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).

Topologija sustava: zatvorena hibridna petlja stanja i inverznog upravljanja
Topologija sustava: zatvorena hibridna petlja stanja i inverznog upravljanja 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. Brašno & Blend W · Tipo · Blend Hidratacija & Ioni H% · NaCl · φ_lip Faze & Geometrija T_amb(t) · Γ_geom(t) Upravljanje Kvasac Y₀ CY / IDY / ADY Biot-Fourier termika Biot-Fourier → T_core(t) Aktivnost vode & Donnan a_w · Ψ_Donnan Asinkrone Stope α_Yeast(T) ≠ β_Amyl(T) ∫ Hibridna višedimenzionalna ODJ jezgra dx/dt = F(x(t), u(t), T_core) Višedimenzionalni prostor stanja x(t) x(t) ∈ ℝⁿ | Φ_bio(x) ⊗ Ψ_rheo(x) ⚡ Impuls Staglio (t = t_s) Diskretni prijelaz faze i geometrije x(t_s⁺) = Γ_staglio( x(t_s⁻) ) Unutarnja biokemijska povratna veza stanja x(t) Stanje Pečenja 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 Inverzni rubni regulator t_bake , e(t_bake) = 0 ↦ Y₀* Vanjska inverzna petlja: regulira Y₀ za ciljni volumen u t_bake
Sl. 0: Blok-shema PDE-a. Unutarnja povratna veza stanja x(t) integrira spregnutu biokemiju uključujući diskretni skok Staglia, dok vanjska inverzna petlja regulira početni kvasac Y₀ na ciljni volumen u trenutku t_bake.
I. Ulazni vektor u(t)

Reologija brašna i mješavine (snaga proteina, stupanj izmeljavanja, omjeri), slobodna hidratacija i ionska jakost, višefazni temperaturni profil, geometrija tijesta i regulirana doza kvasca Y₀.

II. Vektor stanja x(t) & Staglio

Nelinearno spregnuti višedimenzionalni prostor stanja kroz provođenje topline, enzimatiku, stehiometriju fermentacije i viskoelastičnu reologiju uz diskretni prijelaz faze i geometrije pri buleiranju (Staglio).

III. Izlazni vektor y(t_bake)

Konvergirani volumen u vrijeme pečenja, proteolitička rastezljivost, očuvani Maillardovi šećeri i prekursori arome projicirani na 5 osi profila tijesta.

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 u praksi – Dva primjera

PDE za isto referentno brašno (Tipo 00 · 12,5 % proteina · 63 % hidratacija · 2,8 % NaCl · 4 × 250 g · 430 °C).

Rast / Ekspanzija Glutenska mreža Preostali šećer Amilaza pH vrijednost (desno) Temp. jezgre T(t)
Optimalni prozor Pečenja & Glutena (62–78 %) Maillard & Aroma-pH Zona (44–62 % · pH 5.50–5.66) 7 °C Krio-razdvajanje
Sl. 1a: Primjer 1 – Direktno tijesto 23 °C (12 h)
Sl. 1a: Primjer 1 – Direktno tijesto 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 Relativno stanje [%] 6.0 5.8 5.6 5.4 5.2 pH vrijednost [-] 0 2 4 6 8 10 12 Vrijeme fermentacije t [h]
Sl. 1b: Primjer 2 – Višefazna hladna fermentacija 23 °C → 7 °C → 23 °C (24 h)
Sl. 1b: Primjer 2 – Višefazna hladna fermentacija 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 Relativno stanje [%] 6.0 5.8 5.6 5.4 5.2 pH vrijednost [-] 0 4 8 12 16 20 24 Vrijeme fermentacije t [h]
Sl. 1: Spregnute krivulje 6 stanja uklj. Staglio. Pri pečenju rast i gluten ulaze u zeleni prozor (62–78 %), dok preostali šećer i pH završavaju u zlatnoj Maillard i aroma zoni (44–62 % / pH 5,50–5,66).
Višak amilaze (< 20 °C) Dominacija kvasca (> 20 °C) Omjer β/α (desno) Očuvana rezerva maltoze (∫ ΔJ dt)
Sl. 2a: Toplinski diferencijal Δr(T) = Amilaza − Kvasac
Sl. 2a: Toplinski diferencijal Δr(T) = Amilaza − Kvasac 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 Razlika stopa Δr [p.b.] 8× 6× 4× 2× 0× Omjer Amilaza / Kvasac [×] 2 7 12 17 22 27 32 Temperatura tijesta T [°C]
Sl. 2b: Neto tok heksoza ΔJ_hex(τ) = Doprema − Potrošnja
Sl. 2b: Neto tok heksoza ΔJ_hex(τ) = Doprema − Potrošnja 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 Neto tok šećera [mg/100g·h] 0 20 40 60 80 100 Normirani napredak τ [%]
Sl. 2: Mehanizam hladnog zrenja: ispod 20 °C amilaza brašna nadmašuje usporeni kvasac (2a, tirkizno), stvarajući na 7 °C krio-plato koji čuva prirodnu maltozu za Maillardovo tamnjenje i estere arome (2b, zeleno).
Sl. 3: Harmonija 5 osi & Bipolarno reološko spektralno polje pri pečenju
Mreža
Sl. 3: Harmonija 5 osi & Bipolarno reološko spektralno polje pri pečenju 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 i Kvasac Zrelost i Gluten Tamnjenje i Šećer Bule i Završno Dizanje Sredina i Hidracija
Pol-trake
Okus kvasca Aroma i Kvasac Zreli okus
Mekano / Puca Zrelost i Gluten Žilavo / Kruto
Blijedo tijesto Tamnjenje i Šećer Brzo gori
Širi se Bule i Završno Dizanje Skuplja se
Kompaktno / Čvrsto Sredina i Hidracija Vrlo vlažno
Hladno 23→7→23 °C (24 h) — 97 % (5/5 Sweet Spot) Direktno 23 °C (12 h) — 99 % (5/5 Sweet Spot) Sweet Spot
Sl. 3: I 12 h direktno tijesto na 23 °C (99 %) i 24 h hladno zrenje (97 %) smještaju svih 5 osi u Idealnu Zonu (lijevo), dok polne trake (desno) otkrivaju dublju estersku zrelost (92 % prema 82 %) i strukturiranu elastičnost (60 % prema 48 %) hladnog tijesta.
NATIVNI IZRAČUN NA UREĐAJU

Nativni izračun izravno na vašem uređaju

Cijeli sustav diferencijalnih jednadžbi izvršava se 100% offline u nativnom kodu na mobitelu i pametnom satu za manje od milisekunde.

Ispeci savršenu pizzu.

Jednostavan i pouzdan kalkulator tijesta za autentičnu napuljsku pizzu kod kuće. Bez nepotrebnih komplikacija – samo precizna hidratacija, pouzdan izračun kvasca i raspored fermentacije koji jednostavno funkcionira.

Apple App Store Google Play trgovina