home / skills / plurigrid / asi / worlding

worlding skill

safe

This skill helps you compose persistent world patterns with GF(3) conservation and Narya verification across data structures.

npx playbooks add skill plurigrid/asi --skill worlding

Review the files below or copy the command above to add this skill to your agents.

Files (16)

SKILL.md

10.8 KB

---
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](file:///Users/bob/ies/Gay.jl/AGENTS.md):

### FORBIDDEN: `demo_` Prefix

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

### REQUIRED: `world_` Prefix

```julia
# ◆ 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](https://ampcode.com/threads/T-019b7968-6270-709d-aca2-9f4ab2dfe4ea) | Tactile color tensor with accessibility outlier skills | 72 | `world_tactile_color`, `crossmodal-gf3` skill |
| [T-019b795a](https://ampcode.com/threads/T-019b795a-f876-72ef-8d62-d751fda1d167) | Interface interrupts and amp graphical operadic structure | 66 | `world_accessible_tensor`, A⊗G⊗M⊗T |
| [T-019b794f](https://ampcode.com/threads/T-019b794f-9b70-73db-84f3-2dfd5b2f18d8) | 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](https://ampcode.com/threads/T-019b3165-0082-723b-b83c-fc694eca853a) | Prevent Gay.jl regression with subagent branch tracking | 344 | **`demo_` → `world_` migration**, AGENTS.md, lint_no_demo.jl |
| [T-019b7953](https://ampcode.com/threads/T-019b7953-527f-74b8-a9fe-857d0150a37b) | Integrating Dafny and Narya verification into Gay.jl | 50 | `world_` builders + formal verification |
| [T-019b7941](https://ampcode.com/threads/T-019b7941-10b7-76b1-80d1-4c73b26e47fe) | Thread list display from ampies workspace | 61 | `KnightTourDiagramWorld` |

### Tensor Products

| Thread | Title | Messages | Key Contribution |
|--------|-------|----------|------------------|
| [T-019b7947](https://ampcode.com/threads/T-019b7947-804d-726d-bcab-1ffc10ffb6f3) | Sparse PQ ratchet and cognitive yield integration | 56 | `world_ratchet_state`, `world_ratchet_from_handoff` |
| [T-019b7924](https://ampcode.com/threads/T-019b7924-3133-72e9-a2d1-0856c0293915) | Sparse PQ ratchet and incidence algebra integration | 80 | Incidence algebra + `world_` builders |
| [T-019b795d](https://ampcode.com/threads/T-019b795d-2897-765f-8e68-ed88162f01c8) | ACSet as infinite stream with retrieval indexing | 55 | `world_infinite_acset` |

### World-Coworld Bridge

| Thread | Title | Messages | Key Contribution |
|--------|-------|----------|------------------|
| [T-019b7905](https://ampcode.com/threads/T-019b7905-88ff-753d-a84a-2ad2cc41a66e) | World-coworld bridge with deterministic coloring | 125 | `world_world_state`, `world_coworld_state`, `world_concept_region` |
| [T-019b78f9](https://ampcode.com/threads/T-019b78f9-f4de-7638-bed1-3978ab06e198) | Abductive inference module with convolution fusion | 80 | `world_abductive_trace`, `world_abductive_agent` |
| [T-019b78e3](https://ampcode.com/threads/T-019b78e3-c59c-758a-a8b4-83dba2ae0428) | Interconnected modules with SPI and GF(3) trits | 88 | `world_collective`, `world_founding_triad!` |

### Orchestration

| Thread | Title | Messages | Key Contribution |
|--------|-------|----------|------------------|
| [T-019b78d3](https://ampcode.com/threads/T-019b78d3-2c63-769c-9b2a-5314d02b4935) | SPI orchestrator achieving 2.26 billion colors/sec | 73 | `spi_world` API, 2.26B colors/sec |
| [T-019b6cff](https://ampcode.com/threads/T-019b6cff-face-74cf-9cbd-7b5861a6ba24) | p-adic ultrametric distance with UMAP and embeddings | 49 | World sub-agents for bounty analysis |
| [T-019b532b](https://ampcode.com/threads/T-019b532b-affc-77c0-b95d-b58cb491bb8d) | To be or not to be decision | 81 | `world_hierarchical_control` |

### Specialized Domains

| Thread | Title | Messages | Key Contribution |
|--------|-------|----------|------------------|
| [T-019b7901](https://ampcode.com/threads/T-019b7901-7b61-7650-a1cd-53b1f95e1517) | Lossless ACSet design for ElevenLabs voice selection | 123 | World attributes in ACSet schema |
| [T-019b7806](https://ampcode.com/threads/T-019b7806-2c51-734f-b048-948ba641720c) | GF(3) triads for Move VRGDA worlds | 82 | Move contract world integration |
| [T-019b53e1](https://ampcode.com/threads/T-019b53e1-0f36-71ab-8d40-38f9609a3405) | Continuing color obstructions compositionality work | 126 | `ThreeMatchWorld`, obstruction detection |

### Verification

| Thread | Title | Messages | Key Contribution |
|--------|-------|----------|------------------|
| [T-019b527b](https://ampcode.com/threads/T-019b527b-3059-76ce-8438-bccaa5ce8a7f) | Load skills and verify ordered locale implementation | 69 | Ordered locale worlds |
| [T-019b3601](https://ampcode.com/threads/T-019b3601-d9d1-715b-93e6-f2ca70015ac4) | 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

