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Asi worlding

Gay.jl world_ pattern: persistent composable state builders with GF(3) conservation, Möbius invertibility, and Narya verification

install
source · Clone the upstream repo
git clone https://github.com/plurigrid/asi
Claude Code · Install into ~/.claude/skills/
T=$(mktemp -d) && git clone --depth=1 https://github.com/plurigrid/asi "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/worlding" ~/.claude/skills/plurigrid-asi-worlding-024905 && rm -rf "$T"
manifest: skills/worlding/SKILL.md
source content

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:

MethodPurposeExample
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

ThreadTitleMessagesKey Contribution
T-019b7968Tactile color tensor with accessibility outlier skills72
world_tactile_color
, 
crossmodal-gf3
skill
T-019b795aInterface interrupts and amp graphical operadic structure66
world_accessible_tensor
, A⊗G⊗M⊗T
T-019b794fMöbius knight tours and interface interrupt operads53
world_interface_interrupt_operad
, 
world_tensor_product

Core Pattern Migration

ThreadTitleMessagesKey Contribution
T-019b3165Prevent Gay.jl regression with subagent branch tracking344
demo_
→ 
world_
migration, AGENTS.md, lint_no_demo.jl
T-019b7953Integrating Dafny and Narya verification into Gay.jl50
world_
builders + formal verification
T-019b7941Thread list display from ampies workspace61
KnightTourDiagramWorld

Tensor Products

ThreadTitleMessagesKey Contribution
T-019b7947Sparse PQ ratchet and cognitive yield integration56
world_ratchet_state
, 
world_ratchet_from_handoff
T-019b7924Sparse PQ ratchet and incidence algebra integration80Incidence algebra + 
world_
builders
T-019b795dACSet as infinite stream with retrieval indexing55
world_infinite_acset

World-Coworld Bridge

ThreadTitleMessagesKey Contribution
T-019b7905World-coworld bridge with deterministic coloring125
world_world_state
, 
world_coworld_state
, 
world_concept_region
T-019b78f9Abductive inference module with convolution fusion80
world_abductive_trace
, 
world_abductive_agent
T-019b78e3Interconnected modules with SPI and GF(3) trits88
world_collective
, 
world_founding_triad!

Orchestration

ThreadTitleMessagesKey Contribution
T-019b78d3SPI orchestrator achieving 2.26 billion colors/sec73
spi_world
API, 2.26B colors/sec
T-019b6cffp-adic ultrametric distance with UMAP and embeddings49World sub-agents for bounty analysis
T-019b532bTo be or not to be decision81
world_hierarchical_control

Specialized Domains

ThreadTitleMessagesKey Contribution
T-019b7901Lossless ACSet design for ElevenLabs voice selection123World attributes in ACSet schema
T-019b7806GF(3) triads for Move VRGDA worlds82Move contract world integration
T-019b53e1Continuing color obstructions compositionality work126
ThreeMatchWorld
, obstruction detection

Verification

ThreadTitleMessagesKey Contribution
T-019b527bLoad skills and verify ordered locale implementation69Ordered locale worlds
T-019b3601Three-qubit gates quantum computing116Semantically closed world

World Functions (578 total)

By Category

CategoryCountExample Functions
Core RNG12
world_gayrng
, 
world_incremental_hashing
, 
world_distributed_fingerprint
Tensor Products8
world_a
, 
world_g
, 
world_m
, 
world_agm_hatchery_tensor
Accessibility6
world_tactile_color
, 
world_accessible_interrupt_operad
Parallelism15
world_parallel_search
, 
world_genetic_search
, 
spi_world
Conceptual Spaces8
world_quality_dimension
, 
world_domain
, 
world_color_space
Crypto/Ratchet4
world_ratchet_state
, 
world_ratchet_from_handoff
Games/Collective6
world_collective
, 
world_founding_triad!
, 
world_project
Abductive4
world_abductive_trace
, 
world_abductive_agent
, 
world_abductive_field
ALIFE3
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 PatternWorld_ 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."

SDF Interleaving

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):

Primary Chapter: 10. Adventure Game Example

Concepts: autonomous agent, game, synthesis

GF(3) Balanced Triad

worlding (−) + SDF.Ch10 (+) + [balancer] (○) = 0

Skill Trit: -1 (MINUS - verification)

Secondary Chapters

  • Ch5: Evaluation
  • Ch3: Variations on an Arithmetic Theme
  • Ch6: Layering
  • Ch1: Flexibility through Abstraction
  • Ch4: Pattern Matching
  • Ch7: Propagators

Connection Pattern

Adventure games synthesize techniques. This skill integrates multiple patterns.