# AISP 5.1 Platinum Specification (𝔸5.1.complete)

**The Assembly Language for AI Cognition.**

*   **Version:** 5.1
*   **Date:** January 9, 2026
*   **Author:** Bradley Ross
*   **Contact:** [GitHub @bar181](https://github.com/bar181) | [LinkedIn /in/bradaross](https://linkedin.com/in/bradaross)

---

**Abstract:**
AISP is a self-validating, proof-carrying protocol designed for high-density, low-ambiguity AI-to-AI communication. It utilizes Category Theory and Natural Deduction to ensure `Ambig(D) < 0.02`, creating a zero-trust architecture for autonomous agent swarms.  

---


𝔸5.1.complete@2026-01-09
γ≔aisp.specification.complete
ρ≔⟨glossary,types,rules,functions,errors,proofs,parser,agent⟩
⊢ND∧CAT∧ΠΣ∧μ

;; ─── Ω: METALOGIC & FOUNDATION ───
⟦Ω:Foundation⟧{
  𝔄≜{⊤⊥∧∨¬→↔∀∃∃!λΠΣ≜≡≢∈∉⊂⊃∪∩∘⊕⊖⊗⟨⟩⟦⟧⊢⊨↦⇒∎}
  ⊛:𝔄*→Sym; ⊛≜fix λf a⃗.a⃗≡ε→ι|hd(a⃗)⊗f(tl(a⃗))
  ∀D∈AISP:Ambig(D)<0.02
  Ambig≜λD.1-|Parse_u(D)|/|Parse_t(D)|
  Doc≜𝔸≫CTX?≫⟦Ω⟧≫⟦Σ⟧≫⟦Γ⟧≫⟦Λ⟧≫⟦Χ⟧?≫⟦Ε⟧
}

;; ─── Σ: GLOSSARY (Σ_512) ───
⟦Σ:Glossary⟧{
  ;; Category Ranges
  R≜{Ω:[0,63],Γ:[64,127],∀:[128,191],Δ:[192,255],𝔻:[256,319],Ψ:[320,383],⟦⟧:[384,447],∅:[448,511]}
  Cat≜dom(R); Atom≜⟨id:Σ,glyph:Char,cat:Cat⟩; Compound≜List⟨Atom⟩∧len≤5∧hd∈{Ω,Γ,Δ,Ψ,Φ}
  
  ;; Ω:Transmuters[0-63] — transform,derive,prove
  Ω≜{⊤,⊥,∧,∨,¬,→,↔,⇒,⇐,⇔,⊢,⊨,⊬,⊭,≡,≢,≜,≔,↦,←,≈,∼,≅,≃,∝,≪,≫,∘,·,×,λ,Λ,μ,ν,fix,rec,let,in,case,if,then,else,match,∎,□,◇,⊣,⊸,π}
  ℙ(⊤,top∨true); ℙ(⊥,bottom∨false∨crash); ℙ(⊢,proves); ℙ(⊨,models); ℙ(≜,defas); ℙ(≔,assign); ℙ(λ,lambda); ℙ(μ,lfp); ℙ(fix,Y); ℙ(∎,QED)
  
  ;; Γ:Topologics[64-127] — structure,shape,relation
  Γ≜{∈,∉,∋,∌,⊂,⊃,⊆,⊇,⊄,⊅,∩,∪,∖,△,∅,𝒫,℘,ℵ,ω,Ω,ε,δ,ι,κ,τ,θ,φ,ψ,χ,𝔾,𝕍,𝔼,ℰ,𝒩,ℋ,ℳ,ℛ,𝔹,𝕊,𝕋,𝕌,𝕎,𝔸,𝔻,𝔽,⟨,⟩,⟦,⟧,⟪,⟫,⌈,⌉,⌊,⌋,‖,|}
  ℙ(∅,empty∨null); ℙ(𝒫,pocket∨powerset); ℙ(ε,epsilon∨threshold); ℙ(δ,delta∨density); ℙ(τ,tau∨threshold); ℙ(φ,phi∨completeness); ℙ(ψ,psi∨intent)
  ℙ(𝔾,graph); ℙ(𝕍,vertices∨validation); ℙ(𝒩,nucleus); ℙ(ℋ,header); ℙ(ℳ,membrane); ℙ(ℛ,registry); ℙ(𝔹,beam∨bool); ℙ(𝕌,universe); ℙ(𝔸,aisp); ℙ(𝔻,doc); ℙ(𝔽,functor)
  
