]. The institution recognizes that the conflict cannot be managed by effort or integrity; it must be prevented by role-separation.

**Mapped back:** The researcher-patent-holder example shows the behavioral-incompatibility form of inter-role conflict. The institutional response (conflict-of-interest rules, prohibitions on treating family members) shows that structurally intractable conflicts are managed by preventing the conflicted role-combination, not by managing the individual's response to the conflict.

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 related prime (1):** `relation_constraint_enforcement`

notes: Density-pass batch DP-29 G2 (sociology + anthropology + peace/conflict cluster, batch 2 of 2): collective_efficacy, role_conflict, culture_lag. Legacy #200. Kahn-Wolfe-Quinn-Snoek-Rosenthal 1964 foundational empirical study. Merton 1957 role-set concept. Goode 1960 role-strain theory. Greenhaus-Beutell 1985 time/strain/behavior dimensions. Sieber 1974 role-accumulation counter-thesis. Hochschild 1989 gender-asymmetric burden analysis. Role conflict bridges to collective_efficacy (multi-role occupancy affects group coordination), social_norms (roles are carriers of norms), and culture_lag (cultural change often outpaces institutional accommodation, creating new role conflicts). FACT ID range D29-061..D29-075. Passing to Pass B for reference integration and solution archetype authoring.


Role Fluidity

one_liner: Role fluidity allows the same occupant to move among positions that a rigid system assigns to separate actors, so producer/consumer, leader/follower, or requester/provider functions can alternate without changing occupant identity.

core_idea:
Role fluidity is the structural condition in which an occupant is not permanently
assigned to one functional position but can move among several roles as state,
task, relation, or time changes. The occupant remains identifiable while the
expectation-bearing slot changes. A peer may request a resource in one exchange
and provide it in the next; a participant may consume an artifact, modify it, and
later mentor another contributor.

The abstraction separates two mappings. In a rigid regime, each occupant maps to
one stable role. In a fluid regime, a transition rule maps the same occupant to
different roles across occasions. The load-bearing fact is not that several
roles exist, but that their occupancy sets overlap across time or context.

structural_signature:
- **the persistent occupant** — the entity whose identity continues across role changes
- **the role repertoire** — two or more positions with distinct functional expectations
- **the nonexclusive occupancy rule** — one occupant is eligible for several roles
- **the switching condition** — task, state, relation, time, election, or need selects the active role
- **the retained identity** — changing role does not create a different occupant
- **the boundary effect** — distinctions such as producer/consumer cease to partition the population
- **the coordination requirement** — other participants must know which expectations currently apply

what_it_is_not:
- **Not Role Conflict.** Conflict places incompatible expectations on an occupant at the same time. Fluidity permits movement among roles and can avoid simultaneous conflict.
- **Not lack of structure.** The roles and transition conditions may be sharply specified even when assignments are not permanent.
- **Not multitasking alone.** Tasks count only when they instantiate distinct expectation-bearing positions.
- **Not ordinary turnover.** Replacing one occupant with another preserves fixed role assignment; fluidity lets the same occupant cross role boundaries.
- **Not Specialization.** Specialization narrows units into stable partial functions. Role fluidity loosens exclusive assignment and may trade specialization efficiency for adaptability.

broad_use:
In peer-to-peer networks, every node can be client and server, sometimes within
one session. Distributed systems rotate leader and follower roles after elections
while node identities persist. Cross-trained emergency teams move members among
triage, transport, coordination, and relief roles as load changes.

In cultural production, readers become writers, users become maintainers, and
novices become mentors. In biology, organisms or cells can alternate reproductive,
foraging, signaling, or defensive roles under state-dependent rules. The local
role labels differ; the occupant-repertoire-transition structure remains.

clarity:
Role fluidity distinguishes population composition from assignment topology. A
system can contain the same people or components yet change fundamentally when
role membership becomes overlapping and reversible. It also explains why a
producer/consumer count can become misleading: the two labels no longer identify
disjoint populations.

manages_complexity:
Rather than describing every observed role change separately, the analyst records
an occupant-role eligibility matrix and a transition rule. Capacity, bottlenecks,
and accountability can then be analyzed from how quickly and reliably occupants
move across the matrix.

abstract_reasoning:
The defining test holds occupant identity fixed and varies context. If the
expectation-bearing position changes under a stable rule, role fluidity is
present. If the occupant is replaced, the case is turnover; if both expectation
sets apply simultaneously and cannot be reconciled, it is role conflict.

The prime predicts a trade: increasing eligible-role overlap raises adaptive
capacity and reduces bottlenecks, but increases switching cost, state ambiguity,
training burden, and the risk that accountability becomes unclear.

knowledge_transfer:
The client/server symmetry of a peer-to-peer protocol transfers to mutual-aid
organizations and participatory production: design the role repertoire, make
eligibility nonexclusive, provide a visible transition signal, and preserve
state needed to resume a prior role.

formal_abstract:
Let occupants \(A\) and roles \(R\) be linked by an eligibility relation
\(E \subseteq A \times R\). Fixed assignment constrains each occupant to one
role. Role fluidity exists when at least one occupant is eligible for multiple
roles and a transition function selects among them across states.

applied_industry:
An open-source user reports a bug, submits a patch, reviews another patch, and
later maintains the module. The same identity crosses consumer, contributor,
reviewer, and steward roles through explicit permission and recognition
transitions.

title: Adaptability versus specialization

body:
Broad eligibility absorbs changing
load but sacrifices some depth and adds training cost.

title: Fluidity versus accountability

body:
Moving roles can obscure who owns a
decision unless role occupancy is observable at the relevant time.

title: Low barriers versus unsafe transition

body:
Easy movement grows participation
but some roles require competence, authorization, or separation of duties.

notes: _(New cross-domain prime created to resolve a mixed-DAG missing-parent gate; queued for Claude style, source, and citation harmonization.)_