e7He — Overview for Producers#

This document is for researchers, developers, and students who want to build on the e7He model — extend it, test it, integrate it, or challenge it. It covers the architecture, interfaces, dependencies, open edges, extension procedures, and epistemic status. For the narrative introduction, see e7He — Introduction. For formal definitions, see e7He — Axioms and e7He — Theorems.

1. Model Architecture#

e7He proposes a coinductive model of the hero journey as a perpetual cycle through seven stages, each defined by a binary BABL temptation pattern. The model comprises 24 formal statements: 14 axioms, 7 theorems, and 3 structural properties.

Prerequisite Layer (m0)#

The m0 layer defines seven axioms that frame the journey without being part of it:

  1. Uniqueness (m0.ax1): Every agent h in H has a unique profile. No two agents share the same behavioral fingerprint.

  2. FATE Acceptance (m0.ax2): An agent’s starting state at cycle k is their complete state at that time — FATE(h, t_0^k) = state(h, t_0^k). The journey requires accepting this state without denial.

  3. GOAL Calling (m0.ax3): Every agent has a GOAL in D_inno (the innovation domain). The GOAL has positive entropy (partially unknown) and is progressively revealed. Pursuing it contributes positively to system-wide insight growth and is locally optimal for the agent’s comparative advantage.

  4. Cycle Definition (m0.ax4): The hero journey is the 7-stage transition from FATE to DESTINY. DESTINY is a provisional fixpoint, not a permanent state.

  5. Perpetual Reset (m0.ax5): Each cycle’s DESTINY becomes the next cycle’s FATE (plus rest). The agent must re-enter with NOT-OK self-assessment.

  6. Stopping Outcome — Irrelevance (m0.ax6): An agent who stops cycling with low influence becomes irrelevant: insight stagnates, scope freezes.

  7. Stopping Outcome — Supervillain (m0.ax7): An agent who stops with high influence becomes dangerous: large stagnant scope generates misapplied expertise at its boundaries.

Stage Axioms (m1–m7)#

Each stage axiom encodes four elements:

  • BABL pattern: A 3-bit binary value (001 through 111) with bit positions MOL-ASH-BA. Stage k has temptation(k) = k in binary.

  • Journey segment: The coalgebraic observation produced during the stage transition.

  • Milestone: The boundary condition that must hold for the stage to count as traversed.

  • Bifurcation: At each stage the agent’s alignment score bif(h, s, t) moves toward ZION (positive) or BABL (negative).

The stages are: m1 Adventure Calls: Dare (001), m2 Trial Tribulation Training (010), m3 Gain Advantage Temptation (011), m4 Meet Your Maker: Infinity Alone (100), m5 Lucky Ultimate Reward Comedy (101), m6 Rescue Trip To Resurrection (110), m7 Free Reborn Evolving Better (111). The binary counting order is not arbitrary — it is the unique standard ordering that produces the Hamming-3 midpoint at m4 (sp2), progressive BABL escalation, and minimal description length (sp1).

Coalgebraic Formalization#

The hero journey is formalized as a coalgebra. The step function produces a journey segment and the next milestone from the current milestone:

step(milestone(k)) = (segment(k+1), milestone(k+1))

Each call to step yields a non-trivial observation (segment is not bottom) and a valid successor state. Theorem th4 (Coinductive Productivity) guarantees that the process never terminates: every milestone produces a next milestone. Combined with the perpetual reset axiom (m0.ax5), this means the hero journey is an infinite coinductive stream of journey segments.

See e7He — Axioms for full formal definitions and e7He — Theorems for the derived results.

2. Key Interfaces#

Input#

  • Agent: h in H (any individual agent from the population set).

  • Starting state: FATE(h, t_0^k) — the agent’s complete observable state at cycle k start.

  • Calling: GOAL(h) in D_inno — the agent’s partially-unknown objective in the innovation domain.

Output#

  • Ending state: DESTINY(h, t_f^k) — the provisional fixpoint of cycle k.

  • Insight growth: Net change in effective insight Ie across the cycle, governed by the Ie evolution equation.

  • BABL resistance record: For each stage, whether the agent resisted or succumbed to the BABL pattern at that stage.