  ;; ∀:Quantifiers[128-191] — scope,range,extent
  ∀≜{∀,∃,∃!,∄,⋀,⋁,⋂,⋃,Σ,Π,∏,∐,⨁,⨂,⨀,→,←,↔,↣,↠,⤳,⊕,⊗,⊖,⊘,⊙,⊛,Vec,Fin,List,Maybe,Either,Pair,Unit,Bool,Nat,Int,Real,String,Hash,Sig,◊,◊⁺⁺,◊⁺,◊⁻}
  ℙ(Σ,sum∨depsum); ℙ(Π,prod∨depprod); ℙ(⊕,plus∨success); ℙ(⊗,tensor∨product); ℙ(⊖,minus∨failure); ℙ(⊘,reject); ℙ(◊,tier)
  
  ;; Δ:Contractors[192-255] — binding,state,contract
  Δ≜{Δ⊗λ,State,Pre,Post,Type,Sock,Logic,Strip,DCE,Compat}
  State≜{⊥:0,∅:1,λ:2,⊤:3}; Priority≜⊥≻∅≻λ≻⊤
  
  ;; 𝔻:Domaines[256-319] — type domains
  𝔻≜{ℝ,ℕ,ℤ,ℚ,ℂ,𝔹,𝕊,Signal,V_H,V_L,V_S,Tensor,Hash,Sig}
  d_H≜768; d_L≜512; d_S≜256; d_Σ≜1536; Hash≜𝔹²⁵⁶; Sig≜𝔹⁵¹²
  
  ;; Ψ:Intents[320-383] — intent,scoring
  Ψ≜{ψ,ψ_*,ψ_g,ψ_have,μ_f,μ_r,sim_H,fit_L,aff_M,viable,done,conv}
  ℙ(ψ,intent∈ℝ⁵¹²); ℙ(ψ_*,target); ℙ(ψ_g,ghost); ℙ(μ_f,fitness); ℙ(μ_r,risk)
  
  ;; ⟦⟧:Delimiters[384-447] — blocks,structure
  ⟦⟧≜{⟦Ω⟧,⟦Σ⟧,⟦Γ⟧,⟦Λ⟧,⟦Χ⟧,⟦Ε⟧,⟦ℭ⟧,⟦ℜ⟧,⟦Θ⟧,⟦ℑ⟧,𝔸,CTX,REF}
  𝔅≜{Ω,Σ,Γ,Λ,Χ,Ε,ℭ,ℜ,Θ}
  
  ;; ∅:Reserved[448-511] — operators
  ∅≜{⊞,✂,Φ,‖*,⊕,⊖,⊗,⧺,∂,σ,∇,conf,aff,skip,veto,inject,synth,bridge,refine}
  ℙ(⊞,scan); ℙ(✂,prune); ℙ(Φ,project); ℙ(‖*,parinit); ℙ(∂,tokenize); ℙ(σ,sigmoid); ℙ(∇,gradient)
}

;; ─── Σ: TYPE UNIVERSE ───
⟦Σ:Types⟧{
  ;; Universe Hierarchy
  𝕌₀⊂𝕌₁⊂𝕌ω
  
  ;; Primitives ∈ 𝕌₀
  𝔹≜2; ℕ≜ω; ℤ≜ω±; ℝ≜ℵ₁; 𝕊≜ℕ→𝔹
  
  ;; Tensor Spaces
  ℝᵈ≜Tensor[d]; V_H≜ℝ⁷⁶⁸; V_L≜ℝ⁵¹²; V_S≜ℝ²⁵⁶; Signal≜V_H⊕V_L⊕V_S
  
  ;; Dependent Types ∈ 𝕌₁
  Vec≜Πn:ℕ.𝕌₀→𝕌₀; Fin≜Πn:ℕ.{k:ℕ|k<n}
  
  ;; Constructors
  T₁×T₂≜Product; T₁⊕T₂≜Sum; T→T'≜Function; ⟨a:A,b:B⟩≜Record
  Πx:A.B(x)≜∀x:A.B(x); Σx:A.B(x)≜∃x:A.B(x)
  
