PIZZATASTICO DOUGH ENGINE (PDE)

Coupled Dough Biochemistry in Real Time

The Pizzatastico Dough Engine (PDE) links published cereal-chemistry and yeast-kinetics models into a closed system of differential equations across your entire fermentation schedule.

MODEL ARCHITECTURE

Dynamic Computation Across Temperature Phases

During dough fermentation, yeast metabolism, enzymatic gluten relaxation, starch cleavage by amylases, and organic acid formation occur simultaneously—yet each responds differently to transitions between room and cold proofing.

The Pizzatastico Dough Engine (PDE) couples these biochemical processes in a time-resolved differential equation system, accounting for the thermal cooling and warming inertia of the dough mass as well as custom flour blends (Tipo 00, Tipo 0, Tipo 1).

System Topology: Closed-Loop Hybrid State-Space & Inverse Control
System Topology: Closed-Loop Hybrid State-Space & Inverse Control Patent-style closed-loop Reduced-Order PDE control schematic (spatially reduced, Biot-Fourier coupled hybrid continuous-discrete state-space system) of the Pizzatastico Dough Engine (PDE): exogenous input vector u(t) drives Biot-Fourier thermal conduction, Raoult-Donnan water activity, and asynchronous enzyme/yeast couplers into a non-linear multi-state ODE core with inner biochemical state feedback x(t), a discrete hybrid Staglio phase and geometry transition operator x(t_s+) = Gamma_staglio(x(t_s-)), and an outer inverse boundary-value controller regulating Y0 so expansion V(t_bake) matches target V_target at baking time. Flour & Blend W · Tipo · Blend Hydration & Ions H% · NaCl · φ_lip Schedule & Geometry T_amb(t) · Γ_geom(t) Control Input Y₀ CY / IDY / ADY Biot-Fourier Thermal Biot-Fourier → T_core(t) Water Activity & Donnan a_w · Ψ_Donnan Asynchronous Rates α_Yeast(T) ≠ β_Amyl(T) ∫ Hybrid Multi-State ODE Core dx/dt = F(x(t), u(t), T_core) Multi-State Phase Space x(t) x(t) ∈ ℝⁿ | Φ_bio(x) ⊗ Ψ_rheo(x) ⚡ Staglio Impulse (t = t_s) Discrete Phase & Geometry Transition x(t_s⁺) = Γ_staglio( x(t_s⁻) ) Inner Biochemical State Feedback x(t) Baking State y(t_bake) • V(t_bake) [+71.5% Vol] • S_glut, P/L [Rheology] • S_sug, pH [Maillard] • 5D Radar & Pole Bars − V_target + Σ e = V_target − V(t_bake) → 0 Inverse Boundary-Value Controller t_bake , e(t_bake) = 0 ↦ Y₀* Outer Inverse Loop: Regulates Y₀ for Exact Target Volume at t_bake
Fig. 0: Patent-style signal-flow schematic of the PDE. An inner biochemical state-feedback loop x(t) integrates coupled kinetics including the discrete Staglio phase transition, while an outer inverse boundary-value loop regulates initial yeast Y₀ to hit exact target expansion at desired baking time t_bake.
I. Input Vector u(t)

Flour & blend rheology (protein strength, milling extraction, blend ratios), free hydration & ionic strength, multi-phase ambient schedule, dough geometry, and the regulated yeast dose Y₀.

II. State Vector x(t) & Staglio

Non-linearly coupled multi-state space spanning thermal conduction, enzyme kinetics, fermentation stoichiometry, and viscoelastic rheology, subject to a discrete phase and geometry transition at balling (Staglio).

III. Output Vector y(t_bake)

Converged baking expansion at mealtime, proteolytic extensibility, preserved Maillard reducing sugars, and aroma precursors — projected onto the 5-axis dough profile.

SCIENTIFIC FOUNDATION

Published Literature in the PDE Core

Every term in the engine is grounded in established cereal chemistry and microbiology:

📚 Wieser (2007) pH- & temperature-dependent proteolysis

1. Endogenous Aspartic Proteases & Gluten Maturation

Endogenous flour aspartic proteases relax the gluten network as a function of pH and temperature. The PDE models structural maturation across bulk and final proof independently of gas production.

🌡️ Sharpe-DeMichele / Schoolfield Thermodynamic S. cerevisiae kinetics

2. Cardinal Temperature & Membrane-Lipid Transition

Biophysical temperature model for Saccharomyces cerevisiae covering the full range from cold membrane-lipid phase transition in the fridge to the cardinal optimum.