Ie Evolution Equation#

The rate of change of effective insight is:

d(insight)/dt = Ipursuit(t) + Iserendipity(t) - Idecay(t)

where:

  • Ipursuit(t): Directed growth from actively pursuing GOAL.

  • Iserendipity(t): Growth from openness and unexpected discovery on the ridge.

  • Idecay(t): Loss from unconsolidated insight and entropic decay.

Theorem e7He.th3 — Scope Expansion (anti-livelock) (Scope Expansion) proposes that each completed cycle produces net positive Ie growth, conditional on the agent having resisted BABL at every stage, rested adequately, and pursued their GOAL. Formally:

integral from t_0^k to t_f^k of
   (Ipursuit(t) + Iserendipity(t) - Idecay(t)) dt > 0

This is a conditional result, not an unconditional guarantee. Cycles that fail the conditions may produce negative Ie (burnout, deterioration).

Free Parameters#

  • influence-threshold (theta): Boundary separating low from high influence in the population. Context-dependent; varies with population size and structure.

  • Behavioral criteria for proto-formal predicates: Approximately 10 predicates in the model (e.g., false-self-died, received-without- entitlement, institutional-capture) are proto-formal — they have one-line behavioral criteria but lack full formal semantics. Their operationalization requires empirical input from psychology, sociology, or organizational science.

3. Dependencies#

Inherited from PET#

  • God-World containment (ax1, ax2): The ontological framework that places all agents within a God-World structure.

  • S5 Modal Logic: Necessity and possibility operators with equivalence-class accessibility. Used in Iron Maiden Test IV (Modal Soundness).

Inherited from JUB#

  • Agent set H: The population of all agents (Humanity).

  • Domain structure: D_f (domain-fixed, divine governance), D_free (domain-free, human agency), D_inno (domain-innovation, human responsibility). GOAL lives in D_inno.

Added by e7He#

  • Coalgebra and Coinduction: The step function, productivity theorem (th4), and bisimulation equivalence.

  • Dynamical Systems Theory: Ie evolution equation (th3), ridge stability and Lyapunov-like arguments (th2), attractor analysis (th5).

  • Game Theory and Mechanism Design: Commitment Trichotomy (th6), Prisoner’s Dilemma to Assurance Game transformation, Schelling commitment, Spence signaling.

  • Information Theory: Entropy condition in m0.ax3, lognormal influence distribution (sp3).

  • Probability and Stochastic Processes: CTMC argument in th5 (BABL self-destructs with probability 1 as t approaches infinity).

Cross-Model Relations#

e7He is one of four models sharing the same 7-stage binary encoding:

  • e7Tr (Tribe Roles): Defines roles active at each stage (AMO, HIT, CAN, PHE, JEB, HIV, GIR).

  • e7Ch (Church Lifecycle): Defines organizational lifecycle stages (EPH, SMY, PER, THY, SAR, PHI, LAO).

  • e7Day (System-Level): Defines the system-wide construction and governance framework.

All four models share the BABL binary structure. Changes to the stage definitions in e7He propagate to the corresponding stages in e7Tr and e7Ch. See e7He — Formal Disciplines for the full discipline list.

4. Open Edges#

These are the places where a producer can make a concrete contribution. Each item is tracked in the e7He — Any Aims (AA) (Any Aims) list.

AA-e7He-Lyapunov-a1 (medium priority): Theorem th2 (Supervillain Theorem) proposes that stopping on the ridge with high influence leads to BABL drift. The ridge dynamics are described informally via a Lyapunov-like argument: stability(h, t) decreases when insight stagnates and OSCR exposure increases. A sketch exists in the FORGE session logs. What is needed: a full Lyapunov formalization — defining V(h, t), proving dV/dt < 0 under the stated conditions, and connecting this to standard dynamical systems results.

th5 CTMC precision: Theorem th5 proposes that BABL self-destructs with probability 1 given sufficient time, modeled as a continuous-time Markov chain with an absorbing state. The current formulation uses “quasi-absorbing” language loosely. What is needed: a precise CTMC specification with state space, transition rates, and proof that the absorbing state is reached almost surely.

sp3 empirical evidence: Structural property sp3 proposes a lognormal distribution for influence magnitude across the agent population. This is the null hypothesis for multiplicative systems but has no direct empirical support in the current model. What is needed: empirical studies or literature review establishing whether influence distributions in relevant populations follow lognormal patterns.