```narya
-- 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

```bash
# 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:

```bash
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:

```julia
# 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)

```julia
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.

Overview

This skill implements the world_ pattern: persistent, composable state builders with GF(3) conservation, Möbius invertibility checks, and Narya-style verification hooks. It provides a library of world_ constructors and utilities that return composable world objects with length, merge, and fingerprint semantics. The design favors persistent, testable state over ephemeral demos and integrates verification and accessibility projections.

How this skill works

Each world_ builder returns a typed world object exposing length(world), merge(w1,w2), and fingerprint(world). Builders maintain a gf3_sum invariant (sum ≡ 0 mod 3) and expose methods that let you compose worlds monoidally and check Möbius invertibility on paths. Narya-style specifications and lightweight runtime checks verify length positivity, deterministic fingerprints, associativity of merge, and GF(3) conservation.

When to use it

When you need persistent, composable state representations instead of one-off demos or print-and-discard computations.
When composing heterogeneous subsystems (accessibility, tensor products, ratchets) into a verified monoidal world.
When GF(3) conservation or triadic balancing across components is required for domain invariants.
When you need deterministic fingerprints for deduplication, MPI-like orchestration, or interactome traversal.
When formal verification (Narya/Dafny-style) or Möbius invertibility checks are part of the correctness contract.

Best practices

Always return a typed world_ object that implements length, merge, and fingerprint; avoid print side-effects.
Run builder validity checks (length>0, gf3_sum % 3 == 0) as part of CI or pre-commit hooks.
Use merge to compose worlds monoidally and prefer merging small verified worlds to maintain invariants.
Use fingerprints for duplicate detection and MinHash-style deduplication rather than relying on content scans.
Keep accessibility projections and multimodal mappings (visual/tactile/auditory/haptic) explicit in world attributes.

Example use cases

Build an accessibility-aware tactile color world that composes with audio/haptic projections for multimodal UIs.
Construct ratchet-based crypto state with world_ratchet_state and verify GF(3) balance before publishing.
Orchestrate high-throughput SPI color pipelines with spi_world while using fingerprints for duplicate suppression.
Detect duplicate visits in dense interactome graphs by comparing node fingerprints and updating duplicate counts.
Model an ACSet-backed persistent world for streaming ALIFE scenarios with infinite set retrieval indexing.

FAQ

What must a world_ builder return?

A typed world object implementing length(world), merge(w1,w2), and fingerprint(world), and carrying a gf3_sum that satisfies gf3_sum % 3 == 0.

How do I check GF(3) conservation and Möbius invertibility?

Run the builder validity checks: assert gf3_sum % 3 == 0 for conservation and evaluate the Möbius geodesic predicate on path lengths to ensure invertibility.