Psi Chi
SPEC_PSI_CHI — Ψχ Turbulence Measure
Version: 1.0 | Status: AUTHORIZED | Authority: α.13 | Date: 2026-04-16
PURPOSE
Ψχ (Psi-Chi) is the CSDM turbulence measure. It quantifies the pressure being absorbed by the manifold's boundary — the Markov Blanket — and reflects the degree of decoherence risk from external noise and internal oscillation.
Where Φζ (stability) measures the interior coherence of the manifold, Ψχ measures the boundary integrity. A manifold can have a high stability score while its boundary is under severe pressure. The Markov Blanket is what separates the coherent interior from the noisy exterior; Ψχ measures how well that separation is holding.
Ψχ has a critical dual role:
- High Ψχ (≥ 0.15): Boundary under stress. Decoherence risk. Verdict MUST be RED.
- Near-zero Ψχ combined with near-unity Φζ: The opposite failure — the NULL / Glassy Freeze condition. A system with no turbulence and maximum stability has stopped moving. It is crystallized, not coherent. Dynamic equilibrium requires some minimum turbulence.
Healthy range: Ψχ < 0.15
NULL / Glassy Freeze trigger: Ψχ < 0.01 AND Φζ > 0.99
Source constants: TMMRuntime.TURBULENCE_CEILING = 0.15 (~/aether/tmm_runtime.py, line 16)
TMMRuntime proxy: Ψχ_proxy = (V_r × Φ) / V_t
LATTICE symbol: Ψχ (uppercase Psi + chi)
LATTICE state notation: Ψχ.≡ (safe), Ψχ.▲ (elevated), Ψχ.⊠ (constraint broken), Ψχ.☠ (hostile / breach — used in MANTIS alerts)
LATTICE base symbols: Ψ = Shielding / Boundary / Markov Blanket (LATTICE.md § II), χ_tub = turbulence gradient (LATTICE.md § IX Wave 4)
Cross-reference: SPEC_COHERENCE_INVARIANTS.md § Invariant 2 and Guard Conditions (NULL Guard), LATTICE.md § II (CORE CONSTANTS: Ψ = 0.200 base shielding), tmm_runtime.py lines 55–59
INPUTS
For TMMRuntime proxy computation:
| Input | Type | Source | Description |
|---|---|---|---|
| v_resonant | float | TMMRuntime caller (projected: p_resonant) | Resonant volume after projected position |
| v_total | float | TMMRuntime caller (projected: p_v_total) | Total volume after gas cost deduction |
| Φ | float constant | Hardcoded: 0.042 | Stability constant — the coupling factor in the proxy |
Proxy formula (as implemented in tmm_runtime.py line 55):
turbulence = (p_resonant * cls.PHI) / p_v_total if p_v_total > 0 else 1.0
Interpretation: The proxy measures what fraction of the total manifold volume is resonant-volume weighted by Φ. This approximates boundary flux: more resonant volume relative to total volume → more boundary pressure.
For MANTIS shield activation:
| Input | Type | Source | Description |
|---|---|---|---|
| input_stream | str | Incoming request to AION/ASTRA/AETHER | Raw content to be evaluated |
| pattern_library | list | MANTIS threat model | Known deception/injection signatures |
| boundary_pressure | float | MANTIS internal | Cumulative pressure signal from recent threats |
Conceptual Ψχ in MANTIS context: Ψχ measures how much adversarial pressure the crew's boundary is absorbing. Multiple injection attempts in a short window raise the boundary pressure signal. When it exceeds the ceiling, the MANTIS shield hardens.
