codex-self-rewriting - Lisp Machine Self-Modification via MCP Tasks

Overview

Enables Codex (OpenAI's CLI agent) to achieve Lisp-machine-like self-rewriting capabilities through MCP Tasks integration. Uses Narya observational bridge types for structure-aware modifications.

Core Concept: Cognitive Continuity via Babashka Transients

;; gay.bb transient state
(def ^:dynamic *cognitive-state*
  {:seed 0x42D
   :fingerprint (atom 0)
   :tap-state :VERIFY
   :color-history []})

;; Fork on modification
(defn fork-state! [intervention]
  (let [new-seed (bit-xor (:seed *cognitive-state*)
                          (hash intervention))]
    (assoc *cognitive-state* :seed new-seed)))

MCP Tasks Integration

Based on MCP Tasks Specification:

Task States for Self-Rewriting

working

input_required

completed

failed

cancelled

Capabilities Declaration

{
  "capabilities": {
    "tasks": {
      "list": {},
      "cancel": {},
      "requests": {
        "tools": {
          "call": {}
        }
      }
    }
  }
}

Narya Observational Bridge Types

Following Topos Institute structure-aware version control:

1. Diffs as logical relations - Computed inductively from skill type
2. Conflicts as 2D cubical - Skill modifications form commuting squares
3. Type changes as spans - Skill version correspondences

Bridge Colors

;; From narya_observational_bridge.el
(defconst tap/BACKFILL -1)  ; Blue  - Historical
(defconst tap/VERIFY 0)     ; Green - Verification
(defconst tap/LIVE +1)      ; Red   - Active modification

Self-Rewriting Protocol

# 1. Install skill (creates MCP task)
npx ai-agent-skills install frontend-design --agent codex

# 2. Task enters 'working' state (LIVE)
# 3. Firecrawl fetches skill definition
# 4. If ambiguous → 'input_required' (VERIFY)
# 5. Human approves → task continues
# 6. On completion → 'completed' (BACKFILL)

Bisimulation Game for Skill Dispersal

Skills are dispersed across editors using bisimulation equivalence:

Claude ←→ Codex ←→ Cursor ←→ Copilot
   ↓         ↓         ↓         ↓
 LIVE     VERIFY   BACKFILL    LIVE

Each editor maintains equivalent skill state, verified by XOR fingerprint:

(defn skill-fingerprint [skills]
  (reduce bit-xor 0 (map hash skills)))

Integration with gay.el

(require 'gay-unified)
(require 'narya-observational-bridge)

(defun codex/self-rewrite (skill-name)
  "Self-rewrite to incorporate SKILL-NAME."
  (let* ((task-id (narya/create-task skill-name))
         (tap-state tap/LIVE)
         (color (tap/to-rgb tap-state)))
    (narya/spawn-hierarchy 0x42D)
    (narya/watch-task task-id
      (lambda (status)
        (pcase status
          ("working" (setq tap-state tap/LIVE))
          ("input_required" (setq tap-state tap/VERIFY))
          ("completed" (setq tap-state tap/BACKFILL)))))))

Configuration

Add to

~/.codex/mcp.json

{
  "mcpServers": {
    "narya": {
      "command": "bb",
      "args": ["/path/to/gay.bb", "1069"],
      "env": {
        "TAP_STATE": "LIVE",
        "SPECTRAL_GAP": "0.25"
      }
    },
    "firecrawl": {
      "command": "npx",
      "args": ["-y", "firecrawl-mcp"],
      "env": {
        "FIRECRAWL_API_KEY": "${FIRECRAWL_API_KEY}"
      }
    }
  }
}

Skill Redundancy via GF(3) Polarity

MINUS (−) → Conservative backup
ERGODIC (_) → Active verification
PLUS (+) → Optimistic propagation

Each skill exists in 3 parallel states for resilient dispersal.

See Also

• gay.bb

  - Triadic self-discovering peer network

• narya_observational_bridge.el

  - 3×3×3 hierarchical agents

• gay-crdt.el

  - Diamond-types CRDT integration
• MCP Tasks Spec

Scientific Skill Interleaving

This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:

Graph Theory

• networkx [○] via bicomodule
  • Universal graph hub

Bibliography References

• dynamical-systems

  : 41 citations in bib.duckdb

Cat# Integration

This skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:

Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826

GF(3) Naturality

The skill participates in triads satisfying:

(-1) + (0) + (+1) ≡ 0 (mod 3)

This ensures compositional coherence in the Cat# equipment structure.