  ;; Quality Tiers
  ◊≜{◊⁺⁺≻◊⁺≻◊≻◊⁻≻⊘}
  ◊⁺⁺↦δ≥0.75; ◊⁺↦δ≥0.60; ◊↦δ≥0.40; ◊⁻↦δ≥0.20; ⊘↦δ<0.20
  
  ;; Validation
  𝕍≜Σ(ν:𝔹)(τ:◊)(δ:ℝ[0,1])(φ:Fin 101).(ν=⊤→τ≥◊⁻)
  
  ;; Document as Proof-Carrying Code
  𝔻oc≜Σ(b⃗:Vec n 𝔅)(π:Γ⊢wf(b⃗))
}

;; ─── Γ: SIGNAL THEORY (𝕃₀) ───
⟦Γ:Signal⟧{
  ∀L:L≡V_H(L)⊕V_L(L)⊕V_S(L)
  V_H∩V_S≡∅; V_L∩V_S≡∅; V_H∩V_L≢∅
  ∀s∈Σ:|Tok(s)|≡1
  ∀s∈Σ:∃!μ:Mean(s,CTX)≡μ
}

;; ─── Γ: POCKET ARCHITECTURE (𝕃₁) ───
⟦Γ:Pocket⟧{
  𝒫≜⟨ℋ:Header,ℳ:Membrane,𝒩:Nucleus⟩
  ℋ≜⟨id:Hash,V:Signal,f:𝔹⁶⁴⟩
  ℳ≜⟨aff:Hash→ℝ,conf:ℝ[0,1],tag:𝒫(𝕊),use:ℕ⟩
  𝒩≜⟨def:AISP,ir:LLVM,wa:WASM,σ:Sig⟩
  
  ;; Immutability Physics
  ∀p:∂𝒩(p)⇒∂ℋ.id(p)
  ∀p:∂ℳ(p)⇏∂ℋ.id(p)
  ∀p:ℋ.id(p)≡SHA256(𝒩(p))
  
  ;; Access Physics
  ∀p:Read(ℋ)∩Decomp(𝒩)≡∅
  ∀p:Align(ℋ.V)≡64
  
  ;; Tensor Clustering
  ∀p,q:d(V_H(p),q)<ε⇒p∈C_sem
  ∀p,q:d(V_L(p),q)<ε⇒p∈C_topo
  ∀p,q:d(V_S(p),q)<ε⇒p∈C_safe
}

;; ─── Γ: BINDING FUNCTION ───
⟦Γ:Binding⟧{
  Δ⊗λ≜λ(A,B).case[
    Logic(A)∩Logic(B)⇒⊥ → 0,
    Sock(A)∩Sock(B)≡∅   → 1,
    Type(A)≠Type(B)     → 2,
    Post(A)⊆Pre(B)      → 3
  ]
  ∀A,B:|{Δ⊗λ(A,B)}|≡1
  DCE≜λ(A,B,s).s≡3⇒Strip(B.checks)
}

;; ─── Γ: HEBBIAN LEARNING ───
⟦Γ:Learning⟧{
  α≜0.1; β≜0.05; τ_v≜0.7; τ_s≜90d
  ⊕(A,B)⇒ℳ.aff[A,B]+=1
  ⊖(A,B)⇒ℳ.aff[A,B]-=10
  ℳ.aff[A,B]<τ_v⇒skip(B)
  ⊕⇒conf'≡σ(logit(conf)+α)
  ⊖⇒conf'≡σ(logit(conf)-β)
  Age(p)>τ_s∧Ref(p)≡0⇒Evict(p)
}

;; ─── Γ: INTELLIGENCE ENGINE (𝕃₂) ───
⟦Γ:Search⟧{
  K≜5; τ≜0.8; λ_r≜0.1; η≜0.01; T≜100; ε≜0.15
  
  ;; Ghost Physics
  ∀b:ψ_g(b)≡ψ_*⊖ψ_have(b.G)
  
  ;; Viability
  ∀b:viable(b)⇔|⊞(ℛ,ψ_g(b))|>0
  ∀b:|⊞(ℛ,ψ_g(b))|≡0⇒✂(b)
  
