Editing Openai/69596681-3f7c-8006-b9fd-01d9d8191763 (section)

=== Assistant: Understood. ===
Understood. Below is a MAXIMALLY CONCENTRATED, ALGORITHMIC NORMAL FORM (ANF) that collapses Blocks 0–19 into a single machine-learning–style executable semantics. This is not narrative; it is a formal compression intended for static analysis, CI enforcement, and mechanized reasoning. No new degrees of freedom are introduced. This is a refinement, not an extension.

ALGORITHMIC NORMAL FORM (ANF) — EXECUTABLE SEMANTICS

STATE SPACE
Let Σ_run = ⟨S_spec,D,seed,Artifacts,Flags,Verdict⟩
Initial: Artifacts=∅, Flags=∅, Verdict=⊥

SPEC LOCK
S_bytes := CanonicalSerialize(S_spec)
MethodHash := SHA256(S_bytes)
assert(MethodHash == embedded_hash) else INVALID

AXIOM GUARD
∀ Ai∈A: assert(Ai==true) else INVALID

TYPE SYSTEM
assert(TypeCheck(S_spec,D)) else INVALID

DATA GATE
Q := DataValidity(D)
if Q==INVALID: Verdict:=1; goto ATTRIBUTION

MODEL
P := PredictionOperator(S_spec)
b frozen

RESIDUALS
∀i: r_i := φ(y_i) − φ(P_i(θ,b))
Σ := blockdiag(Σ_i)
assert(SPD(Σ)) else INVALID

STRUCTURAL
V_struct := OR_i [ r_iᵀ Σ_i⁻¹ r_i > τ_struct ]
if V_struct: Verdict:=1; goto ATTRIBUTION

FEASIBILITY
Feasible := ∃θ∈M_IR s.t. V_struct(θ)==0
if !Feasible: Verdict:=1; goto ATTRIBUTION

IDENTIFIABILITY
J := ∂r/∂θ
F := Jᵀ Σ⁻¹ J
k_min := rank(F)
if k_min==0: Verdict:=1; goto ATTRIBUTION
θ_id := Project(θ, range(F))

LIKELIHOOD
ℒ(r|θ_id) := (1−ε)𝓝(r|0,Σ)+ε𝓣(r|0,Σ,ν)
logℒ := log ℒ

EVIDENCE
Z := ∫ ℒ(r|θ_id) π(θ_id) dθ_id   // via Block 11
ΔlnZ := lnZ − lnZ₀
EvidenceFailure := [ΔlnZ < Λ]
if EvidenceFailure: Verdict:=1; goto ATTRIBUTION

ROBUSTNESS (MC)
for j=1…N_MC:
 D_j := Π(D,seed_j)
 I_j := CollapseIndicator(D_j)
 if (1/j)∑_{t≤j}I_t ≥ f_c: RobustnessFailure:=1; break
if RobustnessFailure: goto PRECISION

PRECISION
for p=p₀…p_max:
 D_p := Ψ_p(D)
 if CollapseIndicator(D_p): PrecisionFailure:=1; break
if PrecisionFailure: Verdict:=1; goto ATTRIBUTION

VERDICT
Verdict := 0

ATTRIBUTION
G := BuildFailureDAG(Flags,precedence)
Emit(G)

CERTIFICATION
if Verdict==0:
 for k=1…H:
  𝒟_k := ⋃_{i≤k}D_i
  if CollapseIndicator(𝒟_k): CERTIFIED_STAND:=0; goto AUDIT
 CERTIFIED_STAND:=1

AUDIT
Bundle := MerkleSeal({MethodHash,DataHash,Artifacts,Verdict,CERTIFIED_STAND})
Emit(Bundle)

END ANF

ALGORITHMIC PROPERTIES (ML-RELEVANT)

• Deterministic finite-state transducer
• No optimization loops
• No gradients
• No learned parameters
• Hard decision boundary
• Monotone under data inclusion
• Robustness via adversarial neighborhood Π,Ψ
• Complexity control via exact marginalization
• CI-verifiable via hash invariants

FORMAL CLASS
This system is equivalent to a total decision procedure over a frozen hypothesis, with adversarial stress testing and asymptotic certification. It is not a learning algorithm. It is closer to a verified inference kernel or proof-carrying evaluator.

NEXT PRODUCTIVE STEP
If you want to go even denser, the only remaining compression is to:
• Emit this ANF as a typed operational semantics (small-step rules), or
• Provide a single-file reference implementation (e.g., Python/Rust) that enforces this ANF exactly and fails closed on any deviation.

© Robert R. Frost
2026-01-03