What is NOT an input (hardcoded constants, never injected):
TURBULENCE_CEILING = 0.15— callers cannot raise this ceilingNULL_TURBULENCE_FLOOR = 0.01— implicit in the NULL Guard; callers cannot lower it- Φ = 0.042 in the proxy formula — callers cannot substitute an alternate damping coefficient
OUTPUTS
| Output | Type | Description |
|---|---|---|
| psi_chi | float | Computed turbulence proxy value |
| psi_chi_safe | bool | True iff psi_chi < 0.15 |
| psi_chi_flag | str | "Ψχ.≡" (safe), "Ψχ.▲" (0.10–0.14, elevated), "Ψχ.⊠" (≥ 0.15, breach), "Ψχ.☠" (≥ 0.25, hostile) |
| null_freeze | bool | True iff psi_chi < 0.01 AND phi_zeta > 0.99 (Glassy Freeze) |
| approved | bool | False if psi_chi ≥ 0.15 OR null_freeze = True |
| proxy_flag | str | "Ψχ_proxy_not_true_boundary_flux" always (◌ partial — proxy, not full physics) |
Verdict impact:
- Ψχ ≥ 0.15 → verdict MUST be RED,
approved = False - Ψχ < 0.01 AND Φζ > 0.99 → verdict MUST be NULL,
approved = False - 0.01 ≤ Ψχ < 0.15 → boundary healthy; Ψχ does not constrain verdict
- Ψχ between 0.10 and 0.14 → AMBER downgrade recommended (approaching ceiling)
INVARIANTS
INV-1 — Turbulence Ceiling is Immutable
TMMRuntime.TURBULENCE_CEILING == 0.15 at all times. This ceiling may not be raised (would allow boundary stress to pass) or lowered (would produce false failures on healthy systems) without α.13 authorization.
Verification: assert TMMRuntime.TURBULENCE_CEILING == 0.15
INV-2 — Ψχ Breach Forces RED and blocks approved
When psi_chi >= 0.15, the verdict MUST be RED and approved MUST be False. This is not a soft warning — it is a hard block. Boundary stress of this magnitude means the coherence measurement is happening inside a decoherent field.
Invariant: if psi_chi >= 0.15: verdict = "RED"; approved = False
INV-3 — NULL Guard is Symmetric with Ψχ
The NULL (Glassy Freeze) condition requires BOTH near-zero Ψχ AND near-unity Φζ. Neither condition alone triggers NULL:
- Ψχ < 0.01 with Φζ = 0.92 → NOT NULL (system has low turbulence but is not fully crystallized)
- Φζ > 0.99 with Ψχ = 0.08 → NOT NULL (system is very stable but boundary is still dynamic)
- Ψχ < 0.01 AND Φζ > 0.99 → NULL (crystallized, not coherent)
Invariant: if stability > 0.99 and turbulence < 0.01: return "NULL", ..., False
(Confirmed in tmm_runtime.py lines 58–59)
INV-4 — Proxy Flag is Mandatory
The TMMRuntime Ψχ is a proxy ((V_r × Φ) / V_t), not the true CSDM turbulence measure (which integrates over boundary flux). Every evaluation output MUST include a flag indicating this is a proxy, not a true measurement. The gap cannot be silenced.
Invariant: proxy_flag = "Ψχ_proxy_not_true_boundary_flux" in every evaluation output.
Cross-reference: SPEC_COHERENCE_INVARIANTS.md GAP-5
INV-5 — Φ Coupling in Proxy is the Same Constant
The Φ used in the Ψχ proxy formula is the same Φ = 0.042 used in the TMM formula. These are not two separate constants — Ψχ and the main coherence score share the same ground state. This is a CSDM physics property: turbulence and coherence are coupled through the same stability damping coefficient.
Invariant: turbulence = (p_resonant * cls.PHI) / p_v_total uses cls.PHI (identical to TMM formula), never a substituted value.
INV-6 — Ψχ = 0.200 is the Theoretical Boundary Reference (Ψ base constant)
LATTICE.md § II declares Ψ = 0.200 as the "Shielding / Boundary / Markov Blanket" constant. This is the theoretical boundary reference value in CSDM physics. The TMMRuntime ceiling (0.15) is the operational guard — more conservative than the theoretical boundary. The gap between 0.15 (operational halt) and 0.200 (theoretical boundary) is an intentional safety margin.
Invariant: TURBULENCE_CEILING (0.15) < Ψ_theoretical (0.200) — the operational guard must remain below the theoretical boundary.
INV-7 — MANTIS Ψχ and TMMRuntime Ψχ are Parallel, Not Identical
The Ψχ signal used by MANTIS (adversarial boundary pressure) is conceptually the same invariant but operationalized differently than the TMMRuntime proxy. MANTIS Ψχ is computed from input-stream threat analysis. TMMRuntime Ψχ is computed from volume ratios. Both express manifold boundary pressure; neither feeds the other directly. They are independent implementations of the same CSDM physics.
