Unworld Moments

Σ trits per triad = (+1) + (0) + (-1) = 0 ✓

Interleaved Streams (Seed: 1069)

Stream 1 (construct/+1):  #E7B367 #EACC11 #CF86ED ...
Stream 2 (coordinate/0):  #46F27F #E2282A #EE55F2 ...
Stream 3 (reflect/-1):    #F0D127 #6179EB #2DED13 ...

Parametrised Optics ⊛ Agency

Each parallel triad executes via the ⊛ operator:

         P (23 parallel parameters)
         │
         ⊛ (agency: fanout)
         │
    ┌────┴────┬────────┬────────┐
    ▼         ▼        ▼        ▼
  Triad₁   Triad₂  ...      Triad₂₃
    │         │        │        │
    └────┬────┴────────┴────────┘
         │
         ⊛ (agency: merge)
         │
         ▼
      S' (final state)

Cognitive Moment Mapping

Implementation

from dataclasses import dataclass
from typing import List, Tuple
from concurrent.futures import ThreadPoolExecutor
import hashlib

@dataclass
class CognitiveMoment:
    """Single cognitive moment with trit assignment."""
    index: int
    action: str  # construct, coordinate, reflect
    trit: int    # +1, 0, -1
    color: str   # deterministic from seed
    state_transition: Tuple[str, str]

    def execute(self, state: dict) -> dict:
        """Execute moment, producing new state."""
        # BDD: Given-When-Then as pure function
        precondition = self.state_transition[0]
        postcondition = self.state_transition[1]

        if state.get('phase') == precondition:
            return {**state, 'phase': postcondition, 'moment': self.index}
        return state

@dataclass
class CognitiveTriad:
    """GF(3)-balanced triple of moments."""
    index: int
    construct: CognitiveMoment   # +1
    coordinate: CognitiveMoment  # 0
    reflect: CognitiveMoment     # -1

    @property
    def gf3_sum(self) -> int:
        return (self.construct.trit +
                self.coordinate.trit +
                self.reflect.trit) % 3

    def execute_parallel(self, state: dict) -> dict:
        """Execute all three moments simultaneously via ⊗."""
        assert self.gf3_sum == 0, "GF(3) violation!"

        # Parallel execution (⊗ not >>>)
        with ThreadPoolExecutor(max_workers=3) as executor:
            futures = [
                executor.submit(self.construct.execute, state),
                executor.submit(self.coordinate.execute, state),
                executor.submit(self.reflect.execute, state)
            ]
            results = [f.result() for f in futures]

        # Merge via ⊛ (parametrised optic backward pass)
        return self._merge_results(results)

    def _merge_results(self, results: List[dict]) -> dict:
        """Merge parallel results preserving GF(3)."""
        merged = {}
        for r in results:
            merged.update(r)
        merged['triad'] = self.index
        merged['gf3_verified'] = True
        return merged

class UnworldMoments:
    """
    Make all 69 cognitive moments happen simultaneously.

    Transforms sequential BDD scenarios into parallel triadic fanout.
    """

    SEED = 1069  # Balanced ternary: [+1, -1, -1, +1, +1, +1, +1]

    def __init__(self, moments: List[CognitiveMoment]):
        assert len(moments) == 69, "Must have exactly 69 moments"
        self.moments = moments
        self.triads = self._group_into_triads()

    def _group_into_triads(self) -> List[CognitiveTriad]:
        """Group 69 moments into 23 GF(3)-balanced triads."""
        triads = []
        for i in range(23):
            base = i * 3
            triads.append(CognitiveTriad(
                index=i + 1,
                construct=self.moments[base],      # +1
                coordinate=self.moments[base + 1], # 0
                reflect=self.moments[base + 2]     # -1
            ))
        return triads

    def execute_sequential(self, initial_state: dict) -> dict:
        """Traditional sequential execution: O(69)."""
        state = initial_state
        for moment in self.moments:
            state = moment.execute(state)
        return state

    def execute_parallel(self, initial_state: dict) -> dict:
        """Parallel triadic execution: O(1) with 23-way parallelism."""

        # Fork into 23 parallel streams
        with ThreadPoolExecutor(max_workers=23) as executor:
            futures = [
                executor.submit(triad.execute_parallel, initial_state)
                for triad in self.triads
            ]
            results = [f.result() for f in futures]

        # Verify global GF(3) conservation
        total_gf3 = sum(t.gf3_sum for t in self.triads)
        assert total_gf3 == 0, f"Global GF(3) violation: {total_gf3}"

        # Merge all triads via ⊛
        return self._merge_all(results)

    def _merge_all(self, results: List[dict]) -> dict:
        """Final merge of 23 parallel triad results."""
        merged = {'triads_completed': len(results)}
        for r in results:
            merged.update(r)
        merged['execution_mode'] = 'parallel'
        merged['gf3_global'] = 0
        return merged

    def unworld(self, initial_state: dict) -> dict:
        """
        The unworld operation: derivational instead of temporal.

