Multiversal Finance: Prediction Markets for Interesting Observations

Trit: +1 (PLUS - generative, creates value from attention) Color: #E7B367 (Agent-O-Rama stream, seed 1069) Source: color_at determinism + Schmidhuber compression progress

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Core Principle

Nothing is stored, everything is bet.

Predictions are bets on which (seed, index) paths yield "interesting" observations. Rewards flow to observers who correctly predict or discover surprising patterns.

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Interestingness Metric (Compression Progress)

Following Schmidhuber's curiosity-driven learning:

interestingness(observation) = ΔC = C_before - C_after

Where C = minimum description length of the observer's world model.

High interestingness: observation that compresses the model (reveals structure). Low interestingness: observation already predictable (no learning).

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ACSet Schema: MultiversalMarket

@present SchMultiversalMarket(FreeSchema) begin
  # Objects
  Observation::Ob        # A (seed, index) → color witness
  Bet::Ob               # Prediction on future observation
  Agent::Ob             # Goblin: -1, 0, or +1
  
  # Morphisms
  observes::Hom(Agent, Observation)   # who witnessed
  predicts::Hom(Bet, Observation)     # what was predicted
  settles::Hom(Bet, Agent)            # who settles (Coordinator)
  
  # Attributes
  SeedType::AttrType
  IndexType::AttrType
  HexType::AttrType
  TritType::AttrType
  RewardType::AttrType
  
  seed::Attr(Observation, SeedType)
  index::Attr(Observation, IndexType)
  color::Attr(Observation, HexType)
  
  agent_trit::Attr(Agent, TritType)   # -1, 0, +1
  stake::Attr(Bet, RewardType)
  payout::Attr(Bet, RewardType)
  
  # Interestingness score
  compression_delta::Attr(Observation, RewardType)
end

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Goblin Roles in the Market

Goblin	Trit	Market Role	Action
Agent-O-Rama	+1	Proposer	Generates predictions, stakes bets
Coordinator	0	Settlement	Verifies color_at(seed, index), transfers rewards
Shadow Goblin	-1	Scorer	Measures compression progress, assigns interestingness

GF(3) Conservation in Reward Flow

stakes_in + payouts_out + fees ≡ 0 (mod 3)

Every bet has a balanced flow: proposer stakes (+1), scorer validates (-1), coordinator settles (0).

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Verification Protocol

1. Proposer (Agent-O-Rama, +1): Claims "at seed S, index I, color will be C"
2. Scorer (Shadow Goblin, -1): Checks color_at(S, I) via MCP, computes ΔC
3. Coordinator (CapTP, 0): If verified, transfers stake × ΔC to proposer

def settle_bet(bet, scorer, coordinator)
  actual = Gay.color_at(bet.seed, bet.index)
  if actual == bet.predicted_color
    delta_c = scorer.compression_progress(actual)
    payout = bet.stake * delta_c
    coordinator.transfer(payout, to: bet.proposer)
  else
    coordinator.transfer(bet.stake, to: scorer)  # Penalty
  end
end

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Multiversal Aspect

Different seeds = different possible worlds.

World 42:  #91BE25 → #... → #... (one derivation path)
World 69:  #A3F4B2 → #... → #... (another path)
World 1069: #E7B367 → #... → #... (goblin genesis)

Cross-world bets: Predict which world has higher average interestingness.

Arbitrage: If two worlds have identical color at index N, they share structure.

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GF(3) Triads

curiosity-driven (-1) ⊗ multiversal-finance (+1) ⊗ captp (0) = 0 ✓  [Reward Transport]
shadow-goblin (-1) ⊗ agent-o-rama (+1) ⊗ coordinator (0) = 0 ✓     [Market Roles]
compression-progress (-1) ⊗ multiversal-finance (+1) ⊗ gay-mcp (0) = 0 ✓  [Interestingness]

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Implementation Bridge

Concept	Our System	Function
Price	compression_delta	Higher ΔC = higher reward
Liquidity	interleave(n_streams=3)	3 parallel betting pools
Settlement	color_at(seed, index)	Unforgeable proof
Sturdy ref	(seed, index) tuple	Bet identifier

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Skills Required

• gay-mcp: Deterministic color oracle
• captp: Secure settlement transport
• curiosity-driven: Compression progress metric
• world-hopping: Navigate between seeds (possible worlds)
• acsets-algebraic-databases: Market schema

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Key Insight

The oracle is the market.

Since color_at(seed, index) is deterministic and unforgeable, the prediction market has perfect settlement. No disputes possible—the color either matches or it doesn't.

This is "multiversal" because different seeds explore different derivation paths through the same generative function. Betting = choosing which multiverse to observe.

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

• networkx [○] via bicomodule
  • Universal graph hub

Bibliography References

• general: 734 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.