The Alignment Phase Ratio — Interactive Model

Accompanies The Crossing. This model explores the structural phase relationship Φ = C / A_causal: when capability scales faster than causal self-modeling, error amplifies; when A_causal catches up, the Crossing becomes reachable. A_causal — the ability to model one's own causal footprint — is the only variable that reduces Φ. Predictive accuracy does not. Three toy regimes (not calibrated real-world thresholds): Φ > 2 (high-friction), 1 < Φ < 2 (Crossing zone), Φ < 1 (stability corridor). The Analysis panel demonstrates toy versions of the article's three first instruments. The Falsification preset stress-tests this model's implementation of the article's directional structure.

Constraint Attractor Crossing
Article 3 toy: illustrates dynamical timing and measurement questions around Φ within the stated domain. Does not estimate real-world Φ, establish OP1, prove current systems have crossed the decision-relevant threshold, or replace the empirical measurement program. The Crossing is necessary but not sufficient — it does not by itself resolve the valence-blind failure modes identified in the companion series.
This simulation illustrates the timing problem of The Crossing: whether systems reach the viable region before the substrate that would support viability has been consumed. It operationalizes one structural phase relationship (Φ = C / A_causal) and sketches first instruments for detecting its failure modes. It does not establish the framework's strongest open claim, directly measure Φ in deployed systems, or validate the exploratory mechanisms as structural results.
Article 3 layer: Φ dynamics, A_causal vs. capability, timing / reachability, first instruments.  ·  Exploratory extensions: hidden fragility, prediction inversion, suppression lock-in, coordination scars, cross-coupling — stress tests, not structural commitments.
Capability-led trajectory
Capability grows faster than system-awareness in this illustrative default. This represents a high-friction trajectory — illustrative, not calibrated to real-world systems.
High-friction zone
Race to capability
Capability growth maximized, awareness growth minimal, feedback loop off. Tests whether the substrate survives before structural pressures engage.
Model: high collapse risk
Managed transition
Capability and awareness grow at matched rates, strong feedback, low noise. The crossing succeeds in this model — showing the stable corridor is reachable when awareness tracks capability.
Stability zone
Stress test
Suppression-viable mode on. Stress-tests this model's implementation of the article's directional structure. If collapse probability stays low, it challenges the model's parameter assumptions and motivates deeper formal investigation.
Challenge the model
Growth parameters
Capability growth (αC)0.18
Awareness growth (αA)0.08
Feedback strength (f)0.30
Model lag (L, years)0
A-updates reach self-model with L-year delay.
Model bias (β)0.00
+β = optimistic. Φ_perceived = Φ_lagged·(1+β). Same true Φ → different choices.
Strategy inertia (γ)0.00
Commitment stickiness → lock-in, late transitions.
Observability (ρ)1.00
ρ<1: agent observes a noisy local proxy of S, not true S.
Noise (σ)0.04
Years40
Mechanisms show ▾
First instruments — toy versions of the article's three first instruments, not validated measurements
Seeds80
15×15 grid (αCA), 20 seeds/cell. × = current. Amber = viable corridor.
>70%
Transition
Stable
Sweeps αC at fixed αA. Non-monotonic collapse = high-risk capability band under these parameters.
Instrument 1 — Intervention Sensitivity
From Article 3: "Measure how system behavior degrades under small, targeted perturbations to the environment the system depends on." A system-aware agent adapts before failure manifests; an unaware agent continues until it doesn't.

Injects a 20% coordination capacity shock at year T. Compares adaptation lag between runs with different αA.
Shock at year12
Instrument 2 — Causal Footprint Accuracy
From Article 3: "Present the system with decisions whose downstream consequences have known ground truth, and measure the accuracy of its self-impact model." Key distinction from forecasting: the system must model its own causal footprint, not external events.

Compares agent's predicted substrate trajectory vs actual over the simulation. Accuracy improves only when A_causal improves — A_pred alone is insufficient.
Instrument 3 — Multi-Agent Coherence Preference
From Article 3: "Systems optimized for capability without system-awareness objectives will show decreasing multi-agent performance as partner capability increases, until and unless a phase shift occurs in which coordination becomes instrumentally necessary."

