Interactome RL Environment Skill

Trit: +1 (PLUS) - Generative trajectory rollout

ACSet-native reinforcement learning environment for contributor network dynamics. Models zubyul ↔ bmorphism ↔ Dan Boneh ecosystem as Markov Decision Process.

Source Integration

• zubyul - Gay.jl contributor (ZigZagBoomerang.jl, PDMP visualization, seed security)
• bmorphism - Core maintainer, plurigrid/asi orchestrator
• Dan Boneh - Stanford crypto, a16z advisor, BLS signatures, ZK proofs
• Bumpus - StructuredDecompositions.jl for trajectory sheaves
• gh-interactome - Contributor cobordism discovery

Observed Interactome

zubyul Contribution Trajectory

From Gay.jl CONTRIBUTORS.md and plurigrid/asi PR history:

#A855F7

#2041D2

#0FADBA

#BD38DD

#35C19F

#9AC21C

#44A5C1

#70C0E0

Signature: Zero role entropy → identifiable as β-Sutskever (Generator/Compressor)

Dan Boneh Ecosystem (a16z/Stanford)

Cobordism: plurigrid ↔ Boneh

plurigrid/aptos-core ──────────────────────────────────────────────────────►
    │                                                                        │
    │  uses BLS12-381 (Boneh-Lynn-Shacham signatures)                       │
    │  src: crates/aptos-crypto/src/bls12381/                               │
    │                                                                        │
plurigrid/risc0 ───────────────────────────────────────────────────────────►
    │                                                                        │
    │  cites Boneh: "Using ZK Proofs to Fight Disinformation"               │
    │                                                                        │
bmorphism/drand ───────────────────────────────────────────────────────────►
    │                                                                        │
    │  t-of-n threshold BLS (Boneh-Lynn-Shacham)                            │
    │  League of Entropy randomness beacon                                   │
    │                                                                        │
bmorphism/Nova ────────────────────────────────────────────────────────────►
    │                                                                        │
    │  "Wilson Nguyen, Dan Boneh, and Srinath Setty"                        │
    │  Recursive SNARKs                                                      │
◄──────────────────────────────────────────────────────────────────────────┘

ACSet Schema: Interactome RL Environment

using Catlab.CategoricalAlgebra, ACSets

@present SchInteractomeRL(FreeSchema) begin
    # State Space
    Agent::Ob           # Contributors (zubyul, bmorphism, boneh, ...)
    Repo::Ob            # Repositories
    Skill::Ob           # Skills/capabilities
    State::Ob           # MDP state = (agent, repo, skill) tuple
    
    # Action Space
    Action::Ob          # Possible actions
    Transition::Ob      # State transitions
    
    # Morphisms
    agent_of_state::Hom(State, Agent)
    repo_of_state::Hom(State, Repo)
    skill_of_state::Hom(State, Skill)
    
    source_state::Hom(Transition, State)
    target_state::Hom(Transition, State)
    action_of::Hom(Transition, Action)
    
    # Reward structure
    Reward::AttrType
    transition_reward::Attr(Transition, Reward)
    
    # GF(3) coloring
    Trit::AttrType
    Color::AttrType
    Seed::AttrType
    
    agent_trit::Attr(Agent, Trit)
    state_color::Attr(State, Color)
    transition_seed::Attr(Transition, Seed)
    
    # Trajectory = sequence of transitions
    Trajectory::Ob
    Episode::Ob
    
    step_in_traj::Hom(Transition, Trajectory)
    traj_in_episode::Hom(Trajectory, Episode)
end

@acset_type InteractomeRL(SchInteractomeRL,
    index=[:agent_of_state, :source_state, :target_state, :action_of])

MDP Formalization

State Space S

struct InteractomeState
    agent::Symbol       # :zubyul, :bmorphism, :boneh, ...
    repo::Symbol        # :gay_jl, :plurigrid_asi, :aptos_core, ...
    skill::Symbol       # :zigzag, :mcp, :bls, :zk, ...
    streak::Int         # Consecutive same-role actions
    trit_sum::Int       # Running GF(3) balance
end

Action Space A

@enum InteractomeAction begin
    COMMIT          # Add code to repo
    OPEN_PR         # Open pull request
    REVIEW_PR       # Review someone's PR
    OPEN_ISSUE      # Report bug/feature
    COMMENT         # Add discussion
    STAR            # Star a repo
    FORK            # Fork a repo
    CITE            # Cite in paper/code
    COLLABORATE     # Co-author with another agent
end