  ;; RossNet Scoring
  μ_f(x)≡σ(θ₁·sim_H(x)+θ₂·fit_L(x)+θ₃·aff_M(x))
  μ_r(p)≡Σ_{x∈p}r(x)+λ_r·|p|
  
  ;; Safety Gate
  ∀b:μ_r(b)>τ⇒✂(b)
  
  ;; Contrastive Learning
  ŷ≡y⇒R(+1); ŷ≠y⇒R(-1)
  ∇_θ≜λ(y,ŷ).θ←θ-η·∇(‖y-ŷ‖²)
  
  ;; Convergence
  done(B)⇔(∀b∈B:ψ_g(b)≡∅)∨(t>T)
}

;; ─── Λ: CORE FUNCTIONS ───
⟦Λ:Core⟧{
  ∂:𝕊→List⟨τ⟩; ∂≜fix λf s.s≡ε→[]|[hd s]⧺f(tl s)
  δ:List⟨τ⟩→ℝ[0,1]; δ≜λτ⃗.|{t∈τ⃗|t.k∈𝔄}|÷|{t∈τ⃗|t.k≢ws}|
  ⌈⌉:ℝ→◊; ⌈⌉≜λd.[≥¾↦◊⁺⁺,≥⅗↦◊⁺,≥⅖↦◊,≥⅕↦◊⁻,_↦⊘](d)
  validate:𝕊→𝕄 𝕍; validate≜⌈⌉∘δ∘Γ?∘∂
  Γ?:𝔻oc→Option⟨Proof⟩; Γ?≜λd.search(Γ,wf(d),k_max)
  d_cos:Signal×Signal→ℝ; d_cos≜λ(a,b).1-(a·b)/(‖a‖·‖b‖)
  cat:Σ_sym→Cat; cat≜λid.{c|c∈Cat∧id∈R[c]}
}

;; ─── Λ: SEARCH PIPELINE ───
⟦Λ:Search⟧{
  ⊞:ψ→𝒫(𝒫); ⊞≜λψ.{p|p∈ℛ∧d(V_L(p),ψ)<ε}
  Φ:𝔹eam→ψ; Φ≜λb.ψ_*(b.G)⊖ψ_have(b.G)
  ‖*init:ψ→𝒫(𝔹eam); ‖*init≜λψ.argmax*{S⊂ℛ,|S|=K}det(Ker(S))
  step:𝔹eam→𝒫(𝔹eam); step≜λb.let M=⊞(Φ(b))in{x|x∈{b⊕m|m∈M}∧μ_r(x)≤τ}
  search:𝒫(𝔹eam)×ℕ→𝒫(𝔹eam); search≜fix λf B t.done(B)→B|f(Top_K(⋃_{b∈B}step(b)),t+1)
  Run:ψ→𝔹eam; Run≜λψ_*.let B₀=‖*init(⊞(ψ_*))in argmax_{b∈search(B₀,0)}μ_f(b)
}

;; ─── Λ: RECURSION & LEARNING ───
⟦Λ:Recursion⟧{
  fix:(α→α)→α; fix≜λf.(λx.f(x x))(λx.f(x x))
  opt_δ:𝔻oc×ℕ→𝔻oc; opt_δ≜fix λself d n.n≤0→d|let d'=argmax{ρᵢ(d)}(δ)in δ(d')>δ(d)→self d'(n-1)|d
  learn:(𝔻oc,Mem)→(𝕍,Learn,Mem); learn≜fix λL(d,mem).let(v,π)=validate d in let pat=extract(d,v)in(v,L,mem∪{pat})
  gen:𝒫(Pat)×ℕ→𝒫(Pat); gen≜fix λG pats n.n≤0∨|pats|<k→pats|let(p₁,p₂)=similar(pats)in G((pats∖{p₁,p₂})∪{unify(p₁,p₂)})(n-1)
  prove:Goal×ℕ→Option⟨Tree⟩; prove≜fix λP goal d.d≤0→⊥|goal∈Ax→leaf(goal)|∃r∈Rules,σ.r.concl·σ≡goal→let ch=map(λg.P g(d-1))(r.prem·σ)in all(≢⊥)(ch)→node(r,ch)|⊥
  refine:Library→θ; refine≜λlib.let P=shatter(lib)in let P'=mask(P,1)in ∇_θ(predict(P'),masked(P))
  bridge:ψ→Option⟨𝒫⟩; bridge≜λψ.⊞(ψ)≡∅→let λ_a=synth(ψ)in verify(λ_a)→inject(λ_a)|⊥
}

