15-EFT.WP.Methods.Falsification v1.0 | Appendix A: Unified Terms & Symbols

Appendix A: Unified Terms & Symbols

I. Scope & Objectives

• This appendix consolidates the common terminology, symbols, and legal combinations used throughout the volume. It is the single source of truth for cross-chapter references and implementation bindings. Coverage includes hypotheses & assertions, statistical tests, adversarial & mutation methods, online gating, audit & compliance, cross-domain equivalence, and release management.
• Conventions: wrap all inline symbols in backticks; parenthesize every fraction and composite operator; declare the domain and measure for any integral; align all timelines to the monotonic time base; run a dimensionality check before publication.

II. Naming Rules & Typesetting Conventions

• Fractions & operators
  Write any a/b*c as ( a / b ) * c; enclose grad/div/curl and integrals in ( • ).
• Probability & expectations
  Conditional/posterior: p(y | x, theta), p(theta | D); expectation: E_{p(z)}[ f(z) ]; continuous form ( ∫ f(z) p(z) dz ).
• Paths & measures
  Path integrals: ( ∫_{gamma(ell)} f(ell) d ell ); volume/surface/line measures: dV/dS/d ell.
• Time & alignment
  Monotonic base tau_mono; published timestamp ts; mapping ts = alpha + beta * tau_mono.
• Two arrival-time forms (canonical examples)
  Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
  General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
• Dimensions & dimensionless
  Always run check_dim(expr); arguments to log/exp/ln must be dimensionless.
• Unified numbering
  Postulates P51-*; minimal equations S52-*; metrology flows Mx-5*; bindings I50-*.

III. Core Terms & Definitions

1. Basic objects
   • Hypothesis: the set of claims to be tested.
   • Assertion: a property constraint over observables.
   • Oracle: oracle(y_true, y_pred) -> score.
   • Test: the 5-tuple ( D, H0, H1, T(x), C_alpha ).
   • Metamorphic relation MR_k: an equivalence or order-preserving mapping x -> x_prime.
   • CounterExample: an x or (x, x_prime) that violates an assertion.
   • Attack: adversarial_attack(runtime, x, method, eps).
2. Data & domains
   Data domain D, inputs X, outputs Y, parameters theta, runtime runtime.

IV. Statistical Tests & Error-Control Symbols

• Hypothesis testing
  H0, H1, test statistic T(x), rejection region C_alpha.
  Significance & power: alpha, beta, power = 1 - beta.
  p_value, effect_size, equivalence margin delta_equiv.
• Multiple testing
  Family-wise error rate FWER; false discovery rate FDR; target q_star; m tests; R rejections; V false rejections.
  Definition: FDR = E[ ( V / max(R,1) ) ].
• Sequential/adaptive tests
  SPRT; alpha-spending; stop/continue rules and spent significance alpha_spent.
• Equivalence testing
  TOST; exemplar pass criterion: | effect_size | ≤ delta_equiv (chapter-specific details prevail).

V. Coverage, Mutation & Adversarial Symbols

• Coverage & mutation
  Test-case coverage cov_case; spec coverage
  cov_spec = ( |C_hit| / |C_total| ).
  Kill-rate kill_rate = ( |mut_killed| / |mut_all| ); mutant mut_i.
• Metamorphics & negatives
  MR_k, fuzz, mutation, adversarial(epsilon).
• Adversarial budgets & norms
  epsilon_linf, epsilon_l2, attack_steps; resource budgets budget.cpu/gpu/mem, budget.power.
• Input-level operators
  mutate(x; op, budget).
• Model-level operators
  gradient_attack, quantize_jitter.
• Pipeline-level operators
  delay/jitter/failover.

VI. Online Gating & Consistency Symbols

• SLO & timing
  Latency TS.latency, throughput TS.thrpt, error rate TS.error.
• Gating decision
  GateDecision ∈ {pass, hold, block}.
• Online/offline consistency
  Discrepancy delta_offon; inference reliability R_infer = 1 - delta_offon.
• Double-run & non-regression
  eq_rate = ( 1/N ) * Σ 1[ y_cand == y_base ];
  dist = ( 1/N ) * Σ L( y_cand_i , y_base_i );
  delta_baseline = ( score_cand - score_base ); gates tau_nonreg, tau_eq, tau_dist.
• Drift metrics
  D_KS, MMD; drift significance alpha_drift.
• Exposure & rollback
  Exposure curve blast_frac(t); change risk budget risk_budget.change; rollback_trigger, rollback_window.

