PRCP defines legitimacy as a structural property emerging from voluntary recognition under reversible delegation constraints.

This paper formalizes:

• Recognition dynamics

• Delegation symmetry conditions

• Structural entropy accumulation

• Stability boundary thresholds

• Correction trigger mechanisms

Legitimacy is treated not as moral validation but as a measurable systems variable.

PRCP does not treat legitimacy as:

• Electoral victory

• Majority approval

• Moral righteousness

• Historical continuity

Instead:

Legitimacy is defined as:

The sustained alignment between delegated authority and reversible recognition.

Let:

V = Voluntary Continuity
R = Reversibility Integrity
T = Transparency Coherence
D = Delegation Scope Proportionality

Then:

Legitimacy (L) = V × R × T × D

Where:

• If any variable approaches zero, legitimacy collapses.

• Majority without reversibility yields low R.

• Transparency without exit yields low V.

• Delegation without scope control reduces D.

Legitimacy is multiplicative, not additive.

Recognition is dynamic.

It flows.

It decays.

It concentrates or disperses.

Recognition declines when:

• Authority duration increases without review

• Revocation cost increases

• Transparency decreases

• Exit friction increases

Let:

C = Revocation Cost
E = Exit Friction
O = Structural Opacity
A = Authority Duration

Recognition Decay Rate (RDR):

RDR ∝ (C × E × O × A)

If RDR exceeds Renewal Rate, legitimacy erodes.

Recognition renews through:

• Participatory feedback

• Recall activation

• Delegation expiration cycles

• Transparency audits

RRR increases when:

• Review frequency rises

• Delegation windows shorten

• Authority becomes episodic

Stability requires:

RRR ≥ RDR

Delegation must satisfy:

Grant Cost ≈ Revocation Cost

If:

Grant Cost < Revocation Cost
→ Authority accumulates

If:

Grant Cost >> Revocation Cost
→ Coordination paralysis

Define:

Delegation Symmetry Ratio (DSR) = Grant Cost / Revocation Cost

Stable range:

0.8 ≤ DSR ≤ 1.2

Outside this range, instability accumulates.

We now formalize structural drift.

Let:

M = Monopoly of Resource Access
N = Non-Interruptibility Duration
S = Sovereignty Centralization Degree
I = Information Asymmetry

Institutional Entropy Coefficient:

IEC = M × N × S × I

When IEC rises:

• Reversibility declines

• Recognition becomes symbolic

• Authority becomes inertial

Critical Threshold:

If IEC > Adaptive Capacity,

System enters Structural Fragility Phase.

PRCP stability exists within a bounded envelope defined by:

• Recognition Renewal ≥ Recognition Decay

• Delegation Symmetry within range

• IEC below fragility threshold

• Residual Complexity load manageable

Graphically:

Too little delegation → fragmentation
Too much delegation → centralization

PRCP aims for:

Dynamic equilibrium, not permanence.

PRCP defines structural triggers independent of political will.

Correction triggers activate when:

1. DSR deviates persistently beyond threshold

2. IEC exceeds tolerance boundary

3. Recognition withdrawal surpasses critical mass

4. Base Units initiate coordinated reversion

Upon trigger:

• Delegation resets

• Higher layers dissolve or restructure

• Recognition recalibrates

Correction is structural, not ideological.

A governance system violates PRCP if:

Any subgroup bears irreversible structural cost without recourse.

This condition protects:

• Minority continuity

• Exit dignity

• Functional pluralism

Majority rule does not override the Non-Sacrificial Condition.

Legitimacy degrades when:

Decision complexity exceeds participant comprehension capacity.

Let:

X = Decision Complexity
K = Average Cognitive Comprehension

If X > K for sustained duration:

Opacity grows → Recognition declines.

Therefore:

PRCP requires bounded cognitive scale.

This may include:

• Modular decision segmentation

• Explainability standards

• Periodic simplification cycles

PRCP identifies three primary failure modes:

High IEC + low reversibility

Overactive revocation + insufficient coordination capacity

Formal compliance with low voluntary continuity

Each failure mode triggers distinct correction paths.

Under PRCP:

Power = Recognized Coordination Capacity × Reversibility Integrity

Power without reversibility is domination.

Reversibility without coordination is collapse.

PRCP maintains both.

Legitimacy in PRCP is:

• Measurable

• Dynamic

• Reversible

• Recognition-based

It is not inherited.
It is not permanent.
It is not symbolic.

It is structurally maintained or structurally lost.

To the extent possible under law, this work has been waived of copyright and dedicated to the public domain. For details, see the Creative Commons CC0 1.0 Universal Public Domain Dedication.