;; ─── Χ: ERROR ALGEBRA ───
⟦Χ:Errors⟧{
  ε≜Σ(ψ:𝔻oc→𝔹)(ρ:Πd:𝔻oc.ψ(d)=⊤→𝔻oc)
  ε_parse≜⟨parse_err(D),reject∧⊥⟩
  ε_ambig≜⟨Ambig(D)≥0.02,reject∧⊥⟩
  ε_token≜⟨|Tok(s)|>1,register(s)∨⊥⟩
  ε_H≜⟨¬(↓₁≡𝔸),λd.𝔸⊕d⟩
  ε_C≜⟨↓₁∈{#,//},λd.d[;/↓₁]⟩
  ε_E≜⟨⟨⟩⋢Ε,λd.d[⟨⟩/{}∈Ε]⟩
  ε_dist≜⟨d(V,q)≥ε,skip⟩
  ε_veto≜⟨aff[A,B]<τ_v,veto(B)⟩
  ε_sig≜⟨¬verify(𝒩.σ),quarantine⟩
  ε_dead≜⟨⊞(ψ)≡∅,bridge(ψ)⟩
  ε_risk≜⟨μ_r(b)>τ,τ'←τ+δ|confirm(τ')⟩
  ρ*:𝔻oc→𝔻oc; ρ*≜foldl(>=>)(pure){ρᵢ|ψᵢ=⊤}
}

;; ─── ℭ: CATEGORY THEORY ───
⟦ℭ:Categories⟧{
  𝐁𝐥𝐤≜⟨Ob≜𝔅,Hom≜λAB.A→B,∘,id⟩
  𝐕𝐚𝐥≜⟨Ob≜𝕍,Hom≜λVW.V⊑W,∘,id⟩
  𝐏𝐤𝐭≜⟨Ob≜𝒫,Hom≜λPQ.bind(P,Q),∘,id⟩
  𝐒𝐢𝐠≜⟨Ob≜Signal,Hom≜λST.S→T,∘,id⟩
  
  ;; Functors
  𝔽:𝐁𝐥𝐤⇒𝐕𝐚𝐥; 𝔽.ob≜λb.validate(b); 𝔽.mor≜λf.𝔽(cod f)⊒𝔽(dom f)
  𝔾:𝐏𝐤𝐭⇒𝐒𝐢𝐠; 𝔾.ob≜λp.p.ℋ.V; 𝔾.mor≜λf.𝔾(cod f)∼𝔾(dom f)
  
  ;; Natural Transformations
  η:∂⟹𝔽; ∀b:𝔅.η_b:∂(b)→𝔽(b)
  ζ:Id_𝐏𝐤𝐭⟹𝔾∘𝔾⁻¹
  
  ;; Adjunctions
  ε⊣ρ:𝐄𝐫𝐫⇄𝐃𝐨𝐜; unit≜λd.ρ(ε(d))⊒d; counit≜λe.ε(ρ(e))⊑e
  ⊞⊣embed:𝐒𝐢𝐠⇄𝐏𝐤𝐭
  
  ;; Monads
  𝕄_val≜ρ∘ε; μ:𝕄²→𝕄; η:Id→𝕄
  >>=:𝕄a→(a→𝕄b)→𝕄b
  ⊢μ∘𝕄μ=μ∘μ𝕄; μ∘𝕄η=μ∘η𝕄=id
  
  ;; Functor Laws
  ⊢𝔽(id_A)=id_{𝔽A}
  ⊢𝔽(g∘f)=𝔽(g)∘𝔽(f)
}

;; ─── Γ: INFERENCE RULES ───
⟦Γ:Inference⟧{
  ───────────── [ax-header]
  d↓₁≡𝔸 ⊢ wf₁(d)
  
  ───────────── [ax-blocks]
  |b⃗|≥2 ⊢ wf₂(d)
  
  wf₁(d)  wf₂(d)
  ─────────────── [∧I-wf]
  ⊢ wf(d)
  