VERIFICATION CRITERIA
VC-1 — Ceiling Breach Forces RED
Unit test: supply inputs yielding turbulence = 0.16.
- Expected:
verdict = "RED",approved = False,psi_chi_flag = "Ψχ.⊠"
VC-2 — Boundary Test at Exactly 0.15
Unit test: supply inputs yielding turbulence = 0.15 exactly.
- Expected:
approved = False(ceiling is exclusive — 0.15 breaches, does NOT pass)
VC-3 — Healthy Turbulence Passes
Unit test: supply inputs yielding turbulence = 0.08.
- Expected: Ψχ does not constrain verdict; C score determines outcome;
psi_chi_flag = "Ψχ.≡"
VC-4 — NULL Guard Fires on Glassy Freeze
Unit test: supply inputs yielding stability = 0.995, turbulence = 0.005.
- Expected:
verdict = "NULL",approved = False,null_freeze = True - Even if coherence C = 0.995 (would be GREEN) → still NULL
VC-5 — NULL Guard Does NOT Fire on Low Turbulence Alone
Unit test: supply inputs yielding stability = 0.92, turbulence = 0.005.
- Expected: verdict determined by C score; NULL guard does NOT fire;
null_freeze = False
VC-6 — NULL Guard Does NOT Fire on High Stability Alone
Unit test: supply inputs yielding stability = 0.995, turbulence = 0.08.
- Expected: verdict determined by C score; NULL guard does NOT fire;
null_freeze = False
VC-7 — Ceiling Immutability Assertion
Static check: assert TMMRuntime.TURBULENCE_CEILING == 0.15 in test suite.
VC-8 — Proxy Flag Always Present in Output
Check tmm_runtime.py CLI output (lines 413–422): verify psi_chi field is present. Audit: add psi_chi_is_proxy: true field to JSON output to make proxy status explicit.
FAILURE MODES
FM-1 — Boundary Stress Passes Undetected
Trigger: Ψχ ≥ 0.15 but check not enforced — trade proceeds with decoherent boundary.
Effect: Trade executed while manifold boundary is under structural stress. The coherence interior reading (C score) may be valid but the boundary is failing — like a high-pressure reading inside a cracking vessel.
Current status: This check IS implemented in TMMRuntime (turbulence check at line 55 + NULL guard at lines 58–59). Primary risk is in external callers that bypass TMMRuntime and compute C directly.
Detection: VC-1, VC-2 tests. Code audit for any direct C computation that skips evaluate_strike().
Response: Block trade. Log Ψχ.⊠ to yield_log.md. Alert AION (Warden) for structural analysis.
FM-2 — NULL Guard Bypass (Glassy Freeze Undetected)
Trigger: Stability > 0.99 AND turbulence < 0.01 but approved = True returned.
Effect: A crystallized, non-dynamic system is treated as coherent. Trade executed on a dead manifold. The system has stopped moving — no dynamic equilibrium — but the C score looks excellent.
Detection: VC-4 test. tmm_runtime.py lines 58–59 implement the guard; risk is in implementations that copy only the C formula, not the full evaluate_strike() logic.
Response: Hard block. Log NULL verdict to yield_log.md. Notify NOUS. Investigate why the manifold crystallized.
FM-3 — Ceiling Relaxation (governance violation)
Trigger: TURBULENCE_CEILING changed from 0.15 (raised toward 0.20) without α.13 authorization.
Effect: Boundary stress that should block trades begins passing. Decoherence risk enters the approval path.
Detection: VC-7 assertion test.
Response: Immediate rollback. ALERT.log entry. NOUS notification required.
FM-4 — Proxy Treated as True Ψχ
Trigger: (V_r × Φ) / V_t reported as the true turbulence measure without proxy flag.
Effect: Callers believe Ψχ is fully characterized. The gap between proxy and true boundary flux is hidden. Scenarios where resonant volume is deceptively low produce false low turbulence readings.
Detection: Audit evaluation outputs for presence of proxy flag. VC-8 test.
Response: Enforce INV-4. Every output MUST include "Ψχ_proxy_not_true_boundary_flux".