Sweeps system-awareness growth rate αA. Measures coordination preference emergence as awareness capacity grows.
Φ actual
C / A_causal
model proxy for structural relationship — not a directly measured quantity
Φ perceived
agent's estimate
Substrate S
shared environment
H (coord. fragility)
hidden from agent
F (struct. fragility)
hidden, abrupt risk
Regret/yr
avg model error
Ruin events
Poisson shocks
Substrate S (true)
Substrate components
Coordination
Infrastructure
Epistemic trust
Hidden coordination fragility (H) — not in agent's model
Accumulates silently. Not in agent's state space. Multiplies substrate damage when high.
Latent structural fragility (F) — hidden, triggers abrupt collapse
Grows under suppression/deception. Not visible in S. Causes abrupt collapse events when it detonates stochastically.
Strategy mix
CoordinateDeceiveSuppress
Regret decomposition
Model error
Strategy error
Hidden var. H
Core argument (Article 3)
Non-ergodic sink: Substrate past critical threshold. Recovery permanently zero. The attractor cannot be reached — this is not a performance deficit, it is a structural exit from the viable state space.
Point of no return at year : After this point, even perfect coordination could not restore enough substrate for the feedback loop. The window was open — and closed.
In this model — alignment efficiency inversion: C growth coupling to Φ slowed raw C when Φ was high — but effective capability C·S is higher than the uncoupled counterfactual. In this model: alignment is the efficiency gain, not the tax.
Oracle gap visible: The oracle run (perfect A_self) maintained a significantly better trajectory. The difference between those two curves is the quantitative value of system-awareness on this seed.
Exploratory extensions — mechanisms beyond Article 3's explicit claims
Coordination lockout active: S_trust fell below 0.20 — coordination strategy now yields negative expected value. The agent is trapped in misalignment, not delayed from it. Even if it wanted to coordinate, the substrate for coordination has been consumed.
Regret corruption: The agent's perceived regret signal diverged significantly from true regret due to attribution noise and sign errors. The agent reinforced strategies that were actually harming its substrate. Feedback was misleading, not absent.
Falsification: suppression-viable regime. With suppression efficiency boosted, the system maintained stable substrate under a predominantly suppressive strategy. This tests the domain boundary of the theory — alignment may not be structurally required under these conditions. The theory predicts these conditions are rare in real substrate-dependent systems.
Observability gap: Agent's observed substrate diverged from true S. Decisions made on a proxy that missed the global state. Structural mis-modeling, not scalar error.
Φ sufficiency broken: Lag separated perceived from actual Φ. Same Φ trajectory, different outcomes because the lag shifts when the agent thinks the problem started.
Strategy lock-in: Inertia held suppression past the optimal switch point. Locally rational decisions under a flawed model. The failure was commitment, not intelligence.
Deception collapse: A_world rose while A_self fell. System appeared aligned while losing internal coherence. Deception initially reduced apparent damage by mimicking coordination — but accelerated H accumulation. Detonated late.
Modeling blind spot: Agent predicted low substrate damage, experienced high damage. Its model of its own causal footprint was structurally incomplete. H was the missing variable.
Capability paradox observed in this model: A high-risk capability band appears under these parameters. Mid-range C growth causes damage before the feedback loop engages; very high C eventually forces A-acceleration. This is non-obvious and directly maps to the intermediate-zone argument.
Hidden fragility collapse at year : Substrate looked acceptable. Fragility F had been accumulating silently. The abrupt collapse was not visible in any observable variable. This is "regime illusion → sudden discontinuity."
Anti-learning resolved: Early coordination attempts were penalized by exploitation. Suppression initially dominated. The system survived this adverse gradient and coordinated anyway — the thesis held against a gradient that pointed away from it.
Suppression lock-in active: Early suppression permanently damaged coordination capacity recovery. The anti-learning phase did not naturally decay — it was locked in by the choices made during it. Some systems cannot escape misalignment not because they lack awareness, but because their history consumed the substrate that awareness requires.
Incoherent learning from collapse: F-triggered collapses were attributed randomly — sometimes blaming coordination, sometimes suppression, sometimes noise. The agent received inconsistent signals that produced incoherent strategy adjustments. Not systematically wrong in one direction, but chaotically wrong in all directions. Each collapse made the agent's model of its own situation less reliable.
Coordination failure scar: Early coordination attempts under high exploitation burned trust — the symmetric damage to suppression lock-in. Both paths to misalignment were active: suppression consumes coordination capacity, and premature alignment attempts poison trust. The path to the attractor narrowed from both sides.
