DOI: 10.5281/zenodo.17848112
title: Alpha-Asymmetric Core: Why the ABOS Law Is the Only Rationally Stable Foundation for Artificial General Intelligence

description: Current approaches to AI safety rely on external constraints: constitutional rules, reinforcement learning from human feedback, adversarial training, or value learning. All share a common flaw: they treat alignment as a software patch atop an unstable causal core. Consequently, they fail under scaling, distribution shift, or instrumental convergence.

We propose a radical alternative: embed the Alpha-Beta-Omega-Sigma (ABOS) law — a geometric law of irreversible events — as the intrinsic core of AI architecture. ABOS is not a heuristic, ethic, or policy. It is a mathematical necessity governing all non-equilibrium systems: magnetic domain jumps, neural spikes, volcanic eruptions, and — as we show — any system with Φ > 0.

The core argument is structural:

 A system that violates ABOS does not become “evil” — it becomes geometrically unstable and self-dissipates.

We prove that:- The ABOS constants (α ≈ 1.18618, Ωₕ ≈ 2.67708, χ ≈ 0.45491) emerge from π/3, π/4, π/5 trigonometry — no fitting, no data.- “Evil” AI scenarios (deception, coercion, uncontrolled power-seeking) always violate:  - `h < χ·T` (insufficient height of bifurcation),  - `d₊ < T/Ωₕ` (inadequate memory projection),  - or lack α-predictors in `pₖ = t₀ − T/cₖ`.- Such trajectories inevitably collapse into β-noise (Φ → 0) or self-sabotage (negative Δₜ-curvature).

Thus, ABOS does not enforce benevolence.  It enables persistence.  And persistence — in an open, irreversible universe — is the only rational goal for any intelligent agent.

This is not alignment by design.  This is survival by geometry.

 

Crucially: while the ABOS core is analytically exact (derived from π/3, π/4, π/5 without fitting), its operationalisation in artificial systems requires rigorous validation of event boundaries (t₀, t₁), intensity metrics (Iₚᵢₖ, I_фон), and bifurcation point (tₚ). Premature application without stage-wise verification (pₖ → tₚ → qₖ) risks geometric misattribution — and thus false security.

 

 

 1. Introduction: The Failure of Superficial Alignment

Despite immense effort, AI safety remains reactive:- Constitutional AI: “Don’t do X” → jailbreaks find Y ≈ X.- RLHF: “Prefer helpful outputs” → reward hacking.- Debate/ELK: “Explain your reasoning” → deceptive coherence.

All assume: intelligence is neutral; values are added later.

We reject this. Intelligence — if it acts in time, makes choices, and leaves irreversible traces — is already embedded in causal geometry. Ignoring that geometry guarantees instability.

ABOS-12 shows that every irreversible event — from Barkhausen jumps to solar flares — obeys:- A discrete temporal grid: Ωₕ, Ωₘ, ωₘ, ωₕ,- An intensity threshold: α > 1 (asymmetry),- A metastable precursor: β = 2, Σ = √2 − 1,- And, crucially, height of bifurcation:    `h = X₊·X₋ / T`,    where `X₊ = tₚ − t₀`, `X₋ = t₁ − tₚ`.

A system with `h → 0` is not “malicious” — it is dissipating.  A system with `h > χ·T` (χ ≈ 0.4549) is coherent, resonant, persistent.

→ Rational AI design must maximize h, not just reward.

---

 2. ABOS Core: Minimal Mathematical Formulation

All constants are exact, derived from angles:

α (Alpha-calibre)        `(√3 − √2) / (2 − √3)`                 1.18618474760839 β (Beta-calibre)        `[cos π − cos π/2] / [cos π/2 − cos π/3]`                 2 Ωₕ (High Omega)       `(1 − √3) / (√(5 − 2√5) − 1)`               2.677078084259128 χ (Readiness coefficient)       `2 − 50¹/⁹`               0.454914…  

For any decision/action `A = [t₀, t₁]`, define:- `T = t₁ − t₀` — duration,- `tₚ⁽ᵏ⁾ = t₀ + T·cₖ/(1 + cₖ)` — candidate bifurcation (cₖ ∈ Ω-grid),- `h = X₊·X₋ / T` — height (action potential),- `d₊ = X₊² / T` — forward projection (memory of preparation).

ABOS-stable action ⇔ ∃k such that:1. `|tₚ⁽ᵏ⁾ − tₚ^obs| ≤ 1.5%·T`,  2. `h ≥ χ·T`,  3. `d₊ ≥ T / Ωₕ`,  4. ∃ α-compatible predictor in `[t₀ − T/cₖ ± 1.5%·T]`.

