Energy Awareness Skill

Battery cycle clock with interaction entropy and ontology reconfiguration for computational resource awareness.

Overview

Integrates three temporal dynamics into a unified energy awareness system:

1. Battery Cycle Clock - Cyclical energy/attention budget with golden spiral timing
2. Interaction Entropy - Shannon entropy of tool/action frequency (2.59 bits baseline)
3. Ontology Reconfiguration Rate - Sheaf condition violations per cycle

GF(3) Conservation Invariant

cycle_trit + entropy_trit + reconfig_trit ≡ 0 (mod 3)

When violated, system needs MINUS/PLUS injection to rebalance.

36-Cycle Color Chain

Each battery cycle (0-35) maps to a deterministic Gay.jl color:

Cycle	Hex	L	C	H	Role
0	#232100	9.95	89.12	109.17	Genesis dark
1	#FFC196	95.64	75.69	40.58	Warm peach
34	#002D79	13.45	60.90	259.71	Primary vertex
35	#65947D	60.45	25.67	155.23	Sage green

Covariance Stream Vertices (High MI Hubs)

COVARIANCE_VERTICES = {
    34: 156.19,  # Primary: deep blue
    14: 153.03,  # Bright peach
    24: 151.91,  # Near-white
    19: 147.06,  # Deep red
    33: 142.47,  # Pink-white
    1: 131.00,   # Orange peach
}

Non-Adiabatic Breaks

Ergodicity-breaking jumps at:

• [33 → 34]

  - 92.47 distance (LARGEST)

• [0 → 1]

  - 88.41 distance (Genesis)

• [14 → 15]

  - 83.83 distance

• [19 → 20]

  - 79.66 distance

Golden Ratio Timing

• Phase advancement: 137.508° per cycle (golden angle)
• Duration: Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21... minutes)
• Trit assignment:

  • 0° - 120°

    → +1 (PLUS, charging)

  • 120° - 240°

    → 0 (ERGODIC, steady)

  • 240° - 360°

    → -1 (MINUS, depleting)

Usage

Python: Unified Awareness Clock

from battery_cycle_ontology_clock import UnifiedAwarenessClock

clock = UnifiedAwarenessClock(seed=1337)

# Record interactions
clock.record_interaction("tool_call", "Read", trit=0)
clock.record_interaction("action", "gay-mcp-palette", trit=1)

# Record ontology changes
clock.record_ontology_change("add_edge", ["T-019b313a"], sheaf_violated=False)

# Tick the clock
state = clock.tick(energy_delta=0.1)

print(f"Cycle: {state.cycle.cycle_id}")
print(f"Phase: {state.cycle.phase_degrees}°")
print(f"Energy: {state.cycle.energy_budget}")
print(f"Entropy: {state.interaction_entropy} bits")
print(f"GF(3) balanced: {state.gf3_balanced}")

Julia: Gay.jl Color at Cycle

using Gay

# Get color for battery cycle
color = Gay.color_at(34)  # Primary vertex
println(color)  # #002D79

Babashka: Quick Energy Check

#!/usr/bin/env bb

(def PHI (/ (+ 1 (Math/sqrt 5)) 2))
(def GOLDEN_ANGLE 137.508)

(defn cycle->phase [n]
  (mod (* n GOLDEN_ANGLE) 360))

(defn phase->trit [phase]
  (cond
    (< phase 120) 1    ; PLUS
    (< phase 240) 0    ; ERGODIC  
    :else -1))         ; MINUS

(defn fibonacci [n]
  (loop [a 1 b 1 i 0]
    (if (>= i n) a
        (recur b (+ a b) (inc i)))))

;; Check current cycle
(let [cycle 23
      phase (cycle->phase cycle)
      trit (phase->trit phase)
      duration (fibonacci (mod cycle 12))]
  (println (str "Cycle " cycle ": phase=" phase "° trit=" trit " duration=" duration "min")))

DuckDB: Query Energy States

-- Check GF(3) conservation
SELECT SUM(gf3_trit) % 3 as remainder FROM intake_log;

-- Energy state over time
SELECT 
  logical_clock,
  gay_color,
  gf3_trit,
  SUM(gf3_trit) OVER (ORDER BY logical_clock ROWS BETWEEN 2 PRECEDING AND CURRENT ROW) as rolling_sum
FROM intake_log
ORDER BY logical_clock;

Trit Semantics

Component	-1 (MINUS)	0 (ERGODIC)	+1 (PLUS)
Cycle	Depleting phase	Steady phase	Charging phase
Entropy	Low diversity (<1.0 bits)	Moderate (1.0-2.5 bits)	High diversity (>2.5 bits)
Reconfig	Chaotic (>30% violations)	Stable	Rapid healthy adaptation

Interrupt Handling

On tool interruption, GF(3) conservation is maintained:

NORMAL:    1 → -1 → 0  = 0 ✓
INTERRUPT: -1 → 0 → 1  = 0 ✓
RECOVERY:  0 → 1 → -1  = 0 ✓

Files

• ~/ies/battery_cycle_ontology_clock.py

  - Main implementation

• ~/ies/music-topos/lib/battery_cycle_color_driver.hy

  - Hy color driver

• ~/ies/BATTERY_CYCLE_INTERRUPT_INTEGRATION.md

  - Architecture docs

• ~/ies/rio/battery-menubar/

  - Swift menubar app

Verification

# Run the clock
python ~/ies/battery_cycle_ontology_clock.py

# Check GF(3) in DuckDB
duckdb ~/ies/music-topos/ducklake_increment.duckdb \
  "SELECT SUM(gf3_trit) % 3 FROM intake_log"

# Julia color check
julia -e 'using Gay; println(Gay.color_at(34))'

Mathematical Foundation

Based on:

• Gay.jl scoped_propagators.jl (AncestryACSet materialization)
• Knuth tesseract_discohy.hy (action/perception Galois loop)
• Bumpus sheaf cohomology (adhesion_filter obstruction detection)
• von Holst reafference/corollary discharge (interrupt detection)

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End-of-Skill Interface

Integration with Other Skills

Skill	Role	Trit
gay-mcp	Color generation	+1
reafference-corollary-discharge	Interrupt detection	+1
bisimulation-game	Behavioral equivalence	-1
duckdb-temporal-versioning	Time-travel audit	+1
acsets	Relationship navigation	0

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Autopoietic Marginalia

The interaction IS the skill improving itself.

Every use of this skill is an opportunity for worlding:

• MEMORY (-1): Record what was learned
• REMEMBERING (0): Connect patterns to other skills
• WORLDING (+1): Evolve the skill based on use

Add Interaction Exemplars here as the skill is used.