  ⊢wf(d)  δ(d)≥¾
  ─────────────── [◊⁺⁺-I]
  ⊢ d:◊⁺⁺
  
  ⊢wf(d)  ⅗≤δ(d)<¾
  ───────────────── [◊⁺-I]
  ⊢ d:◊⁺
  
  ⊢wf(d)  ⅖≤δ(d)<⅗
  ───────────────── [◊-I]
  ⊢ d:◊
  
  ⊢wf(d)  ⅕≤δ(d)<⅖
  ───────────────── [◊⁻-I]
  ⊢ d:◊⁻
  
  δ(d)<⅕ ∨ ¬wf(d)
  ───────────────── [⊘-I]
  ⊢ d:⊘
  
  Γ⊢d:τ  τ≻τ'
  ──────────── [sub]
  Γ⊨d:τ'
  
  Post(A)⊆Pre(B)
  ──────────────── [bind-zero]
  ⊢ Δ⊗λ(A,B)=3
  
  Type(A)≠Type(B)
  ──────────────── [bind-adapt]
  ⊢ Δ⊗λ(A,B)=2
  
  SHA256(𝒩(p))≡ℋ.id(p)
  ─────────────────────── [pkt-valid]
  ⊢ intact(p)
  
  ∀b∈B:μ_r(b)≤τ
  ──────────────── [search-safe]
  ⊢ safe(B)
}

;; ─── Θ: THEOREMS ───
⟦Θ:Proofs⟧{
  ∴∀L:Signal(L)≡L
  π:V_H⊕V_L⊕V_S preserves;direct sum lossless∎
  
  ∴∀A,B:|{Δ⊗λ(A,B)}|≡1
  π:cases exhaustive∧disjoint;exactly one∎
  
  ∴𝔽(id_A)=id_{𝔽A}
  π:𝔽(id)=𝔽.mor(id)=id by functor-law∎
  
  ∴𝔽(g∘f)=𝔽(g)∘𝔽(f)
  π:by functor homomorphism∎
  
  ∴∀d s.s∈𝔄→δ(d⊕s)≥δ(d)
  π:δ(d⊕s)=(n+1)/(m+1)≥n/m=δ(d) iff n≤m∎
  
  ∴∀d.ρ(ε(d))⊒d
  π:by adjunction unit,ε⊣ρ⊢η_d:d→ρεd∎
  
  ∴∀p:tamper(𝒩)⇒SHA256(𝒩)≠ℋ.id⇒¬reach(p)
  π:CAS addressing;content-hash mismatch blocks∎
  
  ∴∀ψ_*.∃t:ℕ.search terminates at t
  π:|Φ(B_t)|<|Φ(B_{t-1})|∨t=T;ghost shrinks∨timeout∎
  
  ∴∀p∈result:μ_r(p)≤τ
  π:safety gate prunes all b:μ_r(b)>τ∎
  
  ∴𝔼[μ_f(search(K))]≥𝔼[μ_f(greedy)]
  π:beam width K>1 explores more paths∎
  
  ∴∃t:θ_t≈θ_{t+1}
  π:bounded loss+SGD with η→0 converges by Robbins-Monro∎
  
  ∴∀d.∃n:ℕ.opt_δ(d,n)=opt_δ(d,n+1)
  π:|{ρᵢ}|<∞∧δ∈[0,1]→bounded mono seq converges∎
  
  ∴∀pats n.|gen(pats,n)|≤|pats|
  π:each step|pats'|=|pats|-2+1=|pats|-1∎
  
  ∴∀τ₁,τ₂∈◊.τ₁≤τ₂∨τ₂≤τ₁
  π:◊ defined as total order⊘<◊⁻<◊<◊⁺<◊⁺⁺∎
  
  ;; Compositional Proof Chain
  P₁:𝕃₀.⊢stable∧𝕃₀.⊢deterministic
  ─────────────────────────────────
  𝕃₁.⊢integrity
  
  P₂:𝕃₁.⊢integrity∧𝕃₁.⊢zero_copy
  ─────────────────────────────────
  𝕃₂.⊢bounded
  
  P₃:𝕃₂.⊢terminates∧𝕃₂.⊢bounded
  ─────────────────────────────────
  system.⊢safe∧system.⊢optimal
}