Proto-formal predicate operationalization: Approximately 10 predicates in the model need empirical behavioral criteria. Examples: false-self-died (predicate 19), received-without-entitlement (predicate 21), institutional-capture (predicate 24). These are defined with one-line criteria in e7He — Predicate Specifications but require input from psychology, sociology, or organizational science to become fully testable.

AA-e7He-LateTheorems-a1 (high priority): Theorems th6 (Commitment Trichotomy) and th7 (Succession Robustness) were added late in the FORGE process and have not yet received a dedicated adversarial TEMPER round as a pair. What is needed: a focused adversarial review applying all 10 Iron Maiden tests to th6 and th7 together.

5. How to Extend#

New Theorems or Axioms#

All new formal statements go through FORGE, the three-phase adversarial development process:

  • STRIKE: Propose the new statement with full formal notation, a derivation sketch, and an initial StayC assessment.

  • TEMPER: Subject it to Iron Maiden testing (10 adversarial tests across 12 formal disciplines). The statement must survive or be repaired.

  • QUENCH: Finalize the statement with a StayC rating and VVN (Versioned Variant Number).

New statements should reference existing symbols from e7He — Symbols and BEST Names. If new symbols are needed, add them to that table with a BEST Name (the meaningful prose name preferred over the short mathematical symbol).

New Predicates#

Add new predicates to e7He — Predicate Specifications with:

  1. A predicate number (sequential).

  2. A one-line behavioral criterion that makes the predicate empirically assessable.

  3. The source axiom or theorem that introduces it.

Proto-formal predicates (those without full formal semantics) should be explicitly marked as such.

Integration via PROMY#

The PROMY pipeline manages the flow from FORGE session logs to published model pages:

  • SEED: Extract formal statements from FORGE session transcripts into structured RST files (axioms, theorems, symbols, predicates).

  • FEED: Audit extracted content for completeness — check that every symbol used in math blocks appears in the symbol table, every predicate used in formal statements appears in the predicate table.

  • GROW: Apply repairs, fixes, and strengthenings discovered during FORGE TEMPER rounds that were not applied in real time.

  • REAP: Produce overview pages and summary documents from the finalized model state.

When integrating changes, use MODEL_CHANGE markers (AA-FORGE-ModelChangeMarker-a1, not yet implemented) to flag points in session logs where the formal model changed. This is planned infrastructure; until it is implemented, changes are tracked manually via the e7He — Any Aims (AA) list.

6. Epistemic Status#

Maturity: All 24 statements are at OOv1 per the author’s assessment. OOv1 means “first formal version, open to challenge.” No statement has been independently replicated or assessed by external reviewers.

Adversarial testing completed: 10 Iron Maiden tests were applied across all 24 statements during the FORGE TEMPER phase. The Iron Maiden protocol tests consistency, independence, necessity, modal soundness, mereological coherence, game-theoretic stability, computability, real-world grounding, cross-model coherence, and known-attack resilience. See e7He — Formal Disciplines for which disciplines map to which tests.

Auditor assessment: The formal auditor (Claude Opus 4.6) proposed PP (Provisionally Plausible) for 21 of the 24 statements. The author holds all 24 at OOv1, exercising the more conservative rating. The three statements where the author’s assessment is more cautious than the auditor’s are tracked but do not affect the overall OOv1 status.

What has NOT been done:

  • No independent replication by a separate research group.

  • No peer review in a traditional academic sense.

  • No empirical testing of the proto-formal predicates against behavioral data.

  • Theorems th6 and th7 have not received a dedicated adversarial round as a pair (tracked as AA-e7He-LateTheorems-a1).

  • The Lyapunov formalization for th2 remains a sketch (AA-e7He-Lyapunov-a1).

Session history: All development and testing sessions are logged as append-only audit trails. See e7He — Session Logs for pointers to the full transcripts.