plurigrid Transitive Weep Skill
Trit: 0 (ERGODIC/Coordinator)
Domain: open-games, category-theory, flow-networks, self-organization
Algebra: GF(3) conservation via coplay feedback
Overview
Transitive Weep = flow propagation through open games network with self-balancing GF(3) conservation. The "weep" metaphor: value flows like tears through the graph, finding its own level.
╔════════════════════════════════════════════════════════════════════════╗
║ TRANSITIVE WEEP ARCHITECTURE ║
╠════════════════════════════════════════════════════════════════════════╣
║ ║
║ Source ──play──▶ Game₁ ──play──▶ Game₂ ──play──▶ ... ──▶ Balance ║
║ │ │ │ │ ║
║ │ ◀─coplay───┘ ◀─coplay───┘ ◀─coplay──────┘ ║
║ │ ║
║ └────────────────── Σ(trit × flow) ≈ 0 ──────────────────────────┘║
║ ║
║ Play: Forward flow transformation at each node ║
║ Coplay: Backward utility → strategy update for GF(3) balance ║
║ ║
╚════════════════════════════════════════════════════════════════════════╝
Core Concepts
1. Open Games (Play/Coplay)
Each world is an open game with:
- Play:
(incoming_flow, bias) → observation - Coplay:
(utility, global_sum, generation) → strategy_update
struct OpenGame
id::Symbol
trit::Int8 # -1, 0, +1
play::Function # Forward pass
coplay::Function # Backward pass (self-reinvention)
state::State # Mutable: generation, bias, memory
end
2. Transitive Closure
If A weeps to B, and B weeps to C, then A transitively weeps to C:
A →weep→ B →weep→ C ⟹ A →weep*→ C
The flow decays exponentially: flow(C) = flow(A) × w(A,B) × w(B,C) × decay²
3. GF(3) Self-Balancing
The weep stops when global sum is conserved:
Σ(trit_i × flow_i) ≈ 0 (mod 3)
Coplay feedback adjusts routing to prioritize nodes whose trits would correct the running sum.
Triadic World Graph
┌──────────────────────────────────────────┐
│ 26 ACCESSIBLE WORLDS │
└──────────────────────────────────────────┘
MINUS (-1) ERGODIC (0) PLUS (+1)
────────── ────────── ─────────
A: algebraic B: bmorphism C: catcolab
D: ducklake E: elevenlabs F: firecracker
G: gay-colors H: hatchery I: iroh
J: juvix K: kubernetes L: localsend
M: mcp N: narya O: open-games
P: plurigrid Q: quantum R: rama
S: siggraph T: topos U: unison
V: voice W: wasm X: xogot
Y: yoneda Z: zig
Adjacency (Triadic Connections)
Each world connects to worlds that form balanced triads:
{:A [:B :C] ;; -1 → {0, +1} = balanced potential
:B [:A :C :G] ;; 0 → {-1, +1, -1}
:C [:T :N :A] ;; +1 → {0, 0, -1}
:G [:J :R :B] ;; -1 → {-1, +1, 0}
...}
Algorithm
(defn transitive-weep [source initial-flow max-depth]
(loop [frontier [[source initial-flow 0]]
visited #{}
global-sum 0.0
trace []]
;; Early exit: balanced
(when (and (> (count trace) 5) (< (abs global-sum) 0.1))
(return {:status :balanced :trace trace :sum global-sum}))
(let [[node flow depth] (first frontier)
game (get-game node)
result (play! game flow global-sum)]
;; Update global sum
(swap! global-sum + (:contribution result))
;; Coplay: which neighbors would balance?
(let [needed-trit (cond (> global-sum 0.3) -1
(< global-sum -0.3) +1
:else 0)
neighbors (sort-by-trit-distance (get-neighbors node) needed-trit)]
;; Add top neighbors to frontier
(recur (into (rest frontier)
(map #(vector % (* flow 0.7) (inc depth))
(take 2 neighbors)))
(conj visited node)
global-sum
(conj trace result))))))
Game Composition
Sequential: G₁ ; G₂
G₁ ; G₂ : trit(G₁;G₂) = trit(G₁) + trit(G₂)
Flow passes through G₁, then G₂.
Parallel: G₁ ⊗ G₂
G₁ ⊗ G₂ : trit(G₁⊗G₂) = (trit(G₁) + trit(G₂)) mod 3
Flow splits, processes in parallel, recombines.
Balanced Triad Composition
A(-1) ; B(0) ; C(+1) → trit = 0 ✓
Example: Weep from A
A (algebraic-julia) trit:-1 obs:0.905 Δ:-0.905 Σ:-0.905
C (catcolab) trit:+1 obs:0.573 Δ:+0.573 Σ:-0.332 ← balancing!
B (bmorphism) trit:+0 obs:0.317 Δ:+0.000 Σ:-0.332
T (topos) trit:+0 obs:0.401 Δ:+0.000 Σ:-0.332
N (narya) trit:+0 obs:0.201 Δ:+0.000 Σ:-0.332
O (open-games) trit:+1 obs:0.254 Δ:+0.254 Σ:-0.078 ✓ BALANCED!
Status: balanced-early at iteration 6, Σ = -0.078 ≈ 0
DuckDB Schema
CREATE TABLE weep_traces (
trace_id VARCHAR PRIMARY KEY,
source VARCHAR NOT NULL,
node VARCHAR NOT NULL,
depth INT NOT NULL,
observation DOUBLE NOT NULL,
contribution DOUBLE NOT NULL,
running_sum DOUBLE NOT NULL,
utility DOUBLE NOT NULL,
trit TINYINT NOT NULL
);
CREATE TABLE game_compositions (
composition_id VARCHAR PRIMARY KEY,
game_id VARCHAR NOT NULL,
composition_type VARCHAR NOT NULL,
components VARCHAR[] NOT NULL,
combined_trit TINYINT NOT NULL,
gf3_conserved BOOLEAN NOT NULL
);
Integration
| Skill | Trit | Bridge |
|---|---|---|
open-games |
+1 | Play/Coplay semantics |
accessible-worlds |
0 | 26-world superposition |
gay-mcp |
+1 | Color assignment to nodes |
bisimulation-game |
0 | Attacker/Defender structure |
world-hopping |
0 | Badiou triangle navigation |
Self-Reinvention
The weep is autopoietic: each game modifies its own bias based on utility feedback:
function coplay(utility, global_sum, generation)
correction = if global_sum > 0.5 && trit == -1
0.1 # Boost MINUS to correct positive imbalance
elseif global_sum < -0.5 && trit == 1
0.1 # Boost PLUS to correct negative imbalance
else
-0.05 # Default decay
end
correction / (1 + 0.1 * generation) # Diminishing returns
end
Commands
# Run transitive weep demo
bb src/openapi_to_catp.bb --tts-demo
# Query weep traces
duckdb zubyul_interactome.duckdb "SELECT * FROM weep_traces WHERE source='A'"
# Check game compositions
duckdb zubyul_interactome.duckdb "SELECT * FROM game_compositions WHERE gf3_conserved"
Skill Name: transitive-weep
Type: Flow Network / Open Games
Trit: 0 (ERGODIC)
GF(3): Self-balancing via coplay feedback
Autopoietic Marginalia
The interaction IS the skill improving itself.
Every use of this skill is an opportunity for worlding:
- MEMORY (-1): Record what was learned
- REMEMBERING (0): Connect patterns to other skills
- WORLDING (+1): Evolve the skill based on use
Add Interaction Exemplars here as the skill is used.