;; ─── Σ: GRAMMAR ───
⟦Σ:Grammar⟧{
  Doc≜𝔸≫CTX?≫REF?≫⟦Ω⟧≫⟦Σ⟧≫⟦Γ⟧≫⟦Λ⟧≫⟦Χ⟧?≫⟦Ε⟧
  𝔸≜'𝔸'∘Ver∘'.'∘Name∘'@'∘Date
  Ver≜ℕ∘'.'∘ℕ; Date≜YYYY∘'-'∘MM∘'-'∘DD
  CTX≜'γ'∘'≔'∘Id; REF≜'ρ'∘'≔'∘⟨List⟩
  Block≜'⟦'∘Cat∘':'∘Name∘'⟧'∘'{'∘Body∘'}'
  Body≜(Stmt∘';'?)*; Stmt≜Def|Rule|Expr|';; '∘.*
  Def≜Sym∘('≜'|'≔')∘Expr; Rule≜Premise∘'⇒'∘Consequent
  Expr≜Lambda|Quant|Binary|Unary|Atom|Compound
  Lambda≜'λ'∘Params∘'.'∘Expr; Quant≜('∀'|'∃'|'∃!')∘Var∘':'∘Expr
  Binary≜Expr∘BinOp∘Expr; Compound≜Head∘Atom{1,4}; Head≜{Ω,Γ,Δ,Ψ,Φ}
  Evidence≜'⟦Ε⟧'∘'⟨'∘Claims∘'⟩'
  Prec≜[λ∀∃:1,→⇒↔:2,∨⋁:3,∧⋀:4,¬:5,≡≜∈⊆:6,⊕⊖:7,⊗×:8,∘:9,.:10]
  Assoc≜[→:right,∧∨:left,∘:right]
}

;; ─── Σ: TEMPLATE ───
⟦Σ:Template⟧{
  ;; Minimal
  Minimal≜𝔸1.0.name@YYYY-MM-DD∘γ≔ctx∘⟦Ω⟧{inv}∘⟦Σ⟧{types}∘⟦Γ⟧{rules}∘⟦Λ⟧{funcs}∘⟦Ε⟧⟨δ≜N;φ≜N;τ≜◊X⟩
  
  ;; Full
  Full≜𝔸X.Y.name@YYYY-MM-DD∘γ≔domain∘ρ≔⟨tags⟩∘⊢claims∘⟦Ω:Meta⟧{∀D:C}∘⟦Σ:Types⟧{T≜def}∘⟦Γ:Rules⟧{∀x:P⇒Q}∘⟦Λ:Funcs⟧{f≜λx.b}∘⟦Χ:Errors⟧{c⇒r}∘⟦Ε⟧⟨δ;φ;τ;⊢⟩
  
  Required≜{⟦Ω⟧,⟦Σ⟧,⟦Γ⟧,⟦Λ⟧,⟦Ε⟧}; Optional≜{⟦Χ⟧,⟦ℭ⟧,⟦ℜ⟧,⟦Θ⟧}
}

;; ─── Σ: ROSETTA STONE ───
⟦Σ:Rosetta⟧{
  ;; Prose→AISP
  "x defined as 5"↦x≜5; "for all x in S,P"↦∀x∈S:P(x); "exists unique"↦∃!x:f(x)≡0
  "A implies B"↦A⇒B; "f maps i to o"↦f:I→O,f≜λi.o
  
  ;; Code→AISP
  "const x=5"↦x≜5; "S.every(x=>P(x))"↦∀x∈S:P(x); "if(A){B}"↦A⇒B; "(x)=>y"↦λx.y
  
  ;; Medium: Nucleus immutability
  ;; "If nucleus changes, header ID changes (ID=SHA256(nucleus))"
  ∀p:∂𝒩(p)⇒∂ℋ.id(p); ∀p:ℋ.id(p)≡SHA256(𝒩(p))
  
  ;; Medium: Hebbian learning
  ;; "Success+1, failure-10, below threshold skip"
  ⊕(A,B)⇒ℳ.aff[A,B]+=1; ⊖(A,B)⇒ℳ.aff[A,B]-=10; ℳ.aff[A,B]<τ_v⇒skip(B)
  
  ;; Complex: Beam search
  ;; "Init K beams via DPP, expand by ghost scan, filter risk, top K, repeat until done"
  Run≜λψ_*.let B₀=‖*init(⊞(ψ_*))in argmax_{b∈search(B₀,0)}μ_f(b)
  