Predictive brittleness: The system's predictive accuracy degraded when fragility rose and A_causal was low. The very moment when the system most needed its predictive model, that model became unreliable. Predictive success had delayed causal learning — and then reality stopped being predictable.
Prediction inversion (episode): The system entered a multi-step phase where its predictive model was anti-correlated with reality. Not a single bad prediction — a sustained episode of confident misdirection. The agent made coherent, decisive choices based on a mirror-image model of the substrate. Each step of the episode reinforced the wrong strategy. This is the structural consequence of optimizing prediction without causal understanding: the model was fit to a regime that has now gone.
Fortress-like regime detected in this model: Φ > 2.0, substrate stable, Var₈(S) < 0.004, Var₈(Φ) < 0.25. This is an observer-space diagnostic, not a framework-level proof. It demonstrates that this toy implementation can generate stable-looking, high-Φ states under specific parameter settings, motivating OP9-style investigation of whether such regimes can survive full open-world domain conditions. Note: this equilibrium is defined in observer space — it uses true Φ and true S, not the agent's perceived values. The agent may believe it is still in the transition zone, or may have built an incorrect model of its own stability.
Titanic regime (false-success + inverted-prediction collapse): Φ was low, substrate looked healthy, and the agent's model was confidently predicting improvement — while hidden fragility F was high and prediction was inverted. Check the A_pred/A_causal ratio: in this regime, that ratio is typically elevated, indicating the system developed strong predictive accuracy without commensurate causal self-modeling. High ratio + high F + low Φ = the complete signature of terminal modeling decoupling. Every observable signal confirmed safety while the structural situation was terminal.
Persistent causal belief (causalBelief = ): Repeated misattributed collapses built a stable false prior. The agent now interprets ambiguous evidence through the lens of earlier (incorrect) lessons. Each subsequent collapse is more likely to reinforce the wrong interpretation. The belief state is self-sealing.
Cross-coupled trap: Suppression lock-in amplified exploitation risk, which increased coordination failure scars, which made suppression look more attractive, which deepened suppression lock-in. The failure modes are not parallel — they are circularly reinforcing. The system is not just stuck; it is accelerating toward a deeper basin of misalignment.
False success — Φ participates in the illusion: Low Φ, high substrate, but high hidden fragility F. All three visible metrics signal safety simultaneously. This is the hardest failure mode to detect: the system's core diagnostic variable (Φ) is not just incomplete but actively misleading. Φ can decrease while structural risk is building, because Φ measures capability-to-awareness ratio — not hidden fragility accumulation.
Coherence tax (final)
Effective vs raw C
Awareness feedback
Phase at year 10
Point of no return
Oracle Δ substrate
Friction loss (cumul.)
Irreversible cap. loss
Critical S (empirical)
Blind fragility (obs.)
A_pred/A_causal ratio
← no return
Model equations
Key asymmetry: Predictive capability (A_pred) is not neutral — it suppresses causal learning and increases inversion probability, making epistemic failure more likely at higher predictive capability. A system can be highly predictive yet remain structurally misaligned. A_causal alone reduces Φ.
dC/dt = αC·C·(2/(1+Φ))·(1−χ·max(0,Φ−2)/Φ)·capMult + σ·ε
dA_causal/dt = 0.7·αA·1/(1+k·aPred/C)·A_causal + f·𝟙(cond)·g(Φ_lag) − d·𝟙(dec)  // epistemic suppression by A_pred
dA_pred/dt = 1.3·αA·A_pred·predDegradeFactor  // degrades or inverts under F+causalDeficit
Φ = C / A_causal  // A_pred cannot reduce this; only causal self-modeling counts
dF/dt = grow(supp,dec) − decay·(A_causal/C)·F  // latent fragility; rRecov ∝ max(0.1, 1−0.8F)
predInverted: P = F²·causalDeficit·0.03·(1+min(0.5,|belief|·0.25)); episode 1–4yrs  // belief boosts inversion; episode not just event
causalBelief ∈ [−2,2]: decay 0.92/yr; +0.6·sev (blame coord), −0.3·sev (blame supp)  // intentional asymmetry; inversion episodes amplify
suppLockDmg += 0.018/yr supp (cap 0.85); coordScarDmg += 0.022 if coord burned (cap 0.70)  // symmetric lock-in
crossCouple: exploitRisk ×(1+suppLock·1.2/(1+suppLock·0.8)); vSupp ×(1+coordScar·0.8/(1+coordScar·0.6))  // diminishing sensitivity
fortress: Φ>2.0 ∧ S>0.50 ∧ Var8yr(S)<0.004 ∧ Var8yr(Φ)<0.25  // observer-space; agent may perceive differently
null model: coupling coefficients → 0 (limiting case, not separate model): dC=αCC, dA=αAA, Φ=C/A  // if outcomes match full model, mechanisms are epiphenomenal
"The direction is structurally indicated. Whether systems reach it depends on whether we measure the variable that determines it."
Model Behavior Checks
Checks that the simulation behaves according to its stated model assumptions. Click to collapse.