Polysimy Effect Chains

Polysimy Effect Chains Skill

"Multiple meanings flow through constraint networks to common solutions"

Status: NOT IN plurigrid/asi (local only) Trit: 0 (ERGODIC - coordinator) Color: #26D826 (Green) Principle: Effect polysimy → Propagation → Bisimulation → Common fixpoint

Overview

Polysimy = multiple effect interpretations coexisting in a cell/channel. Effect chains = sequences of transformations through propagator networks. Common solution = fixpoint where all polysemic interpretations converge.

This skill bridges:

• propagators (+1) - bidirectional constraint flow
• polysimy-effect-chains (0) - effect coordination
• temporal-coalgebra (-1) - bisimulation verification

Core Concepts

1. Polysemic Cells

Cells that hold multiple effect interpretations simultaneously:

{:id :cell-a
 :effects [{:type :generate :transform inc}
           {:type :coordinate :transform #(* % 2)}
           {:type :validate :transform identity}]
 :value 20
 :trit 0}

2. Effect Chain Composition

Effects compose through the cell, creating a derivation stream:

init(10) → generate(inc) → coordinate(*2) → validate(id) → 22

3. Common Solution via Bisimulation

Two effect chains have a common solution iff they are bisimilar:

bisimilar?(chain-a, chain-b) ⟺
  observe(chain-a).head == observe(chain-b).head ∧
  effects-count(chain-a) ≡ effects-count(chain-b) (mod 3)

API

(require '[polysimy-effect-chains :as pec])

;; Create polysemic cell
(def cell (pec/make-cell :my-cell {:trit 0}))

;; Chain effects
(def chain-a
  (-> cell
      (pec/chain {:type :generate :init 10 :f inc})
      (pec/chain {:type :coordinate :f #(* % 2)})
      (pec/chain {:type :validate :f identity})))

;; Verify common solution
(pec/find-common-solution chain-a chain-b)
;; => {:bisimilar true
;;     :common-value 22
;;     :gf3-conserved true}

GF(3) Integration

Forms valid triads:

propagators (+1) ⊗ polysimy-effect-chains (0) ⊗ temporal-coalgebra (-1) = 0 ✓
gay-mcp (+1) ⊗ polysimy-effect-chains (0) ⊗ sheaf-cohomology (-1) = 0 ✓

Temporary Verification Pattern

For temporary (intermediate) verification before full fixpoint:

(defn verify-temporary [cells depth]
  (loop [d 0]
    (when (< d depth)
      (let [obs (map observe cells)]
        (if (all-bisimilar? obs)
          {:status :bisimilar-at-depth :depth d}
          (recur (inc d)))))))

Commands

# Verify effect chain bisimulation
just polysimy-verify chain-a chain-b

# Find common solution
just polysimy-common [cells...]

# Temporary verification to depth N
just polysimy-temp-verify 10

Relationship to Uncommitted Skills

This skill relates to other local-only skills not in plurigrid/asi:

Mathematical Foundation

Effect Polysimy

$$\text{Poly}(C) = \sum_{e \in \text{Effects}} e \circ C$$

Multiple effects acting on the same cell carrier.

Bisimulation Quotient

$$X / {\sim} \cong \text{codom}(\text{anamorphism to } \nu F)$$

Cells are equivalent iff they unfold to the same infinite stream.

Common Solution Existence

$$\exists \text{common} \iff H^0(\mathcal{U}, \mathcal{F}) \neq \emptyset$$

A common solution exists iff the zeroth cohomology is non-empty.

Skill Name: polysimy-effect-chains Type: Effect Coordination Trit: 0 (ERGODIC) NOT IN: plurigrid/asi (should be committed) GF(3): Coordinates between generators and validators