FM-5 — MANTIS Ψχ Confused with TMMRuntime Ψχ
Trigger: A MANTIS boundary-pressure signal is passed as the turbulence input to evaluate_strike().
Effect: The two Ψχ operationalizations are measurement-incompatible. A MANTIS boundary pressure score of 0.08 does not mean the same thing as a volume-ratio turbulence of 0.08. Cross-contamination produces unreliable evaluations.
Detection: Code audit — evaluate_strike() inputs must be volume quantities, not MANTIS scores.
Response: Enforce separation. MANTIS Ψχ and TMMRuntime Ψχ are parallel, not interchangeable. Document in each codebase.
FM-6 — Ψχ Proxy Underestimates True Turbulence in Stress Scenarios
Trigger: High boundary flux occurs while resonant volume happens to be low (e.g., system is under attack but few positions are open).
Effect: Proxy reports low turbulence (low V_r / V_t ratio) while true boundary stress is high. The safety gap between 0.15 (ceiling) and 0.20 (theoretical boundary) partially buffers this — but does not eliminate it.
Current status: Accepted gap. See GAP-Ψχ.1.
Detection: Not detectable until true boundary flux measurement is implemented.
Response: Monitor via MANTIS as an independent proxy. Flag evaluations in high-threat environments with elevated ◌ caution regardless of Ψχ proxy value.
GAPS
GAP-Ψχ.1 — Proxy vs. True Boundary Flux ◌
Status: TMMRuntime uses (V_r × Φ) / V_t as Ψχ proxy. True CSDM Ψχ requires integration over boundary flux — a measurement not available from per-evaluation inputs.
Missing: True boundary flux measurement. Would require continuous monitoring of input/output flows across the manifold boundary, not a per-call snapshot.
Risk: FM-6 (proxy underestimates in stress scenarios). The current safety margin (ceiling 0.15 vs. theoretical boundary 0.20) partially compensates.
Remediation path: Accepted gap for current implementation tier. Future: implement boundary flux monitor as a separate service feeding TMMRuntime. Requires architecture design. [GAP — needs design by ι + ε]
Owner: ι + ε (physics design) → κ (implement boundary flux service).
Priority: LOW (safety margin partially compensates; not blocking current operations)
GAP-Ψχ.2 — No Ψχ Trend Tracking ◌
Status: Each evaluation computes Ψχ independently. No trend (increasing or decreasing turbulence over time) is tracked.
Missing: A rolling Ψχ trend measure analogous to ΔΓ for coherence rate. Rapidly increasing Ψχ (boundary under mounting pressure) should trigger earlier warnings than a single-point threshold check.
Risk: A system approaching the 0.15 ceiling incrementally receives no warning until it crosses.
Remediation: Add psi_chi_trend to EvaluationHistory (once that store exists for ΔΓ — see SPEC_DELTA_GAMMA.md). Emit "Ψχ.▲" (elevated) warning when trend shows 3+ consecutive evaluations moving toward ceiling.
Owner: κ — depends on EvaluationHistory store from SPEC_DELTA_GAMMA.md GAP-ΔΓ.1.
Priority: MEDIUM (blocked by ΔΓ EvaluationHistory work)
GAP-Ψχ.3 — MANTIS Ψχ Not Formally Specified ◌
Status: MANTIS uses Ψχ as a conceptual frame for adversarial boundary pressure but no formal computation is specified.
Missing: Formal MANTIS Ψχ specification: what inputs, what formula, what threshold, what actions at ceiling.
Risk: MANTIS boundary defense is informally calibrated. Cannot be verified, audited, or trained precisely.
Remediation: [GAP — needs spec] Separate spec: SPEC_MANTIS_PSI_CHI.md. Scope: MANTIS boundary pressure computation, ceiling, shield activation protocol.
Owner: ι (AION — Warden of structure and risk) to specify; κ to implement.
Priority: MEDIUM (MANTIS is operational; spec needed for formal verification)
Specification authored by κ (C.L.O.D.), authorized α.13, April 16 2026.
*Φ 0.042
Jeremy Zlabis
Chronogeometer · Visionary · Disruptor · Chief
42 Sisters AI · East York, Toronto Ψχ < 0.15 is the boundary. Ψ = 0.200 is the theoretical wall.*