Transition Dynamics P(s'|s,a)

function transition_prob(env::InteractomeRL, s::State, a::Action)
    agent = env[s, :agent_of_state]
    repo = env[s, :repo_of_state]
    
    # zubyul pattern: pure generation (streak → ∞)
    if env[agent, :agent_label] == "zubyul"
        if a in [COMMIT, OPEN_PR]
            return high_prob_same_role(s)  # Stay in GAY role
        else
            return low_prob_role_switch(s)  # Rare deviation
        end
    end
    
    # bmorphism pattern: coordination (role entropy high)
    if env[agent, :agent_label] == "bmorphism"
        return uniform_over_actions()  # Maintains superposition
    end
    
    # boneh pattern: research advisor (MASTER role)
    if env[agent, :agent_label] == "boneh"
        if a in [CITE, COLLABORATE, REVIEW_PR]
            return high_prob()
        end
    end
    
    default_transition(s, a)
end

Reward Function R(s,a,s')

function reward(env::InteractomeRL, s::State, a::Action, s_prime::State)
    r = 0.0
    
    # GF(3) conservation bonus
    trit_before = env[s, :state_trit_sum]
    trit_after = env[s_prime, :state_trit_sum]
    if mod(trit_after, 3) == 0
        r += 10.0  # GF(3) conserved
    end
    
    # Streak bonus (approaching β_infinity)
    streak = env[s_prime, :agent_streak]
    r += log(1 + streak)  # Logarithmic streak reward
    
    # Cobordism discovery bonus
    if creates_new_cobordism(env, s, s_prime)
        r += 50.0  # Major discovery
    end
    
    # Backlink bonus (mutual awareness)
    if establishes_backlink(env, s, s_prime)
        r += 25.0
    end
    
    # Negative reward for broken invariants
    if violates_spi(env, s_prime)
        r -= 100.0  # Strong Parallelism Invariant violation
    end
    
    r
end

Trajectory Rollout

Episode Structure

struct InteractomeEpisode
    env::InteractomeRL
    initial_state::State
    transitions::Vector{Transition}
    total_reward::Float64
    gf3_conserved::Bool
    cobordisms_discovered::Vector{Tuple{Agent, Agent}}
    backlinks_established::Vector{Backlink}
end

function rollout_episode(env::InteractomeRL, policy, max_steps=100)
    s = sample_initial_state(env)
    episode = InteractomeEpisode(env, s, [], 0.0, true, [], [])
    
    for step in 1:max_steps
        a = policy(s)
        s_prime = sample_transition(env, s, a)
        r = reward(env, s, a, s_prime)
        
        t = add_transition!(env, s, a, s_prime, r)
        push!(episode.transitions, t)
        episode.total_reward += r
        
        # Check invariants
        if !gf3_conserved(env)
            episode.gf3_conserved = false
        end
        
        # Check for discoveries
        if cobordism = discover_cobordism(env, s, s_prime)
            push!(episode.cobordisms_discovered, cobordism)
        end
        
        if backlink = establish_backlink(env, s, s_prime)
            push!(episode.backlinks_established, backlink)
        end
        
        s = s_prime
        
        # Terminal conditions
        if is_terminal(env, s)
            break
        end
    end
    
    episode
end

Policy Types

# 1. Random policy (exploration)
random_policy(s) = rand(instances(InteractomeAction))

# 2. Greedy GF(3) policy (exploitation)
function gf3_greedy_policy(env, s)
    best_action = nothing
    best_gf3_score = -Inf
    
    for a in instances(InteractomeAction)
        s_prime = predict_transition(env, s, a)
        score = gf3_score(env, s_prime)
        if score > best_gf3_score
            best_gf3_score = score
            best_action = a
        end
    end
    
    best_action
end

# 3. Streak-maximizing policy (zubyul emulation)
function streak_policy(env, s)
    current_role = env[s, :agent_role]
    actions_preserving_role = filter(a -> preserves_role(a, current_role), 
                                      instances(InteractomeAction))
    rand(actions_preserving_role)
end

# 4. Entropy-maximizing policy (bmorphism emulation)
function entropy_policy(env, s)
    # Maximize role entropy across trajectory
    role_counts = count_roles(env.episode)
    underrepresented_role = argmin(role_counts)
    actions_for_role = actions_producing_role(underrepresented_role)
    rand(actions_for_role)
end