💧 Raoult / Norrish / Donnan Free water · NaCl Donnan binding · Osmotic pressure

3. Water Activity & Osmosis

Accounts for biopolymer-bound water in flour, electrostatic Donnan ion binding of NaCl to the gluten network, and osmotic effects on yeast kinetics.

⚖️ Embden-Meyerhof-Parnas + Neuberg Amylase replenishment & fermentation balance

4. Closed Substrate & Hexose Stoichiometry

Closed mass balance from enzymatic cleavage of damaged starch by α/β-amylases through the Embden-Meyerhof-Parnas glycolytic pathway and Neuberg fermentation byproducts.

MODEL TRAJECTORIES

PDE in Practice – Two Examples

PDE for the same reference flour (Tipo 00 · 12.5% protein · 63% hydration · 2.8% NaCl · 4 × 250 g · 430 °C).

Expansion / Rise Gluten Network Residual Sugar Amylase pH Value (right) Core Temp T(t)
Optimal Baking & Gluten Window (62–78 %) Maillard & Aroma-pH Zone (44–62 % · pH 5.50–5.66) 7 °C Cryo-Decoupling
Fig. 1a: Example 1 – Direct Dough 23 °C (12 h)
Fig. 1a: Example 1 – Direct Dough 23 °C (12 h) Coupled 6-state observable Reduced-Order PDE trajectory for 12 h room-temperature direct wheat dough (23 °C, Tipo 00 flour, 12.5% protein, 63% hydration, 2.8% NaCl, 4 x 250 g = 1000 g, 0.129% fresh yeast): 9.64 h bulk fermentation reaching +111.5% physical volume expansion, Staglio balling degassing at t = 9.64 h to +25.9%, and 2.36 h final proof converging at t = 12.0 h inside the emerald Optimal Baking & Gluten Window (+71.5% expansion, 64.3% proteolytic gluten structure) and golden Maillard & Aroma-pH Corridor (51.9% residual sugar = 0.86 g/100g, pH 5.54, 13.2% amylase starch cleavage). Staglio 120 100 80 60 40 20 0 Relative State [%] 6.0 5.8 5.6 5.4 5.2 pH Value [-] 0 2 4 6 8 10 12 Fermentation Time t [h]
Fig. 1b: Example 2 – Multi-Phase Cold Proof 23 °C → 7 °C → 23 °C (24 h)
Fig. 1b: Example 2 – Multi-Phase Cold Proof 23 °C → 7 °C → 23 °C (24 h) Coupled 6-state observable Reduced-Order PDE trajectory for 24 h multi-phase cold maturation (1.39 h warm puntata at 23 °C, 19.00 h cold maturation at 7 °C, 0.75 h Biot-Fourier block acclimation to 13.8 °C, Staglio dividing at t = 21.14 h, and 2.86 h residual-chill-calibrated ball proof at 23 °C, 0.143% fresh yeast): Biot-Fourier cooling inertia and two-stage re-warming across bulk and ball geometry; convergence at t = 24.0 h inside the emerald Optimal Baking & Gluten Window (+71.5% expansion, 73.3% gluten structure) and golden Maillard & Aroma-pH Corridor (59.8% residual sugar = 0.99 g/100g, pH 5.56, 13.1% amylase starch cleavage). 7 °C Staglio 120 100 80 60 40 20 0 Relative State [%] 6.0 5.8 5.6 5.4 5.2 pH Value [-] 0 4 8 12 16 20 24 Fermentation Time t [h]
Fig. 1: Coupled 6-state trajectories including Staglio degassing. At baking time, expansion and gluten integrity converge inside the emerald baking window (62–78%), while residual sugar and pH settle inside the golden Maillard & aroma corridor (44–62% / pH 5.50–5.66).
Amylase Surplus (< 20 °C) Yeast Dominance (> 20 °C) Decoupling Ratio β/α (right) Preserved Maltose Reserve (∫ ΔJ dt)
Fig. 2a: Thermal Rate Differential Δr(T) = Amylase − Yeast
Fig. 2a: Thermal Rate Differential Δr(T) = Amylase − Yeast Thermal rate differential Delta r(T) = beta_amylase(T) - alpha_yeast(T) across dough temperatures 2 °C to 32 °C (normalized to 100% at 20 °C = 0 percentage points): exact bifurcation at T = 20.0 °C; teal positive enzyme surplus zone below 20 °C driven by Sharpe-DeMichele yeast membrane-lipid phase transition (+10.3 pp / 1.31x decoupling at 7 °C; +23.2 pp / 2.81x at 4 °C); rust negative yeast-dominance zone above 20 °C (-4.5 pp at 23 °C down to -36.5 pp at 32 °C). 7°C: +10.3 pp (1.31×) 20 °C (Δr = 0) 23°C: −4.5 pp +40 +20 0 −20 −40 Rate Differential Δr [pp] 8× 6× 4× 2× 0× Amylase / Yeast Ratio [×] 2 7 12 17 22 27 32 Dough Temperature T [°C]
