Appendix A. Every symbol used in the book, defined once.
The chapters introduce symbols where they're first needed; this is the single place they're all collected. A few letters are reused with different meanings in different layers — those collisions are flagged explicitly at the bottom, because they trip up first-time readers.
Symbol Meaning First used
Fthe set of resolvers — capital holders who retroactively declare verdicts Mechanism Pthe set of forecasters — specialists who publish predictions Mechanism Qthe set of candidates / questions under evaluation Mechanism qa single question, with outcome space Ω_q Mechanism i, jindex a forecaster (i ∈ P) and a resolver (j ∈ F) Mechanism
Symbol Meaning First used
p_{i,q,t}forecaster i's probability distribution on q at time t Mechanism r_{j,q}resolver j's subjective verdict on q Mechanism S(p, ω)strictly proper scoring rule; canonically log score ln p(ω) Mechanism p_refreference belief (consensus just before an update); the subtraction baseline Mechanism w_ttime weight (can up-weight earlier forecasts) Mechanism ρ_{i,j,q}reward to i from j on q — marginal movement toward the verdict Mechanism R_{i,j}forecaster i's reputation with resolver j = Σ_q ρ_{i,j,q} Mechanism B_jresolver j's reward budget Mechanism p*the money-optimal forecast (= capital-weighted predicted consensus) Mechanism EU(i→j)decision-value of i's information to j ("extrapolated utility") Math Core §2.5u_qper-question reward-budget factor, set ∝ value-of-information Math Core §2.5
Symbol Meaning First used
θthe true state of a question Math Core §2πa forecaster's honest posterior given evidence Reflexivity λdeference weight — fraction of a verdict driven by the published forecastReflexivity g(p)the resolver's deference-response function Reflexivity Ldeference slope = λ · sup\|g'\|; safety condition L < 1 (= V1 )Reflexivity σ(θ)signal-driven verdict probability (the non-deferring part) Math Core §2
Symbol Meaning First used
Σresidual-correlation matrix across agents (after conditioning on public info) Independence n_effeffective population = 1ᵀ Σ⁻¹ 1; the stack's one security parameterIndependence ρ (here) pairwise correlation within a Sybil cluster — not the reward ρ above Independence knumber of accounts in a cluster (or replication count, §1.4) Independence hhonest fraction of an executor pool Math Core §1.4ν_iagent i's marginal n_eff, gating its UBI share Math Core §4.3
Symbol Meaning First used
δdemurrage rate — decay-unless-circulated; the dispersion dialValue as Flow Mtotal money supply Math Core §4Npopulation, measured in n_eff units Math Core §4w_iwallet balance of agent i Math Core §4e_i, s_iagent i's earn / spend rates Math Core §4ēbound on net earning advantage Math Core §4.2βtarget concentration bound on resolver budgets Math Core §4.2
Symbol Meaning First used
MATERIALIZE(V, R)make value V available at spacetime region R Substrate D(v, x, t)demand field — request intensity for value v at location x, time t Math Core §1p(v, x)price field — posted price of delivering v at x (the substrate's p)Math Core §1λ_v(x)local demand intensity for v at x — not the deference weight λ Math Core §1.2c_s, c_b, c_cstorage / bandwidth / compute cost coefficients Math Core §1.1work(f)reduction-step count of f (the canonical compute unit, from tree calculus) Math Core §1.1
The system is viable iff these hold (see Math Core §7):
Condition Plain meaning Chapter
V1 L < 1perception dominates action (no dark room) Reflexivity V2 cost(mimic k) ≥ cost(be k)boundary integrity; n_eff is sound Independence V3 δ ≥ ē/(M(β−1/N))turnover keeps capital dispersed (enforces A2) Value as Flow V4 switching cost < tyranny premiumexit keeps between-network selection alive Living System V5 verdicts are ex-post counterfactual contrasts the market stays evidence, never a mechanical rule Futarchy and Causality
The five assumptions A1–A5 (shared reality, dispersed capital, repeated game, tamper-evident timestamps, non-reflexivity) are defined in The Five Assumptions .
The same letter carries different meanings across layers. The four to watch:
Fresolver set in the engine, but the free-energy functional F_a in Math Core §0. (Context always disambiguates: a set of people vs. a quantity to minimize.)ρreward contribution ρ_{i,j,q} in the engine, but a pairwise correlation in the n_eff formula.λdeference weight in reflexivity, but λ_v(x) is local demand intensity in the substrate.pforecast distribution p_{i,q,t} in the engine, but p(v,x) is the price field in the substrate.
These overlaps are inherited from each layer's own conventional notation; they were kept rather than invent non-standard symbols.