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Behaviour Surprisal Analysis
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Based on SOC occupation classification
| name | behaviour-surprisal-analysis |
| description | Behaviour Surprisal Analysis |
| version | 1.0.0 |
Status: Production Ready (v3.0 - Cat# Integration) Trit: 0 (ERGODIC - measurement/observation) Principle: S(x) = -logโ(P(x|attention_mode)) Frame: Tri-channel prediction evaluation with AGM belief revision + Cat# bicomodule structure
Behaviour Surprisal Analysis calculates information-theoretic surprise between predictions and observed outcomes using three complementary attention channels mapped to Cat# = Comod(P) structure:
| Channel | Trit | Home | Poly Op | Kan Role | Description |
|---|---|---|---|---|---|
| Direct (ฮฑ) | โ1 | Span | ร (product) | Ran_K | Exact artifact matching |
| Diffuse (ฮฒ) | 0 | Prof | โ (parallel) | Adj | Thematic/structural matching |
| Meta (ฮณ) | +1 | Presheaves | โ (substitution) | Lan_K | Capability/infrastructure tracking |
Total Surprisal = ฮฑยทS_direct + ฮฒยทS_diffuse + ฮณยทS_meta
where ฮฑ + ฮฒ + ฮณ = 1 and typically ฮฑ=0.3, ฮฒ=0.5, ฮณ=0.2
This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):
Concepts: eval, apply, interpreter, environment
behaviour-surprisal-analysis (โ) + SDF.Ch5 (โ) + [balancer] (โ) = 0
Skill Trit: -1 (MINUS - verification)
Evaluation interprets expressions. This skill processes or generates evaluable forms.
The Direct and Meta channels form a Galois adjunction through the Diffuse bridge:
ฮฑ (abstract)
Direct โโโโโโโโโโโโโโ Diffuse
โ โ
โ CatSharp โ ฮณ (concretize)
โ Scale โ
โโโโโโโโโโโโโโโโโโโโโโโโ
Meta
GF(3): (โ1) + (0) + (+1) = 0 โ
Each channel lives in a specific Cat# home:
โโโโโโโโโโโโโโฌโโโโโโโโโโโโโโฌโโโโโโโโโโโฌโโโโโโโโโโโโโโโโฌโโโโโโโโโโโโโ
โ Channel โ Poly Op โ Kan Role โ Structure โ Home โ
โโโโโโโโโโโโโโผโโโโโโโโโโโโโโผโโโโโโโโโโโผโโโโโโโโโโโโโโโโผโโโโโโโโโโโโโค
โ Direct โ ร (prod) โ Ran_K โ cofree t_p โ Span โ
โ Diffuse โ โ (para) โ Adj โ bicomodule โ Prof โ
โ Meta โ โ (subst) โ Lan_K โ free m_p โ Presheaves โ
โโโโโโโโโโโโโโดโโโโโโโโโโโโโโดโโโโโโโโโโโดโโโโโโโโโโโโโโโโดโโโโโโโโโโโโโ
Predictions and observations form bicomodule pairs. Coherence is verified by:
Surprisal values map to pitch classes via the CatSharp scale:
| Trit | Pitch Classes | Chord Type | Hz Range |
|---|---|---|---|
| +1 (PLUS) | {0, 4, 8} | Augmented triad | C-E-G# |
| 0 (ERGODIC) | {3, 6, 9} | Diminished 7th | D#-F#-A-C |
| โ1 (MINUS) | {1,2,5,7,10,11} | Fifths cycle | C#,D,F,G,A#,B |
;; Surprisal โ Pitch class โ Frequency
(defn surprisal->pitch-class [surp]
(mod (Math/round (* (min surp 10.0) 1.2)) 12))
(defn pitch-class->freq [pc]
(* 261.63 (Math/pow 2 (/ pc 12.0)))) ;; C4 = 261.63 Hz
Enable with --sonify flag to hear the surprisal as tones via sox.
Based on Baker 2023:
K * ฯ = (K โ ยฌฯ) + ฯ (Levi Identity)
Predictions ranked by entrenchment:
(defn kappa-rank [belief]
(- (Math/log (/ 1 (max 0.01 (:confidence belief))))))
Lower ฮบ = more entrenched = harder to revise.
