Archetype Library: Idea Patterns → Canonical Models

Before inventing a new model (Phase 5), check whether the idea matches a known archetype. Recognizing an archetype gives you 80 years of accumulated theory for free: known thresholds, closed forms, failure modes, and validation targets.

Rule: if two or more core features match an archetype below, START from its canonical form, then adapt. Always state which archetype you used and what you changed.

The catalog

Idea smells like...	Core signature	Canonical model	Known results you inherit
Spread of disease / behavior / rumor	infection by contact + recovery/forgetting	SIR / SIS / SEIR compartmental	R₀ threshold, final-size equation, herd immunity
New product / technology adoption	innovators + imitation via word-of-mouth	Bass diffusion	adoption curve shape, peak timing formula
Population or market growth with limits	growth slows as it approaches capacity	Logistic growth	carrying capacity K, saturation time
Predator-prey / competing actors	two populations coupling each other's rates	Lotka, Volterra	cycles, coexistence equilibria
Stocking something with random demand	holding cost vs stockout cost	Newsvendor / (s,Q) policy	critical ratio, safety stock formulas
Customers arriving for service	random arrivals, limited servers	M/M/c queueing (Erlang A/B/C)	utilization cliff, Erlang-C wait formula
Something wearing out	survival probability decaying with age/stress	Weibull / exponential reliability	hazard rate, MTBF
Accumulating with interest / compound effects	rate proportional to current amount	Exponential growth/decay	doubling time ln2/r
Choosing under scarcity	maximize/minimize subject to constraints	LP / ILP / NLP	shadow prices, duality
Many self-interested actors	my payoff depends on your choice	Game theory (Nash equilibrium)	best-response analysis, price of anarchy
Keeping a value near target despite noise	sensor + actuator + setpoint	Feedback control (PID/LQR)	stability margins, settling time
Influence depends on who knows whom	heterogeneous contact structure	Network dynamics on graphs	R_eff = R₀·⟨k²⟩/⟨k⟩, super-spreaders
Rare events dominating risk	heavy tails, low probability high impact	Extreme value theory / Poisson processes	tail exponents, return periods
Learning from data to predict	function fitting with uncertainty	Regression / Bayesian inference	posterior intervals, bias-variance
Particles/agents moving under simple rules	local rules, emergent global pattern	Agent-based model / cellular automata	phase transitions, emergence criteria
Quantity conserved across transformations	inflow = outflow + accumulation	Compartmental flow / Kirchhoff-style balance	conservation constraints
Stable queue averages (arrivals, waits, counts)	any long-run queueing system	Little's Law: L = λ·W	universal averaging identity
Two-sided matching (students↔schools, riders↔drivers)	two populations with preferences	Gale, Shapley stable matching	existence of stable matchings, strategy-proofness limits
Competitors choosing locations/prices	payoff depends on rivals' positions	Hotelling competition	principle of minimum differentiation, price wars
Few firms setting quantities/prices	market output affects everyone's price	Cournot / Bertrand oligopoly	Nash output levels, collusion fragility
Infection that returns after recovery	temporary immunity	SIS model	endemic equilibrium, treatment thresholds
Spread across connected cities/sites	patches coupled by travel	Metapopulation (multi-patch) model	invasion threshold, hub vaccination value
Flow between places ∝ size and distance	migration, trade, commuting	Gravity model	calibrated flow matrices from aggregate data
Consensus under peer pressure	individuals align with local majority	Ising / threshold spin models	phase transition, tipping fraction
Connectivity survival under failures	remove nodes/edges until network shatters	Percolation	critical fraction f_c, giant component collapse
Cycles of use → failure → replacement	repeated lifetime events with costs	Renewal, reward process	long-run cost rate formula
Sequential decisions with delayed consequences	act now, see later, decide again	Markov Decision Process	Bellman optimality, policy iteration
Tracking a hidden truth from noisy readings	sensor fusion, forecasting	Kalman filter	optimal linear update equations
Switching regimes inferred indirectly	you observe symptoms, not the regime	Hidden Markov Model	Viterbi/forward algorithms
Sizes dominated by a few huge cases	heavy tails: cities, quakes, outages	Power-law scaling	tail exponent estimation, Pareto cutoffs

How to use it in a session

1. After Phase 2 decomposition, scan the table against each sub-problem (not just the whole idea).
2. Declare matches explicitly: "Sub-problem 'demand randomness' matches the Newsvendor archetype, starting from critical-ratio logic."
3. Adapt, don't adopt blindly: list which canonical assumptions you keep, relax, or replace (feeds back into Phase 4 assumption table).
4. Inherit the validation target: canonical models come with closed-form checks (final size, Erlang-C, EOQ), use them in Phase 7 sanity checks via tools/validate.py patterns.
5. If NOTHING matches: say so explicitly and build from first principles, flagging "this is novel territory" raises the burden of validation, it doesn't lower it.

Anti-patterns

• Don't force-fit an archetype because it's famous (not everything is a network problem).
• Don't stack three archetypes when one covers the goal question, parsimony wins at recommendation time.
• Don't cite inherited results (R₀ thresholds etc.) without checking the archetype's assumptions still hold after your adaptation.