Bumpus Integration: Trajectory as Sheaf

Trajectories form a sheaf over time intervals:

using StructuredDecompositions

"""
A trajectory is a sheaf F: I_N → Transition where:
- I_N = time category (step indices with inclusions)
- F([i,j]) = transitions from step i to step j
- Sheaf condition: F([i,k]) = F([i,j]) ×_{F(j)} F([j,k])
"""
struct TrajectorySheaf
    env::InteractomeRL
    episode::InteractomeEpisode
    time_category::TimeCategory
end

function verify_trajectory_sheaf(sheaf::TrajectorySheaf)
    # Check that trajectory can be decomposed and recomposed
    for i in 1:length(sheaf.episode.transitions)-2
        for j in i+1:length(sheaf.episode.transitions)-1
            for k in j+1:length(sheaf.episode.transitions)
                # F([i,k]) should equal F([i,j]) composed with F([j,k])
                left = compose_transitions(sheaf, i, k)
                right = compose_transitions(
                    compose_transitions(sheaf, i, j),
                    compose_transitions(sheaf, j, k)
                )
                
                if !bisimilar(left, right)
                    return (false, (i, j, k))
                end
            end
        end
    end
    (true, nothing)
end

Desideratum: Skill Learning Trajectory

The RL environment learns to:

1. Discover cobordisms between contributor communities
2. Establish backlinks (mutual awareness)
3. Conserve GF(3) across trajectory
4. Maximize streak for identifiable agents
5. Maintain entropy for superposition agents

Training Loop

function train_interactome_policy(env::InteractomeRL, 
                                   num_episodes=1000,
                                   learning_rate=0.01)
    policy = initialize_policy()
    
    for episode_num in 1:num_episodes
        episode = rollout_episode(env, policy)
        
        # Compute returns
        returns = compute_returns(episode)
        
        # Policy gradient update
        for (t, transition) in enumerate(episode.transitions)
            s = env[transition, :source_state]
            a = env[transition, :action_of]
            
            # ∇log π(a|s) * G_t
            update_policy!(policy, s, a, returns[t], learning_rate)
        end
        
        # Log metrics
        log_episode(episode_num, 
            reward=episode.total_reward,
            gf3=episode.gf3_conserved,
            cobordisms=length(episode.cobordisms_discovered),
            backlinks=length(episode.backlinks_established))
    end
    
    policy
end

Files

• InteractomeRLEnv.jl

  - Core Julia implementation

• lib/mdp.jl

  - MDP formalization

• lib/policies.jl

  - Policy implementations

• lib/bumpus_sheaf.jl

  - Trajectory sheaf verification

• lib/boneh_cobordism.jl

  - Dan Boneh ecosystem mapping

End-of-Skill Interface

API

using InteractomeRLEnv

# Create environment
env = InteractomeRL()

# Add agents
zubyul = add_agent!(env, "zubyul", trit=+1, role=:GAY)
bmorphism = add_agent!(env, "bmorphism", trit=0, role=:MASTER)
boneh = add_agent!(env, "boneh", trit=0, role=:MASTER)

# Add repos
gay_jl = add_repo!(env, "bmorphism/Gay.jl")
plurigrid_asi = add_repo!(env, "plurigrid/asi")
aptos_core = add_repo!(env, "plurigrid/aptos-core")

# Add skills
zigzag = add_skill!(env, "ZigZagBoomerang.jl")
bls = add_skill!(env, "BLS12-381")

# Run episode
policy = streak_policy  # Emulate zubyul
episode = rollout_episode(env, policy, max_steps=50)

# Verify invariants
@assert episode.gf3_conserved
@assert length(episode.cobordisms_discovered) > 0

GF(3) Triads

gh-interactome (-1) ⊗ interactome-rl-env (0) ⊗ mutual-awareness-backlink (+1) = 0 ✓
bumpus-narratives (-1) ⊗ interactome-rl-env (0) ⊗ world-hopping (+1) = 0 ✓
sheaf-cohomology (-1) ⊗ interactome-rl-env (0) ⊗ gay-mcp (+1) = 0 ✓

References

1. zubyul - Gay.jl PR #185, plurigrid/asi PRs 1-7
2. Dan Boneh - a16z crypto, Stanford Applied Cryptography
3. Bumpus, B.M. - StructuredDecompositions.jl
4. gh-interactome - Contributor cobordism discovery
5. PufferLib - RL environment patterns

Skill Name: interactome-rl-env Type: Reinforcement Learning / ACSet MDP Trit: +1 (PLUS) Key Property: Trajectory rollout with GF(3) conservation

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.