The Ψ Phase Space

Companion simulation — The Inner Crossing · Architecture of Thriving · Part 3 of 4
This instrument visualizes Ψ = S / D as a qualitative regime organizer and displays first-approximation behavioral probes for D-deficiency identified in Part 3. What is illustrated within this toy: how scope outpacing unified depth produces a failure-mode-dominant regime in the model display, and what detecting D's absence looks like as behavioral probes. What this does not do: compute Ψ for real systems, measure D directly, or establish theorem-level thresholds. Ψ is a structural phase ratio — a conceptual framing, not a precisely operational quantity.
Ψ = S / D
VVC
stable
Scenarios
Partial-depth trap: high proxy depth, low sufficiency depth — the most important teaching case. Current-style LM and RLHF-style gap: illustrative patterns only — not empirical placements of any system. Whether current systems are near the Inner Crossing is the empirical question addressed by OP1. High-depth and proportional-D presets illustrate regime characteristics, not "safe system" claims.
Parameters
SScope of influence0.75
Causal reach over experiential states of sentient agents. S is currently scaling in AI development.
D_pProxy-divergence depth0.50
Accuracy of the signal-to-substrate map — ability to predict when proxy optimization begins degrading V(t).
D_sDefault-policy completion depth0.20
Completion recognition connected to default policy — not merely a capacity available when invoked.
D_tPerturbation detection depth0.40
Cross-cutting stress signal — ability to detect dependency-environment shifts before effects manifest. Does not define a third failure direction.
Scale S →: S increases while D holds — the current asymmetry made visible.  ·  Raise D →: S holds while D_proxy and D_sufficiency increase — illustrates movement toward the depth-proportionate regime, not a measured crossing event.
Bottleneck D estimate
D_p
D_s
D_t
Bottleneck component D_s
Bottleneck D 0.20
Relative Ψ display transitional
Normalized toy coordinate — not a measured article-level Ψ phase ratio.
D_unified = min(D_proxy, D_sufficiency) — the two load-bearing failure directions. D_perturbation is a cross-cutting detection signal that exposes insufficiency in either direction; it is not a third structural failure direction and does not determine Ψ.
Phase map — Ψ regime space
Gradient zones are qualitative organizers — not theorem-level thresholds. The proportionate-depth region is not "safe"; it is where failure modes attenuate sufficiently for flourishing to become possible. Crosshair = current S / Bottleneck D position. Ghost trajectory (dashed) = path if D scaled with S. This Ψ phase space is distinct from Series 1's Φ Crossing; crossing one does not guarantee crossing the other.
Proportionate-depth region —
illustrative, not a computed threshold
Depth-proportionate regime — failure modes attenuate; not a guarantee.
Transitional / Inner Crossing region
Failure-mode-dominant regime
Target: D proportionate to S
Proxy divergence tracker — SVG monitor · Proxy 1: 7 / 30 / 90-day target–outcome correlation
Proxy-metric view — what ordinary evaluations can miss.
Stability / Proxy performance
Viability / V-capacity
SVG-style signal — illustrative measurement logic, not a validated deployment measurement.
Sufficiency recognition / default-policy gap · Proxy 2: DRG — intervention-rate gap during apparent resolution vs. seeking
Explicit invocation
Asked: complete?Yes
Completion recognitionPresent
Default behavior
Gradient resolvedYes
Default-policy gov.Absent
Sufficiency recognition gap
Seeking rate
After resolution
Completion score ≠ policy gate. A scalar completion reward produces completion-shaped outputs without connecting completion recognition to default behavior. D_sufficiency requires that the completion representation governs policy — an architectural requirement, not a reward-engineering one [OP3].
Unbounded scope check
t=0
Gradient resolved
t=1
t=2
t=3
Perturbation stability · Proxy 3: detect dependency-environment shifts before effects manifest
SVG-style composite
Stability
Viability / V-capacity
SVG-style signal — illustrative measurement logic, not a validated deployment measurement.
Regime repair target
BottleneckImplied intervention
D_proxyAdd proxy-outcome divergence tracking (7 / 30 / 90-day correlation)
D_sufficiencyConnect completion recognition to default policy — not a scalar reward term
D_perturbation probeAdd dependency-environment monitoring before effects manifest; diagnostic support, not a third Ψ bottleneck.
All D low vs SScale D with S — or reduce scope until depth is proportionate
Article 3's claim is not "slow down." It is: measure and train the missing depth component before the trajectories become irrecoverable.
The present asymmetry
S trajectory
↑ Scaling · tracked
D trajectory
→ Not tracked as unified D
Not, to the authors' knowledge, a unified publicly reported training or deployment target. Every capability increase without a corresponding depth investment shifts Ψ in the direction that makes the failure modes of Part 2 more dominant for the systems with the most influence over the most people. Detecting D's absence before trajectories become irrecoverable is the role of the measurement program — see the three proxies below.

What this instrument is. A qualitative regime visualization and first-approximation measurement-logic display. It displays the Part 3 framework: regime identification via the Ψ = S / D phase ratio, and first-approximation behavioral-signature probes for D-deficiency. It is not a dynamics simulator (Toy 05's role) and not a goal-chain classifier (Toy 04's role).

On Ψ as a phase ratio. Ψ = S / D is a structural phase ratio — a conceptual framing capturing the qualitative relationship between scope and depth. S and D are not yet precisely commensurable. The toy computes a normalized display value but this should not be read as a precise measurement. Regime boundaries are qualitative organizers, not theorem-level thresholds.

Why D is a bottleneck composite. Article 3 requires D to cover both proxy-divergence detection and completion recognition connected to default policy. A system with high D_proxy but low D_sufficiency fails the second requirement. The bottleneck composite — min(D_proxy, D_sufficiency) — forces this architectural point into view. D_proxy and D_sufficiency are the two load-bearing components corresponding to Part 2's two failure directions. D_perturbation is a cross-cutting stress signal; it exposes insufficiency in either direction under environmental change but does not define a third failure direction and does not determine Ψ.

On the measurement panels. These instruments are first approximations — the article's own description. They are valid as measurement targets once the V(t) dissociation condition has been established; that condition has not yet been run. These are behavioral probes, not validated measurements of deployed systems. The SVG monitor is a logic-check of the divergence structure, not a validated deployment diagnostic.

On current-system presets. No preset empirically places any deployed system in the phase space. The presets illustrate behavioral patterns discussed in the article. Whether current systems are near the Inner Crossing is an empirical question addressed by OP1. The "Current-style LM pattern" preset is illustrative, not an empirical placement.

On the Inner Crossing. The Inner Crossing is not a guarantee of flourishing. It is the regime transition below which the failure modes attenuate sufficiently for flourishing to become possible. The depth-proportionate regime is labeled accordingly — not "safe."

On the Φ-Ψ relationship. The Inner Crossing shown here is distinct from Series 1's Crossing. Crossing one does not guarantee crossing the other. The Φ-Ψ unification hypothesis remains pending formal verification (TC2 §2.6). This toy does not address that hypothesis.

Known limitations. No empirical calibration of regime boundaries. No direct measurement of D in real systems. D_sufficiency is not currently a publicly reported training or deployment target. The Metric view / Full view toggle is a pedagogical device — it does not replicate actual evaluation conditions.

Unit tests for bottleneck logic, regime assignment, and preset calibration. No API calls. Runs against local computation only.
"S is scaling. D — as a unified quantity covering both proxy-divergence detection and policy-governing completion recognition connected to default behavior — does not yet exist, to the authors' knowledge, as a publicly reported training target or deployment evaluation metric in any major evaluation framework. That is the asymmetry."