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Rate-Dominance Law + Three Collapse Modes (Almost-Code Canonical) v1.0

Collapse is a rate-inequality law. “Causes” are forcing terms.

Summary (Canonical)

Civilisation collapses when the rate of capability loss exceeds the rate of capability regeneration for long enough.
War, disease, climate, policy, money, infrastructure damage are forcing terms that change slopes; they are not the root mechanism.

1) First Principles

1.1 Rates, not labels

“Why did it collapse?” is usually answered with a story-label (war, corruption, famine).
CivOS treats those as external arrows applied to a lattice.

The root truth is structural:

  • Loss/destruction/attrition has a rate
  • Repair/regeneration/replacement has a rate
  • Collapse happens when the inequality flips persistently

2) The Rate-Dominance Law (Core)

Let:

  • Ġ(t) = regeneration rate of core capabilities (training + transfer + repair + replacement)
  • Ḋ(t) = loss/decay/destruction rate (attrition + role extinction + bind deletion)
  • C(t) = capability stock (HRL / RePOC capabilities; exclude money/infra as definition)

Stability:G˙(t) ≥ D˙(t)G˙(t) ≥ D˙(t)

Failure:D˙(t) > G˙(t)persistentlyD˙(t) > G˙(t)persistently

Damage ratio (optional primitive):R(t)=D˙(t)G˙(t)R(t)=G˙(t)D˙(t)​

  • Stable if R(t)≤1R(t)≤1
  • Collapse corridor if R(t)>1R(t)>1

3) The Three Collapse Modes (Complete Phase Space)

All collapse trajectories fall into one of three modes:

Mode I — Amplitude / KO Collapse

Large instantaneous deletion of nodes/binds.
Examples: sudden conquest, decapitation of elites/administration, catastrophic disaster removing core hubs.

Signature:

  • ΔCΔC drops sharply at once
  • Even if Ğ recovers later, the lattice may be too fragmented to route repair

Mode II — Slow Attrition Collapse

Loss rate only slightly exceeds regeneration, but over long time.
Signature:

  • R(t)≳1R(t)≳1 for many cycles
  • Gradual hollowing: skills, roles, institutions thin out quietly

Mode III — Fast Attrition / War Collapse

Loss rate violently exceeds regeneration with high tempo.
Signature:

  • R(t)≫1R(t)≫1 repeatedly
  • Cascading bind deletion; repair latency exceeds shock cycle length

These three modes are sufficient.
Everything else is an arrow that changes Ğ or Ḋ.These three modes are sufficient.
Everything else is an arrow that changes Ğ or Ḋ.

4) Forcing Terms (Arrows) vs Root Mechanism

4.1 Forcing terms

  • War
  • Disease
  • Climate shocks
  • Financial crisis
  • Policy errors
  • Infrastructure failure
  • External blockade

4.2 What forcing terms do (in CivOS)

They modify slopes:

  • Increase Ḋ(t) (destruction, attrition, role loss)
  • Decrease Ġ(t) (training breakdown, transfer failure, coordination collapse)
  • Increase variance → phase shear → accelerates into Mode III

But they are not the core mechanism.

5) System Optimisation (What “Good” Looks Like)

A stable civilisation:

  • maintains buffers so repair can catch up
  • protects core regeneration organs (EducationOS, governance continuity, healthcare repair)
  • keeps repair latency below stress cycle length
  • avoids over-concentration brittleness (redundancy in roles/pipelines)

6) Hidden Fragility (How Collapse Starts Invisibly)

Slow attrition often looks like:

  • declining competence in core roles
  • longer repair cycles
  • brittle dependence on a few hubs
  • increasing exception-handling (symmetry breaks leaking into interior execution)
  • political/coordination noise that destroys transfer reliability

This is Mode II turning into Mode III when a shock hits.

7) Safety Conditions (Non-Negotiables)

To avoid all three modes:

  1. Protect regeneration organs (EducationOS, HRL pipelines)
  2. Maintain redundancy (anti concentration)
  3. FenceOS actuation (truncation+stitching when thresholds trip)
  4. Phase discipline (keep load/tempo inside envelope; avoid shear)

8) Failure Mode Trace (Required)

Buffers thin → regeneration slows → loss rate exceeds regeneration (R>1) → binds delete → repair latency rises → shocks arrive faster than repair → cascade → Mode II becomes Mode III → collapse.
Or: amplitude shock deletes core hubs → routing breaks → regeneration cannot engage → KO collapse.

Almost-Code Spec Block (Copyable)

CivOS.RateDominance.v1.0

Variables:
  C(t) := capability stock (HRL / RePOC)
  Ġ(t) := regeneration rate
  Ḋ(t) := loss/decay/destruction rate
Core Ratio:
  R(t) := Ḋ(t) / Ġ(t)
Stability:
  Stable iff R(t) <= 1
Collapse Corridor:
  Enter iff R(t) > 1 persistently
  Collapse speed increases with magnitude and duration of (R(t)-1)
Collapse Modes:
  Mode_I_AmplitudeKO:
    condition: ΔC(t) << 0 in short Δt (instant node/bind deletion)
  Mode_II_SlowAttrition:
    condition: R(t) slightly > 1 for long horizon
    signature: quiet hollowing, thinning pipelines
  Mode_III_FastAttritionWar:
    condition: R(t) >> 1 with high tempo
    signature: cascades, repair latency > shock cycle length

FAQ (Short)

Q1: Isn’t “war” a cause?
War is a forcing term that spikes Ḋ(t) and often reduces Ġ(t). The root law is still (Ḋ>Ġ).

Q2: Why “three modes only”?
Because all trajectories reduce to either instantaneous deletion, slow rate-overhang, or fast violent overhang.

Q3: What prevents Mode II turning into Mode III?
Buffers, redundancy, fast repair loops, and truncation+stitching control (FenceOS).

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