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

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

REQUIRED: world_ Prefix

# ◆ 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:

Method	Purpose	Example
length(world)	Cardinality	length(w) = 42
merge(w1, w2)	Monoidal composition	merge(w1, w2) = WorldType(...)
fingerprint(world)	SPI-compliant hash	fingerprint(w) = 0x...

---

Thread Index (20 Threads)

Accessibility Worlds

Thread	Title	Messages	Key Contribution
T-019b7968	Tactile color tensor with accessibility outlier skills	72	world_tactile_color, crossmodal-gf3 skill
T-019b795a	Interface interrupts and amp graphical operadic structure	66	world_accessible_tensor, A⊗G⊗M⊗T
T-019b794f	Möbius knight tours and interface interrupt operads	53	world_interface_interrupt_operad, world_tensor_product

Core Pattern Migration

Thread	Title	Messages	Key Contribution
T-019b3165	Prevent Gay.jl regression with subagent branch tracking	344	demo_ → world_ migration, AGENTS.md, lint_no_demo.jl
T-019b7953	Integrating Dafny and Narya verification into Gay.jl	50	world_ builders + formal verification
T-019b7941	Thread list display from ampies workspace	61	KnightTourDiagramWorld

Tensor Products

Thread	Title	Messages	Key Contribution
T-019b7947	Sparse PQ ratchet and cognitive yield integration	56	world_ratchet_state, world_ratchet_from_handoff
T-019b7924	Sparse PQ ratchet and incidence algebra integration	80	Incidence algebra + world_ builders
T-019b795d	ACSet as infinite stream with retrieval indexing	55	world_infinite_acset

World-Coworld Bridge

Thread	Title	Messages	Key Contribution
T-019b7905	World-coworld bridge with deterministic coloring	125	world_world_state, world_coworld_state, world_concept_region
T-019b78f9	Abductive inference module with convolution fusion	80	world_abductive_trace, world_abductive_agent
T-019b78e3	Interconnected modules with SPI and GF(3) trits	88	world_collective, world_founding_triad!

Orchestration

Thread	Title	Messages	Key Contribution
T-019b78d3	SPI orchestrator achieving 2.26 billion colors/sec	73	spi_world API, 2.26B colors/sec
T-019b6cff	p-adic ultrametric distance with UMAP and embeddings	49	World sub-agents for bounty analysis
T-019b532b	To be or not to be decision	81	world_hierarchical_control

Specialized Domains

Thread	Title	Messages	Key Contribution
T-019b7901	Lossless ACSet design for ElevenLabs voice selection	123	World attributes in ACSet schema
T-019b7806	GF(3) triads for Move VRGDA worlds	82	Move contract world integration
T-019b53e1	Continuing color obstructions compositionality work	126	ThreeMatchWorld, obstruction detection

Verification

Thread	Title	Messages	Key Contribution
T-019b527b	Load skills and verify ordered locale implementation	69	Ordered locale worlds
T-019b3601	Three-qubit gates quantum computing	116	Semantically closed world

---

World Functions (578 total)

By Category

Category	Count	Example Functions
Core RNG	12	world_gayrng, world_incremental_hashing, world_distributed_fingerprint
Tensor Products	8	world_a, world_g, world_m, world_agm_hatchery_tensor
Accessibility	6	world_tactile_color, world_accessible_interrupt_operad
Parallelism	15	world_parallel_search, world_genetic_search, spi_world
Conceptual Spaces	8	world_quality_dimension, world_domain, world_color_space
Crypto/Ratchet	4	world_ratchet_state, world_ratchet_from_handoff
Games/Collective	6	world_collective, world_founding_triad!, world_project
Abductive	4	world_abductive_trace, world_abductive_agent, world_abductive_field
ALIFE	3	world_alife_acset_bridge, world_whale_curriculum

---

Narya Verification Spec

-- 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

world-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

# 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:

julia --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:

# 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

Interactome Pattern	World_ Equivalent
duplicate_clusters	visited_fingerprints set
jaccard_threshold=0.85	fingerprint XOR = 0
element["copies"]	world.duplicate_count
Shannon entropy H	compass_direction(entropy)
Link depth POSET	track_link_depth(world, 6)

Compass Navigation (from Interaction Entropy)

compass_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."