Fig. 2b: Net Hexose Flux ΔJ_hex(τ) = Supply − Consumption
Fig. 2b: Net Hexose Flux ΔJ_hex(τ) = Supply − Consumption Time-resolved net hexose mass flux dS_sug/dt = J_amylase(tau) - J_yeast(tau) in [mg / (100g * h)] over normalized process progress tau (0..100%) comparing 12 h direct dough at 23 °C (rust dashed curve descending from -35 to -97.5 mg/100g*h with Staglio CO2-relief step at tau = 80.3%) against 24 h cold-matured dough (navy solid curve rising into a flat -17.4 mg/100g*h cryo-preservation plateau across tau = 5.8%..85.0%). The emerald-shaded integral area between both trajectories depicts the preserved natural maltose reserve (+15.2% more residual reducing sugar at baking time). 7 °C Plateau: −17.4 mg/(100g·h) ∫ ΔJ_hex dt (+15.2% Sugar) 23 °C (12 h) 0 −20 −40 −60 −80 −100 Net Sugar Flux [mg/100g·h] 0 20 40 60 80 100 Normalized Progress τ [%]
Fig. 2: Biophysical mechanism of cold maturation: Below the 20 °C bifurcation point, endogenous cereal amylase outpaces throttled yeast catabolism (2a, teal) — creating a flat cryo-preservation plateau at 7 °C that conserves natural maltose reserves for Maillard browning and ester aroma (2b, green).
Fig. 3: 5-Axis Harmony & Bipolar Rheology Spectrum at Baking Time
Spiderweb
Fig. 3: 5-Axis Harmony & Bipolar Rheology Spectrum at Baking Time 5-axis rheological and sensory radar comparison at baking time between the 12 h direct dough at 23 °C (99% overall harmony: aroma 97.8%, gluten maturation 99.2%, Maillard browning 100.0%, ball relaxation 97.5%, hydration binding 99.2%) and the 24 h multi-phase cold-matured dough 23 °C -> 7 °C -> 23 °C (97% overall harmony: aroma 94.4%, gluten maturation 95.2%, Maillard browning 100.0%, ball relaxation 99.3%, hydration binding 99.2%) on identical 12.5% protein Tipo 00 flour. Both schedules place all 5/5 axes deep inside the outer emerald Sweet-Spot ring. Aroma & Yeast Flour Maturity & Gluten Browning & Sugar Dough Balls & Final Proof Crumb & Hydration
Pole Bars
Yeasty flavor Aroma & Yeast Mature flavor
Soft / Tears Flour Maturity & Gluten Tight / Buckles
Pale dough Browning & Sugar Burns quickly
Spreads flat Dough Balls & Final Proof Springs back
Compact / Firm Crumb & Hydration Very wet
Cold 23→7→23 °C (24 h) — 97 % (5/5 Sweet Spot) Direct 23 °C (12 h) — 99 % (5/5 Sweet Spot) Sweet Spot
Fig. 3: Both the 12 h direct dough at 23 °C (99% harmony) and the 24 h cold proof (97% harmony) place all 5 axes inside the emerald Sweet Spot (left) — while the bipolar pole bars (right) resolve the cold schedule’s shift toward deeper ester maturity (92% vs. 82%) and structured elasticity (60% vs. 48%).
NATIVE COMPUTATION CORE

Live Native Computation on Your Device

The entire coupled differential equation solver runs as a natively compiled core directly on your smartphone and smartwatch in under a millisecond — with zero server dependency for dough math.

Bake the perfect pizza.

A straightforward pizza dough calculator for authentic Neapolitan pizza at home. No gimmicks — just precise hydration, dependable yeast calculation, and scheduling that simply works.

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