VII. Environment, Signatures & Traceability

• Environment lock & anchor
  EnvLock, anchor (joint locator for data/code/parameters/topology).
• Fingerprints & hashes
  hash(•), fingerprint.
• Signature cards
  Graph.sig (compute graph), ParamCard.sig (parameters), InferPipelineCard.sig (inference pipeline).
• Diffs & audit
  DiffCard, ChangeProposal, Evidence.bundle, AuditTrail, CHANGELOG.
• Randomness logging
  rng.seed, rng_family; idempotency requires matching anchor and EnvLock.

VIII. Risk, Loss & Falsification Thresholds

• Empirical risk
  R_emp = ( 1/N ) * Σ L( y_i , y_hat_i ).
• Falsification deltas & reliability
  delta_claim = ( score_claim - score_obs ); R_infer = 1 - delta_offon.
• Typical rejection rules
  delta_baseline < - tau_nonreg, or eq_rate < tau_eq, or dist > tau_dist, or TS.* beyond gates.

IX. Legal Combinations & Conflict Names

1. Legal combinations
   • T_arr expressions pair only with n_eff, c_ref, gamma(ell), d ell.
   • For online comparison, first align with ts = alpha + beta * tau_mono, then compute delta_offon.
   • Reports for metamorphic tests or adversarial attacks must jointly state epsilon_* and budget.*.
2. Conflict names (must not be mixed)
   • T_fil (tension) vs. T_trans (transmission coefficient).
   • n (number density) vs. n_eff (effective refractive index).

X. Unified Numbering & Citation Style

• Numbering ranges
  Postulates P51-*; minimal equations S52-*; metrology flows Mx-5*; bindings I50-*.
• Cross-volume citation
  Fixed form: see companion white paper “Energy Filament”, Chapter x, S/P/M/I ….

XI. Example Expressions & Dimensional Checks

• Path integrals & constant factoring
  T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell ) ;
  T_arr = ( ∫ ( n_eff / c_ref ) d ell ).
• Online consistency
  R_infer = 1 - delta_offon, with dimensionless delta_offon.
• Test power
  power = P( reject H0 | H1 ); if log/exp/ln are involved, their arguments must be made dimensionless.
• Coverage & kill
  cov_spec = ( |C_hit| / |C_total| ); kill_rate = ( |mut_killed| / |mut_all| ).

XII. Quick Lookup (by theme)

• Hypotheses & tests: H0, H1, T(x), C_alpha, alpha, beta, power, p_value, effect_size, delta_equiv, SPRT, alpha-spending.
• Multiple testing: FDR, FWER, q_star, m, R, V.
• Coverage & mutation: cov_case, cov_spec, kill_rate, MR_k, mut_i, fuzz, mutation, adversarial(epsilon).
• Adversarial budgets: epsilon_linf, epsilon_l2, attack_steps, budget.cpu/gpu/mem, budget.power.
• Online gating: TS.latency, TS.thrpt, TS.error, GateDecision, delta_offon, R_infer, eq_rate, dist, tau_nonreg/tau_eq/tau_dist, D_KS, MMD, alpha_drift, blast_frac(t).
• Environment & signatures: EnvLock, anchor, hash(•), fingerprint, Graph.sig, ParamCard.sig, InferPipelineCard.sig, DiffCard, AuditTrail, CHANGELOG, ChangeProposal, rng.seed/rng_family.

XIII. Compatibility & Implementation Notes

• Any new symbol must conform to these conventions and conflict-name rules; register it here at first cross-chapter appearance.
• Generate CoverageReport, RegressionReport, GateLogs, and audit items strictly per this appendix to guarantee traceability, reviewability, and forensic validity.