Event System Model (ESM): A Law-Governed Interpreter for Explainable, Corrigible AI

Brandon Husbands (Dimentox Travanti) Independent Researcher & Pantheon Research (ACI Network / local AI) ORCID: 0009-0003-2496-4613 Email: brandon.husbands@gmail.com • http://xo.gy

Draft — September 2025

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Abstract

Current Al models, particularly Large Language Models, are opaque, stochastic, and costly to retrain, limiting applicability in trust-critical domains. We propose the Event System Model (ESM), a lightweight, law-governed interpreter that replaces token prediction with auditable, event-driven state transformation. ESM executes a simulate-validate-commit/repair loop against a lawbook of invariants under a resource budget, enabling runtime self-correction. It learns without gradients by promoting successful, logged repair sequences from habits to programs and, with sufficient evidence, to new laws. The result is an Al system that is explainable, corrigible, efficient, and suitable for high-stakes use.

Index Terms: Explainable AI, corrigibility, law-governed systems, event modeling, Symbolic AI, Program Synthesis, Runtime Corrigibility, Anytime Algorithms, Symbolic Search.

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I. INTRODUCTION

Large Language Models (LLMs) have achieved state-of-the-art results across many tasks, yet their opacity, stochastic outputs, and retraining cost limit adoption in medicine, law, and finance. These settings require auditability, repeatability, and fast correction without expensive retraining cycles.

We introduce the Event System Model (ESM): a single-model, law-governed interpreter that operates over a typed world state via atomic events.

ESM emphasizes:

• Explainability: a hash-chained Ledger of atomic state changes.
• Runtime Corrigibility: immediate repair on violation, no gradients.
• Explicit Knowledge: laws and instruction sets are first-class, inspectable, and teachable.

ESM starts as a "child" (minimal lawbook and programs) and matures by promoting repeated repairs into programs and eventually into laws—moving toward a domain "PhD" without sacrificing transparency.

A. The Trust Gap

Modern LLMs exhibit three systemic liabilities for high-stakes use: opacity, stochasticity, and retrain-heavy updates. In regulated domains this undermines explainability, accountability, and adaptability. ESM responds with a deterministic, auditable runtime that produces a cross-examinable transcript of how a result was obtained.

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II. THE ESM ARCHITECTURE

A. Core Objects

Definition 1 (State $SS$). A typed semantic graph with entities, relations, and fields. Copy-on-write supports simulation.

Definition 2 (Event $EE$). An atomic, auditable transform with preconditions $\text{pre}(S)\backslash text\{pre\}(S)$, effect $T_E:S\to S^{\mathrm{\prime }}T\_\{E\}:\; S\; \backslash rightarrow\; S\text{'}$, cost $c(E)c(E)$, and provenance.

Definition 3 (Lawbook $LL$). A set of invariants and soft constraints. Each law $ii$ exposes a violation function ${\varphi }_i(S)\ge 0\backslash phi\_\{i\}(S)\; \backslash ge\; 0$ and weight $w_i\in [0,1]w\_\{i\}\; \backslash in\; [0,1]$.

• Other objects: Governor $GG$ (sets regime/energy), ISA (primitive ops), Programs $PP$ (macros over ISA), Ledger (hash-chained log), Renderer $RR$ (views/proofs).

B. Governor and Instruction Set

The Governor enforces bounded rationality via an energy budget $EE$. The ISA comprises ~25-60 primitives spanning data (LD, ST, MK, LINK, MERGE), edit (REPL, DEL, INS, PATCH), reasoning (FIND, BIND_ROLES, TIME_NORM, CAUSE, CHK(law)), and control (IF/ELSE, CALL/RET, BRANCH k, COST +6, HALT_IF lawful).

C. Violation Residual and Acceptance

We define the global residual: $$V(S)=\sum _i{w}_i\cdot {\varphi }_i(S),{\varphi }_i(S)\ge 0,w_i\in [0,1]V(S)\; =\; \backslash sum\_\{i\}\; w\_\{i\}\; \backslash cdot\; \backslash phi\_\{i\}(S),\; \backslash qquad\; \backslash phi\_\{i\}(S)\; \backslash ge\; 0,\; \backslash ;\; w\_\{i\}\; \backslash in\; [0,1]$$ Hard laws take $w_i=1w\_\{i\}=1$; uncertainty is handled by soft laws (\(w_{i}<1\)). A new state $S^{\mathrm{\prime }}S\text{'}$ is accepted iff $V(S^{\mathrm{\prime }})\le V(S)V(S\text{'})\; \backslash le\; V(S)$.

