e7He — Formal Disciplines#

e7He draws on multiple formal disciplines. The primary logic system is inherited from PET/JUB (S5 modal logic + Classical Extensional Mereology + first-order predicate calculus). e7He adds coalgebraic structure and dynamical systems theory for the perpetual-cycle formalization.

All 12 disciplines in the FORGE WisdomBase were loaded during the TEMPER rounds that tested e7He’s 24 statements under the Iron Maiden protocol. Each of the 10 Iron Maiden tests draws on specific disciplines.

Inherited Logics (from PET/JUB)#

  • S5 Modal Logic — necessity and possibility operators with equivalence-class accessibility. Used in Iron Maiden Test IV (Modal Soundness). e7He axioms that use modal operators: m0.ax1 (uniqueness holds necessarily), m0.ax3 (GOAL existence).

  • Classical Extensional Mereology (CEM) — part-whole relationships. Used in Iron Maiden Test V (Mereological Coherence). e7He inherits the God-World containment from PET (ax1, ax2). Agent scope is a mereological part of the system’s total scope.

  • First-Order Predicate Calculus — the base logic for all formal statements. Universal and existential quantification over agents, cycles, stages, and time.

Disciplines Added by e7He#

  • Coalgebra and Coinduction — the hero journey is formalized as a coalgebra with the step function step(μ_k) = (J_{k+1}, μ_{k+1}). Productivity (th4) guarantees non-termination. Bisimulation distinguishes genuinely different journeys from superficially different ones. See WB Sheet 9 (Coalgebra).

  • Dynamical Systems Theory — the Ie evolution equation (th3), ridge stability (th2), and attractor analysis (th5) are dynamical systems concepts. Lyapunov-like arguments underpin the ridge conditional stability. See WB Sheet 5 (Dynamical Systems).

  • Game Theory and Mechanism Design — the Commitment Trichotomy (th6) is a game-theoretic result. Schelling commitment theory, Spence signaling, Nash equilibrium, and the Prisoner’s Dilemma → Assurance Game transformation are central. See WB Sheet 3 (Mechanism Design) and WB Sheet 8 (Social Choice Theory).

  • Information Theory — the entropy condition in m0.ax3 (H(GOAL(h, t)) > 0) and the lognormal influence distribution (sp3) are information-theoretic. See WB Sheet 11 (Information Theory).

  • Probability and Stochastic Processes — the CTMC (continuous- time Markov chain) argument in th5 (BABL self-destructs with probability 1 as t → ∞) requires stochastic process theory. The lognormal distribution (sp3) requires probability theory.

Iron Maiden Test Coverage#

Each of the 10 Iron Maiden tests draws on specific disciplines. All 24 e7He statements were subjected to all 10 tests during TEMPER.

Test

Discipline

What it checks in e7He

I

Consistency (predicate calculus)

No axiom contradicts another; joint satisfiability

II

Independence (proof theory)

Each axiom adds deductive power not derivable from others

III

Necessity (proof theory)

Each axiom unlocks genuinely new reasoning

IV

Modal Soundness (S5)

Necessary vs. contingent claims properly distinguished

V

Mereological Coherence (CEM)

Part-whole relationships respected; no orphan entities

VI

Game-Theoretic Stability

Equilibria are stable under iteration; no exploitable defection

VII

Computability and Decidability

Claims can be checked by finite procedure; no hidden halting

VIII

Real-World Grounding

Claims connect to observable phenomena; not “not even wrong”

IX

Cross-Model Coherence

Alignment with PET/JUB; no unintentional contradiction

X

Known-Attack Resilience

Survives existing 33 con objections; no new undefended surface

See The Iron Maiden — 10 Formal Tests for the full test specifications.