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

See https://huggingface.co/blog/dimentox/esm-paper for Academic paper vs technical.

Author: Brandon Husbands (Dimentox Travanti) Independent Researcher & Pantheon Research (ACI Network / local AI) ORCID: 0009-0003-2496-4613 | Email: [email protected] | URL: http://xo.gy

Draft — September 8, 2025

---

Abstract

Current AI 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 AI system that is explainable, corrigible, efficient, and suitable for high-stakes use.

Keywords: Explainable AI, corrigibility, law-governed systems, event modeling, Symbolic AI, Explainable AI (XAI), Program Synthesis, Runtime Corrigibility, Anytime Algorithms, Symbolic Search

---

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, finance, and safety-critical systems. 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.

The Trust Gap

Modern LLMs exhibit three systemic liabilities for high-stakes use: opacity (reasoning smeared over billions of weights), stochasticity (non-repeatable token sampling and hallucinations), and retrain-heavy updates (massive, brittle fine-tunes). 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.

---

The ESM Architecture

Core Objects

Definition 1 (State S). A typed semantic graph (entities, relations, fields) with copy-on-write semantics for simulation. We denote the state as $SS$.

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

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

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

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 +ε, HALT_IF lawful).

Violation Residual and Acceptance

We define the global residual:

$$V(S)=\sum _i{w}_i\cdot {\varphi }_i(S),{\varphi }_i(S)\ge 0,w_i\in [0,1]\mathrm{.}V(S)\; =\; \backslash sum\_\{i\}\; w\_\{i\}\; \backslash cdot\; \backslash phi\_\{i\}(S),\; \backslash quad\; \backslash phi\_\{i\}(S)\; \backslash ge\; 0,\backslash ;\; w\_\{i\}\; \backslash in\; [0,1].$$

Hard laws take $w\mathrm{\_}i=1w\backslash \_\{i\}\; =\; 1$; uncertainty is handled by soft laws (\(w_{i} < 1\)). A new state $S^{\mathrm{\prime }}S\text{'}$ is accepted iff $V(S^{\mathrm{\prime }})\le V(S)V(S\text{'})\; \backslash le\; V(S)$.

Execution Kernel

# Kernel loop (anytime, energy-bounded)
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)      # macros to try
    while E > 0 and not L.accept(S):
        instr = agenda.next()
        if not pre_ok(instr, S, ctx):
            continue
        S_hat = T(S, instr)                # simulate
        v_hat = V(S_hat, L)                # delta-validate
        if v_hat <= v_prev:                # lawful descent
            Xi.append(instr); S, v_prev = S_hat, v_hat
        else:                              # violation -> repair
            repairs = repair_subroutine(S_hat, L.validate(S_hat))
            for r in repairs:
                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)
                    break  # redirect success
        E -= 1
    return S, Xi

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.

Learning Pipeline (Failure-First)

ESM learns by promoting repairs:

1. Habit: recurring, successful repair subsequences logged in $\mathrm{\Xi }\backslash Xi$.
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.

---

Core Mechanisms and Positioning

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 (e.g., {0→o, 1→ℓ, $→s}). L_IDENTITY proposes MERGE/RENAME. L_TEMP_ORDER proposes endpoint shifts and missing before/after edges.
• Bounded search: iterative deepening on edit radius; evaluate $J=\sum \mathrm{\_}i\varphi \mathrm{\_}i+\lambda \cdot \text{edit\_cost}+\mu \cdot \text{complexity}J=\backslash sum\backslash \_\{i\}\backslash phi\backslash \_\{i\}\; +\; \backslash lambda\; \backslash cdot\; \backslash text\{edit\backslash \_cost\}\; +\; \backslash mu\; \backslash cdot\; \backslash text\{complexity\}$; 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.

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).

---

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 $\mathrm{\mid }S\mathrm{\mid }|S|$.

---

Uncertainty and Modality

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

• Soft laws: in the residual equation, 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.

---

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.

---

Proposed Evaluation

• E1 Lawful Correction (toy): input “w0rdplau” → 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 $L\mathrm{\_}1L\backslash \_\{1\}$; add orthogonal $L\mathrm{\_}2L\backslash \_\{2\}$; disable $L\mathrm{\_}2L\backslash \_\{2\}$; re-test $L\mathrm{\_}1L\backslash \_\{1\}$. Expect unchanged $L\mathrm{\_}1L\backslash \_\{1\}$ performance, demonstrating non-destructive teaching.

Table 1: Sample Ledger Trace for E1

---

Strategic Roadmap

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.

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.

Vision

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

---

Theory (Sketch)

Discrete Optimality. Reachable state space as a directed graph; edge weights combine edit cost and residual change. 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.

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 $V(S)V(S)$.

Lyapunov Stability. Let $V(S)V(S)$ be a Lyapunov function; if each accepted commit ensures $V(S\mathrm{\_}t+1)\le V(S\mathrm{\_}t)-\delta \mathrm{\mid }S\mathrm{\_}t+1-S\mathrm{\_}t{\mathrm{\mid }}^{2}V(S\backslash \_\{t+1\})\; \backslash le\; V(S\backslash \_\{t\})\; -\; \backslash delta\; |S\backslash \_\{t+1\}-S\backslash \_\{t\}|^2$ for some $\delta >0\backslash delta>0$, then $VV$ monotonically decreases and the system stabilizes.

---

Conclusion

ESM reframes AI as jurisprudence: given laws and facts, produce a judgment (a lawful $SS$) with a cross-examinable transcript (\(\Xi\)). 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 (medicine, law, defense) where LLM opacity is untenable.

Future Work: (1) probabilistic extensions (calibrated soft laws), (2) large-graph engineering (sharding, distributed validators), (3) an Archivist router to coordinate specialized ESMs without sacrificing the single-model core.

---

References

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

---

Appendices

Kernel (Full) and Example Program

# Kernel (full) with small tabu and beam repair
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(Sfix, L)
                    accepted = True; break
            if not accepted:
                tabu.add((instr, hash(S)))
        E -= 1
    return S, Xi

# Example Program: DICT_CORRECT
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 []