PRCP defines legitimacy as a structural property emerging from voluntary recognition under reversible delegation constraints.

This paper formalizes:

• Recognition dynamics

• Delegation symmetry conditions

• Structural entropy accumulation

• Stability boundary thresholds

• Correction trigger mechanisms

Legitimacy is treated not as moral validation but as a measurable systems variable.

PRCP does not treat legitimacy as:

• Electoral victory

• Majority approval

• Moral righteousness

• Historical continuity

Instead:

Legitimacy is defined as:

The sustained alignment between delegated authority and reversible recognition.

Let:

V = Voluntary Continuity
R = Reversibility Integrity
T = Transparency Coherence
D = Delegation Scope Proportionality

Then:

Legitimacy (L) = V × R × T × D

Where:

• If any variable approaches zero, legitimacy collapses.

• Majority without reversibility yields low R.

• Transparency without exit yields low V.

• Delegation without scope control reduces D.

Legitimacy is multiplicative, not additive.

Recognition is dynamic.

It flows.

It decays.

It concentrates or disperses.

Recognition declines when:

• Authority duration increases without review

• Revocation cost increases

• Transparency decreases

• Exit friction increases

Let:

C = Revocation Cost
E = Exit Friction
O = Structural Opacity
A = Authority Duration

Recognition Decay Rate (RDR):

RDR ∝ (C × E × O × A)

If RDR exceeds Renewal Rate, legitimacy erodes.

Recognition renews through:

• Participatory feedback

• Recall activation

• Delegation expiration cycles

• Transparency audits

RRR increases when:

• Review frequency rises

• Delegation windows shorten

• Authority becomes episodic

Stability requires:

RRR ≥ RDR

Delegation must satisfy:

Grant Cost ≈ Revocation Cost

If:

Grant Cost < Revocation Cost
→ Authority accumulates

If:

Grant Cost >> Revocation Cost
→ Coordination paralysis

Define:

Delegation Symmetry Ratio (DSR) = Grant Cost / Revocation Cost

Stable range:

0.8 ≤ DSR ≤ 1.2

Outside this range, instability accumulates.

We now formalize structural drift.

Let:

M = Monopoly of Resource Access
N = Non-Interruptibility Duration
S = Sovereignty Centralization Degree
I = Information Asymmetry

Institutional Entropy Coefficient:

IEC = M × N × S × I

When IEC rises:

• Reversibility declines

• Recognition becomes symbolic

• Authority becomes inertial

Critical Threshold:

If IEC > Adaptive Capacity,

System enters Structural Fragility Phase.

PRCP stability exists within a bounded envelope defined by:

• Recognition Renewal ≥ Recognition Decay

• Delegation Symmetry within range

• IEC below fragility threshold

• Residual Complexity load manageable

Graphically:

Too little delegation → fragmentation
Too much delegation → centralization

PRCP aims for:

Dynamic equilibrium, not permanence.

PRCP defines structural triggers independent of political will.

Correction triggers activate when:

1. DSR deviates persistently beyond threshold

2. IEC exceeds tolerance boundary

3. Recognition withdrawal surpasses critical mass

4. Base Units initiate coordinated reversion

Upon trigger:

• Delegation resets

• Higher layers dissolve or restructure

• Recognition recalibrates

Correction is structural, not ideological.

A governance system violates PRCP if:

Any subgroup bears irreversible structural cost without recourse.

This condition protects:

• Minority continuity

• Exit dignity

• Functional pluralism

Majority rule does not override the Non-Sacrificial Condition.

Legitimacy degrades when:

Decision complexity exceeds participant comprehension capacity.

Let:

X = Decision Complexity
K = Average Cognitive Comprehension

If X > K for sustained duration:

Opacity grows → Recognition declines.

Therefore:

PRCP requires bounded cognitive scale.

This may include:

• Modular decision segmentation

• Explainability standards

• Periodic simplification cycles

PRCP identifies three primary failure modes:

High IEC + low reversibility

Overactive revocation + insufficient coordination capacity

Formal compliance with low voluntary continuity

Each failure mode triggers distinct correction paths.

Under PRCP:

Power = Recognized Coordination Capacity × Reversibility Integrity

Power without reversibility is domination.

Reversibility without coordination is collapse.

PRCP maintains both.

Legitimacy in PRCP is:

• Measurable

• Dynamic

• Reversible

• Recognition-based

It is not inherited.
It is not permanent.
It is not symbolic.

It is structurally maintained or structurally lost.

To the extent possible under law, this work has been waived of copyright and dedicated to the public domain. For details, see the Creative Commons CC0 1.0 Universal Public Domain Dedication.