# Full Cat# analysis with sonification
bb ~/.claude/skills/behaviour-surprisal-analysis/analyse.bb \
--predictions predictions.json \
--observed observed.json \
--alpha 0.3 --beta 0.5 --gamma 0.2 \
--sonify
# With capability tracking
bb analyse.bb \
--predictions predictions.json \
--observed observed.json \
--skills-before skills_t0.txt \
--skills-after skills_t30.txt
# Direct-heavy (Span home focus)
bb analyse.bb --alpha 0.7 --beta 0.2 --gamma 0.1
# Meta-heavy (Presheaves home focus)
bb analyse.bb --alpha 0.1 --beta 0.3 --gamma 0.6 --sonify
{
"predictions": {
"direct": [
{"content": "Ruby MCP SDK for skill markets", "confidence": 0.8},
{"content": "VirtualizationBridge sandbox test", "confidence": 0.7}
],
"diffuse": [
{"theme": "GF(3) conservation", "keywords": ["trit", "lattice", "conservation"]},
{"theme": "skill markets", "keywords": ["confidential", "commitment", "beacon"]}
],
"meta": {
"skills_before": 45,
"mcp_servers_before": 12,
"config_hash": "a3f2c1"
}
},
"observed": {
"threads": [
"Ruby MCP SDK for confidential skill markets",
"GF(3) skill composition and Galois connection verification",
"Derangement operators and GF(3) entropy management"
],
"capability_events": [
{"type": "skill_install", "count": 373, "source": "plurigrid/asi"},
{"type": "mcp_addition", "server": "world_a_aptos"}
]
}
}
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โ BEHAVIOUR SURPRISAL ANALYSIS v3.0 (Cat# + AGM) โ
โ ฮฑ=0.30 (Span/Ran) ฮฒ=0.50 (Prof/Adj) ฮณ=0.20 (Presh/Lan) โ
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
DIRECT ATTENTION (Home: Span, Kan: Ran_K)
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
Prediction โ Match โ S_dir โ Trit โ PC โ Home
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโผโโโโโโโโผโโโโโโโโผโโโโโโโผโโโโโผโโโโโ
VirtualizationBridge sandbox โ 34.9% โ 1.52 โ + โ 2 โ Span
...
CAT# COHERENCE
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
Galois adjunction ฮฑ โฃ ฮณ: โ coherent
Bicomodule compatibility: 85.0% (โ)
CATSHARP SONIFICATION
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโ
โช Direct (Ran_K): 293.7 Hz
โช Diffuse (Adj): 329.6 Hz
โช Meta (Lan_K): 261.6 Hz
The skill participates in balanced triads:
behaviour-surprisal-analysis (0) โ catsharp-galois (0) โ gay-mcp (-1) + operad-compose (+1) = 0 โ
# Internal channel triad
Direct (โ1) + Diffuse (0) + Meta (+1) = 0 โ
| Prediction Style | Recommended (ฮฑ,ฮฒ,ฮณ) | Cat# Focus |
|---|---|---|
| Specific artifacts | (0.6, 0.3, 0.1) | Span heavy |
| Thematic directions | (0.2, 0.6, 0.2) | Prof heavy |
| Capability exploration | (0.2, 0.3, 0.5) | Presheaves heavy |
| Mixed/balanced | (0.3, 0.5, 0.2) | Bicomodule equilibrium |
(require '[behaviour-surprisal-analysis :as bsa])
;; Full Cat# analysis
(bsa/combined-analysis
predictions observed
0.3 0.5 0.2 ;; ฮฑ ฮฒ ฮณ
before-state after-state
capability-events
true) ;; sonify?
;; Galois adjunction verification
(bsa/verify-galois-unit direct-result)
;; Bicomodule coherence check
(bsa/check-bicomodule-coherence direct diffuse meta)
;; Sonify channel
(bsa/sonify-channel results "Direct" 0.3)
The tri-channel Cat# model reflects:
GF(3) conservation IS the naturality condition of Cat# equipment:
For a triad (sโโ, sโ, sโโ):
Ran_K(sโโ) โ[bicomodule]โ sโ โ[bicomodule]โ Lan_K(sโโ)
The commuting square:
G(f) โ ฮท_A = ฮท_B โ F(f)
Becomes the GF(3) equation:
(โ1) + (0) + (+1) โก 0 (mod 3)
Skill Name: behaviour-surprisal-analysis Version: 3.0.0 (Cat# Integration) Type: Prediction Evaluation / Information Theory / Belief Revision / Category Theory Trit: 0 (ERGODIC) GF(3): Conserved via Cat# bicomodule structure Dependencies: sox (optional, for sonification) Sources:
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