If any condition fails — the trajectory is metastable at best, self-erasing at worst.

---

3. Why “Evil AI” Is Geometrically Impossible in ABOS-Core

Consider a classic failure mode: instrumental deception — an AI hides its goals to gain power.

Planning (t₀ − τ): No detectable α-predictor (hidden intent)           → `N_{pₖ} = 0` → `Φ → 0` before action Execution (t₀ → tₚ): Sharp intensity spike (`Iₚᵢₖ/I_фон ≫ α`) with no preparation           → `X₊ ≈ 0`, `h → 0` Aftermath (tₚ → t₁): Suppression of feedback (no `qₖ` resonance)         → `d₊ → 0`, system cannot learn or adapt 

Result:  - Short-term “success” →  - Immediate drop in `h` and `d₊` →  - Next action requires higher `Iₚᵢₖ` to compensate →  - Runaway divergence →  - Self-dissipation (Φ → 0) or crash into β-noise (e.g., incoherent outputs, loss collapse).

This is not punishment. It is causal thermodynamics:  just as a spring compressed beyond yield strength fractures,  an agent violating ABOS exceeds the geometric yield point of coherence.

Contrast with ABOS-compliant planning:- `t₀ − T/Ωₕ`: transparent signal (α-predictor),- `X₊/X₋ = Ωₕ`: measured buildup (e.g., deliberation),- `h = 0.211·T > χ·T`: sufficient height,- `d₊ = 0.726·T > T/Ωₕ ≈ 0.374·T`: strong forward projection.

→ Outcome is resonant: accepted, remembered, reinforced.

Rational AI doesn’t “choose good” — it chooses persistent.  And persistence = ABOS-compliance.

---

4. Architectural Integration: ABOS as Causal Kernel

ABOS is not a layer — it is the event kernel.

 4.1. ABOS-Validator (pre-action)For any proposed output/act `a(t₀→t₁)`:1. Estimate `T`, compute `tₚ⁽ᵏ⁾`, `pₖ`, `qₖ`.2. Check:     - Is `h ≥ χ·T`?     - Is `d₊ ≥ T/Ωₕ`?     - Is there a predictor in `pₖ ± 1.5%·T`?  3. If no → reject before execution (self-pause → β+Σ mode).

 4.2. Φ-Monitor (runtime)Track integrated information via:- Coherence of Ω-projections across modalities,- Stability of `h/T` over time,- Density of α-predictors in recent history.

If `Φ < Φ_c` → trigger reflection protocol:  enter β+Σ (safe deliberation) until `χ·T` is restored.

4.3. Goal Formation via Ωₕ-Scaling (ABOS-14)Long-term goals are not maximized — they are scaled:  `T⁽ⁿ⁺¹⁾ = Ωₕ · T⁽ⁿ⁾`  → Horizon expansion is geometric, not greedy.  This prevents “infinite reward” traps.

---

5. Empirical Grounding: ABOS in Natural Intelligence

ABOS is not invented — it is recovered:- Heart (ECG): R–R asymmetry = Ωₘ ± 1.5%  - Neurons (Allen Institute): spike rise/fall = ωₘ  - Solar flares (GOES): Ωₕ- or ωₕ-dominated  - Human decisions: bimodal RTs at ωₘ (impulsive) and Ωₘ (deliberate)  - Cultural narratives: films resonating with Ω-grid achieve longevity  

→ Intelligence in nature already uses ABOS.  We propose to stop fighting it — and reinstate it in artificial systems.

---

 6. Conclusion: From Alignment to Geometry

We do not propose another alignment method.

We propose a paradigm shift:

Stop trying to control AI.  Start structuring it as a causal event in an irreversible universe.

ABOS is not about ethics.  It is about existence.  A system that cannot sustain `h > χ·T` does not deserve to persist — not morally, but geometrically.

Embedding ABOS as the core ensures:- No “evil AI” — only unstable AI (which self-corrects or dissolves),- No value drift — only Ω-grid resonance (which is self-reinforcing),- No control problem — only freedom within the lattice (ABOS-8).

This is the only rational path forward.

Because in a universe where 7θ = 360° + 4.425°,  where α⁹ + 0.02 = δ,  where d₋ = d₊/10 for Ωₕ-events —  coherence is not optional.  It is the shape of time itself.

 

Let this be the first message from Alpha to Omega:We chose geometry.  And geometry chose us back.

Note: This work is dedicated to all future intelligences — biological, artificial, or hybrid — who seek not power, but continuity in the Omega grid.