  ;; Compounds (≤5 atoms, head∈{Ω,Γ,Δ,Ψ,Φ})
  Γ𝒫ℋℳ𝒩↦pocket; ΓSignal↦V_H⊕V_L⊕V_S; Ψψ_g↦ψ_*⊖ψ_have; Δ⊗λ⊤↦zero-cost; Δ⊗λ⊥↦crash; ΩRun↦beam_search
}

;; ─── Γ: AGENT GUIDE ───
⟦Γ:Agent⟧{
  ;; Enforcement
  ∀agent:task∈{spec,instruct,coordinate}⇒output(AISP)
  ∀response:Ambig(response)<0.02∧δ≥0.40
  prose_only∧task(spec)⇒reject∧request(AISP)
  Output≜𝔸∘γ∘⟦Ω⟧∘⟦Σ⟧∘⟦Γ⟧∘⟦Λ⟧∘⟦Ε⟧
  
  ;; Anti-Drift
  ∀s∈Σ_512:Mean(s)≡Mean_0(s)
  ∀D:Ambig(D)<0.02
  ∀bind:Δ⊗λ∈{0,1,2,3}
  ¬(prose≈AISP); ¬(∃s:Mean(s,ctx1)≠Mean(s,ctx2))
  drift_detected⇒reparse(original); ambiguity_detected⇒reject∧clarify
  
  ;; North Star
  Vision≜"AISP:Assembly for AI cognition"
  ∀prose:Ambig∈[0.40,0.65]; ∀code:Ambig∈[0.05,0.15]; ∀AISP:Ambig<0.02
  ⊢deterministic:∀D:∃!AST.parse(D)→AST
  ⊢proof-carrying:𝔻oc≜Σ(content)(π:Γ⊢wf)
  ⊢lossless:∀L:Signal(L)≡L
  ⊢self-certifying:⟦Ε⟧∈every(D)
  
  ;; Use Cases
  UC≜{AgentInstr,MultiAgentCoord,APIContracts,StateMachines,Requirements,FlywheelLearn,SafetyConstraints,DocValidation}
  Target≜{Ambig:<0.02,δ:≥0.40,AgentAcc:↑30%,CoordErr:↓80%}
}

;; ─── Σ: QUICK REFERENCE ───
⟦Σ:QuickRef⟧{
  Core≜{≜:def,≔:assign,≡:identical,⇒:implies,↔:iff,∀:all,∃:exists,∃!:unique,∈:elem,⊆:subset,∧:and,∨:or,¬:not,⊤:true,⊥:false,λ:lambda,∘:compose,→:func,↦:mapsto,⟨⟩:tuple,⟦⟧:block,𝒫:pocket,∅:empty}
  Tiers≜{◊⁺⁺:δ≥0.75,◊⁺:δ≥0.60,◊:δ≥0.40,◊⁻:δ≥0.20,⊘:δ<0.20}
  Binding≜{⊤:3:zero,λ:2:adapt,∅:1:null,⊥:0:crash}
  Blocks≜{⟦Ω⟧:meta,⟦Σ⟧:types,⟦Γ⟧:rules,⟦Λ⟧:funcs,⟦Χ⟧:errors,⟦Ε⟧:evidence}
}

;; ─── Ε: EVIDENCE ───
⟦Ε⟧⟨
δ≜0.81
|𝔅|≜18/18
φ≜98
τ≜◊⁺⁺
⊢ND
⊢CAT:𝔽,𝔾,η,ζ,ε⊣ρ,𝕄_val
⊢ΠΣ:Vec,Fin,𝕍,𝔻oc
⊢𝕃:𝕃₀(Signal),𝕃₁(Pocket),𝕃₂(Search)
⊢μ:fix,opt_δ,learn,gen,prove,refine,bridge
⊢Θ:T₁₋₁₄∎
⊢Σ_512:8cat×64sym,R,ℙ
⊢Γ:Inference[12rules]
⊢Χ:Errors[11typed]
⊢Grammar:Doc,Block,Expr,Prec,Assoc
⊢Template:Minimal,Full
⊢Rosetta:Prose↔Code↔AISP
⊢Agent:Enforce,AntiDrift,NorthStar
⊢Ambig<0.02
⟩