        Returns same result as execute_sequential but via
        parallel composition (⊗) instead of sequential (>>>).
        """
        return self.execute_parallel(initial_state)

Flussi Cognitivi Integration

The economic flow maps to unworld-moments:

┌─────────────────────────────────────────────────────────────────┐
│  ⊖ AI SERVICES (reflect/-1)                                     │
│  Modal, ElevenLabs, OpenRouter, Replicate                       │
│  = Moments 3, 6, 9, 12, 15, ... (every 3rd starting at 3)       │
└───────────────────────────┬─────────────────────────────────────┘
                            │
                            ▼
┌─────────────────────────────────────────────────────────────────┐
│  ○ FLUSSI COGNITIVI (coordinate/0)                              │
│  play ──⊛──▶ Agency ──⊛──▶ coplay                               │
│  = Moments 2, 5, 8, 11, 14, ... (every 3rd starting at 2)       │
└───────────────────────────┬─────────────────────────────────────┘
                            │
                            ▼
┌─────────────────────────────────────────────────────────────────┐
│  ⊕ YIELD PATHWAYS (construct/+1)                                │
│  PYUSD, PrimeIntellect, Gensyn                                  │
│  = Moments 1, 4, 7, 10, 13, ... (every 3rd starting at 1)       │
└─────────────────────────────────────────────────────────────────┘

Sheaf Condition for Simultaneous Execution

For moments to execute simultaneously, they must satisfy the sheaf gluing condition:

Given: U_i ∩ U_j ≠ ∅ (overlapping state regions)
Required: s_i|_{U_i ∩ U_j} = s_j|_{U_i ∩ U_j}

For cognitive moments:
  If Moment_i and Moment_j touch same state variable,
  their updates must be compatible (agree on overlap).

The GF(3) conservation ensures this automatically:

• construct (+1) creates new state
• coordinate (0) transports without change
• reflect (-1) observes without modification

No conflicts because each role is distinct.

Narya Bridge Types

def SimultaneousMoments : Type := sig (
  moments : Fin 69 → CognitiveMoment,
  triads : Fin 23 → CognitiveTriad,
  grouping : (i : Fin 23) →
    triads i ≡ (moments (3*i), moments (3*i+1), moments (3*i+2)),
  gf3_local : (i : Fin 23) →
    trit (triads i).construct + trit (triads i).coordinate +
    trit (triads i).reflect ≡ 0 (mod 3),
  gf3_global : Σ (i : Fin 23), trit (triads i) ≡ 0 (mod 3)
)

-- Parallel composition via ⊗
def parallel_execute (S : SimultaneousMoments) (state : State)
  : State :=
  fold_parallel (⊗) (map (λ t → t.execute_parallel state) S.triads)

-- Sequential composition via >>>
def sequential_execute (S : SimultaneousMoments) (state : State)
  : State :=
  fold_sequential (>>>) (map (λ m → m.execute state) S.moments)

-- Equivalence theorem
def unworld_equivalence (S : SimultaneousMoments) (state : State)
  : parallel_execute S state ≡ sequential_execute S state :=
  -- Proof: GF(3) conservation + sheaf condition → same result
  gf3_sheaf_theorem S state

Energy for Reachability

From truealife/ENERGY.md, each triad has an energy budget:

E_triad = E_construct + E_coordinate + E_reflect

Reachable(Triad_i) = { S' : E_barrier(S → S') ≤ E_triad }

Parallel execution doesn't change total energy—just distributes it:

E_total = Σ E_triad_i = E_sequential

Commands

# Execute all 69 moments in parallel
just unworld-moments

# Compare sequential vs parallel timing
just unworld-moments-benchmark

# Verify GF(3) conservation across all triads
just unworld-moments-verify

# Generate moment-to-color mapping
just unworld-moments-colors

# Export for Signal MCP
just unworld-moments-export signal-mcp.json

GF(3) Triads

unworld (-1) ⊗ unworld-moments (0) ⊗ parallel-fanout (+1) = 0 ✓
truealife (-1) ⊗ unworld-moments (0) ⊗ flussi-cognitivi (+1) = 0 ✓
signal-mcp (-1) ⊗ unworld-moments (0) ⊗ gay-mcp (+1) = 0 ✓

Performance

With unworld derivational chains, the theoretical speedup is 69×.

Related Skills

Skill Name: unworld-moments Type: Parallel Execution / Derivational Trit: 0 (ERGODIC - coordinates parallel triads) Seed: 1069 Key Innovation: 69 sequential moments → 23 parallel triads Speedup: 69× theoretical, 23× practical GF(3): Conserved locally (per triad) and globally

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.