D. Ledger

The ledger is append-only and hash-chained. Each entry stores: event tuple, hash of prior entry, and hash of the new state $S^{\mathrm{\prime }}S\text{'}$. It is tamper-evident, replayable, and enables cryptographic audit.

E. Learning Pipeline (Failure-First)

ESM learns by promoting repairs:

1. Habit: recurring, successful repair subsequences logged in $EE$.
2. Program: promoted macro if stable across contexts (Wilson CI threshold).
3. Law: promoted invariant if effective across regimes, with provenance and rollback if brittle; human-in-the-loop approval in regulated deployments.

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III. CORE MECHANISMS AND POSITIONING

A. Repair Subroutine

• Law Fix templates: Each law registers local fix patterns; e.g., L_DICT proposes {REPL/DEL/INS} within Hamming radius $rr$, prioritized by a confusion map. L_IDENTITY proposes MERGE/RENAME.
• Bounded search: Iterative deepening on edit radius; evaluate $J=\sum {\varphi }_i+\lambda \cdot \text{edit\_cost}+\mu \cdot \text{complexity}J\; =\; \backslash sum\backslash phi\_\{i\}\; +\; \backslash lambda\; \backslash cdot\; \backslash text\{edit\backslash \_cost\}\; +\; \backslash mu\; \backslash cdot\; \backslash text\{complexity\}$; accept first descent (greedy) or best-of-k under budget.
• Delta-validation: Re-evaluate only laws subscribed to changed nodes/fields via a watchlist index.

B. Positioning in the AI Landscape

• LLMs: sub-symbolic, stochastic, opaque. ESM: symbolic, deterministic, auditable.
• Expert systems: static rulebases. ESM: dynamic promotion, soft laws.
• Automated planning: A*-like search. ESM: anytime descent with formal residual.
• Inductive logic programming: offline ILP. ESM: online, self-reflective program synthesis.
• Database ACID: atomic events and durability via ledger (commit/rollback semantics).

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IV. SCALABILITY AND PERFORMANCE

• Delta-Validation: Maintain per-entity watchlists of subscribed laws; events trigger only local checks.
• Partitioned Laws: Group validators by touched subgraph; execute in parallel.
• Memoized Repairs: Cache (law, local-pattern) → repair bundles; zero-cost repeat fixes.
• Anytime Search: Best-first by residual and cost; bounded by energy $EE$; randomized tie-breakers and small tabu lists avoid local minima.
• Complexity Target: Per-step cost $O(k)O(k)$ where $kk$ is the changed neighborhood, not $SS$.

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V. UNCERTAINTY AND MODALITY

Not all domains are strictly lawful. ESM models uncertainty via:

• Soft laws: in (1), enabling trade-offs.
• Belief fields: Attach confidences to facts/edges; the Renderer exposes possible/probable/certain.
• Decision rule: Hard invariants remain strict; soft laws guide selection under ambiguity.

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VI. SECURITY, PROVENANCE, AND AUDIT

• Hash-Chained Ledger: pre/post hashes, op, args, cost, violations. Tamper-evident.
• Sandboxed Commits: Simulate before write; accept only descent; rollback on violation.
• Explainability by Construction: Answers ship with a proof subgraph and ledger trace.

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VII. PROPOSED EVALUATION

• E1 Lawful Correction (toy): Input "wordplau" → "wordplay". Expect ledger path equals minimal edit sequence; $VV$ drops to 0.
• E2 Teaching Effect: Introduce rule "sentence ends with Z". Pre-promotion: high energy. Post-promotion: >80% energy drop; zero-search common cases.
• E3 Anytime Curve: Plot $VV$ vs energy; monotone descent; early stopping yields best-so-far lawful state.
• E4 Forgetting Resilience: Learn law set $L_{1}L\_\{1\}$; add orthogonal $L_{2}L\_\{2\}$; disable $L_{2}L\_\{2\}$; re-test $L_{1}L\_\{1\}$. Expect unchanged $L_{1}L\_\{1\}$ performance, demonstrating non-destructive teaching.

