---

name: worlding description: "Gay.jl world_ pattern: persistent composable state builders with GF(3) conservation, Möbius invertibility, and Narya verification" metadata: trit: 0 author: bmorphism version: "1.1.0" thread_count: 20 world_function_count: 578 interactome_bridge: true

Worlding Skill

"Demos print and discard. Worlds compose and persist."

Status: ✅ Production Ready
Trit: 0 (ERGODIC - coordinator)
Source: Gay.jl AGENTS.md + 20 Amp threads
Pattern: world_ prefix for persistent state builders

---

The World Pattern

From Gay.jl/AGENTS.md:

FORBIDDEN: demo_ Prefix

Copy# ◇ FORBIDDEN - prints and discards
function demo_ancestry_tracing(threads)
    println("Tracing ancestry...")  # Side effect!
    # ... computation discarded
end

REQUIRED: world_ Prefix

Copy# ◆ REQUIRED - returns composable structure
function world_ancestry_tracing(threads)::AncestryWorld
    AncestryWorld(materialize_ancestry!(threads))
end

World Builder Requirements

All world_ functions MUST return types implementing:

---

Thread Index (20 Threads)

Accessibility Worlds

Core Pattern Migration

Tensor Products

World-Coworld Bridge

Orchestration

Specialized Domains

Verification

---

World Functions (578 total)

By Category

---

Narya Verification Spec

Copy-- World pattern type in Narya HOTT
def World (A : Type) : Type :=
  sig (
    elements : A,
    length : Nat,
    fingerprint : UInt64,
    merge : World A → World A,
    gf3_sum : Int,  -- Must be 0 (mod 3)
  )

-- World builder constraint
def world_builder_valid (w : World A) : Type :=
  sig (
    length_positive : w.length > 0,
    fingerprint_deterministic : ∀ (seed : UInt64), fingerprint(w, seed) = fingerprint(w, seed),
    merge_associative : ∀ (w1 w2 w3 : World A), merge(merge(w1, w2), w3) = merge(w1, merge(w2, w3)),
    gf3_conserved : w.gf3_sum % 3 = 0,
  )

-- Möbius invertibility for world paths
def moebius_geodesic (path_length : Nat) : Bool :=
  moebius(path_length) ≠ 0

-- Accessible worlds theorem
def accessible_worlds_isomorphism : Type :=
  π_visual(W) ≅ π_tactile(W) ≅ π_auditory(W) ≅ π_haptic(W)

---

GF(3) Triads

Copyworld-memory-worlding (0) ⊗ gay-mcp (+1) ⊗ bisimulation-game (-1) = 0 ✓
worlding (0) ⊗ world-hopping (+1) ⊗ nix-acset-worlding (-1) = 0 ✓
worlding (0) ⊗ unworld (+1) ⊗ duckdb-timetravel (-1) = 0 ✓

---

Commands

Copy# Lint for demo_ violations
julia --project=. scripts/lint_no_demo.jl

# Test world builders
julia --project=. -e 'using Gay; w = world_tactile_color(6); println(length(w))'

# Verify GF(3) conservation
julia --project=. -e 'using Gay; w = world_agm_hatchery_tensor(); println(w.gf3_sum)'

# Generate accessibility projections
julia --project=. -e 'using Gay; w = world_accessible_interrupt_operad(); print_accessible_interrupt_report(w)'

---

Related Skills

• world-memory-worlding — Autopoietic strange loop
• world-hopping — Badiou possible world navigation
• world-runtime — Firecracker microVM worlding
• world-extractable-value — WEV = PoA - 1
• nix-acset-worlding — Nix store as ACSet
• crossmodal-gf3 — GF(3) → {Tactile, Auditory, Haptic}

---

Enforcement

Run before every commit:

Copyjulia --project=. scripts/lint_no_demo.jl

CI will fail on demo_ violations.

---

GitHub Interactome Bridge

The world_interactome_bridge.jl module connects graph-theoretic analysis to the world_ pattern:

"Opened Twice" Detection

When traversing dense interaction graphs, detect duplicate visits via fingerprint XOR:

Copy# From world_interactome_bridge.jl
function opened_twice(w1::InteractionWorld, w2::InteractionWorld)::Bool
    return fingerprint(w1) == fingerprint(w2)  # XOR = 0
end

function detect_duplicate_visit!(world, node)::Bool
    if node.fingerprint in world.visited_fingerprints
        world.duplicate_count += 1
        return true  # "Shortable opened twice"
    else
        push!(world.visited_fingerprints, node.fingerprint)
        return false
    end
end

Mapping to MinHash Deduplication

Compass Navigation (from Interaction Entropy)

Copycompass_direction(0.92)  # => "NORTH" (highest contention)
compass_direction(0.50)  # => "SOUTHEAST" (moderate)
compass_direction(0.20)  # => "SOUTH" (consensus)

---

"The world remembers itself by worlding itself."