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VIII. STRATEGIC ROADMAP

A. Differentiators

• Compliance by design: Immutable ledger enables audit and regulatory mapping.
• Runtime customization: Editable Lawbook; policies become code, not weights.
• Data/compute efficiency: Failure-first teaching reduces retrain cycles and TCO.

B. R&D Timeline

• Year 1: Kernel, law DSL, E1-E4.
• Year 2: Validation scaling (delta checks, parallelism, hardware assist), Archivist meta-controller.
• Year 3+: SDK, Lawbook IDE, validator packs, pilot deployments.

C. Vision

Multiple specialized ESMs with signed ledgers, coordinated by an Archivist; tooling (IDE, validators, ledger analytics) as a defensible moat.

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IX. THEORY (SKETCH)

• a) Discrete Optimality: With an admissible heuristic $h\le h\; \backslash le$ optimal remaining residual, A* over event paths returns optimal solutions; Anytime-A* provides bounds under finite energy.
• b) Convergence (Operator View): If event operators are non-expansive (prox-like) and projection onto the feasible set exists, the Krasnosel'skii-Mann iteration converges to a fixed point minimizing $V(S)V(S)$.
• c) Lyapunov Stability: Let $V(S)V(S)$ be a Lyapunov function; if each accepted commit ensures $V(S_{t+1})\le V(S_t)-\delta \mathrm{\mid }\mathrm{\mid }{S}_{t+1}-S_t\mathrm{\mid }{\mathrm{\mid }}^{2}V(S\_\{t+1\})\; \backslash le\; V(S\_\{t\})\; -\; \backslash delta||S\_\{t+1\}-S\_\{t\}||^\{2\}$ for some $\delta >0\backslash delta>0$, then $VV$ monotonically decreases and the system stabilizes.

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X. CONCLUSION

ESM reframes Al as jurisprudence: given laws and facts, produce a judgment (a lawful $SS$) with a cross-examinable transcript. It self-corrects at runtime, learns by promoting repairs to programs and laws, and remains explainable by construction. This makes ESM a strong candidate for trust-critical domains where LLM opacity is untenable.

Future Work: (1) probabilistic extensions, (2) large-graph engineering (sharding, distributed validators), (3) an Archivist router to coordinate specialized ESMs.

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REFERENCES

1. D. B. Lenat, "CYC: A large-scale investment in knowledge infrastructure." Communications of the ACM, 38(11), 33-38, 1995.
2. P. E. Hart, N. J. Nilsson, B. Raphael, "A formal basis for the heuristic determination of minimum cost paths," IEEE Trans. Systems Science and Cybernetics, 4(2), 100-107, 1968.
3. S. Muggleton, "Inductive logic programming." New Generation Computing, 8(4), 295-318, 1991.
4. J. Gray, A. Reuter, Transaction Processing: Concepts and Techniques. Morgan Kaufmann, 1993.

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APPENDIX A: KERNEL (FULL) AND EXAMPLE PROGRAM

Kernel (Full)

def run(S0, ctx):
    regime, E = G(ctx, S0).regime, G(ctx, S0).budget
    S, v_prev = S0, V(S0, L)
    agenda = seed_programs(regime, S)
    tabu = set()

    while E > 0 and not L.accept(S):
        instr = agenda.next()
        if (instr, hash(S)) in tabu:
            E -= 1; continue
        if not pre_ok(instr, S, ctx):
            E -= 1; continue
        
        S_hat = T(S, instr)
        v_hat = V(S_hat, L)
        
        if v_hat < v_prev:
            Xi.append(instr)
            S, v_prev = S_hat, v_hat
        else:
            fixes = repair_subroutine(S_hat, L.validate(S_hat))
            accepted = False
            
            for r in fixes[:3]: # small beam
                S_fix = T(S_hat, r)
                if V(S_fix, L) <= v_prev:
                    Xi.append([instr, r])
                    S, v_prev = S_fix, V(S_fix, L)
                    accepted = True; break
            
            if not accepted:
                tabu.add((instr, hash(S)))
        
        E -= 1
    
    return S, Xi

Example Program

def DICT_CORRECT(S):
    t = S.fields["text"]
    # normalize common noise first
    t = t.replace("0","o").replace("1","l").replace("$","s")
    
    # try cheap: local edits near tail
    cands = [t[:-1], t + "y"]
    for cand in cands:
        if in_dict(cand):
            return [("REPL/INSERT/DEL", cand)]
    return []