95 live, computable functions in one portable, fully offline file. The complete AlchemyCalc G2 base (CGB depositions, attributed open-science corpus, instruction editor, AutoPhi math accelerator, Fractal Lab, database loader) plus a 45-instruction Carbon pack: Combustion & Fuels (11) · Carbon Cycle & Climate (12) · Carbon Chemistry & Materials (13) · Carbon Accounting (9).
What the Carbon pack computes
stoichiometric air–fuel ratios and CO₂ ledgers for any CₓHₖOₜ fuel, Dulong heating values, excess air, biogas energy, wood-moisture penalty, carbon↔CO₂ mass, tree and forest sequestration, ppm↔gigatonnes, radiative forcing (Myhre), Henry dissolution, carbonate speciation, GWP conversion, fullerene and graphene arithmetic, calcination CO₂, Freundlich and Langmuir adsorption, CO₂ compression work, δ¹³C signatures, photosynthesis ledger, driving/flight/grid accounting, carbon pricing, net-zero pathways, CCS penalty.
95
live functions — every one attributed
45
Carbon instructions in the themed pack
12.2 M/s
log-gamma evaluations — accelerator, measured
10±308
numerical range, honestly displayed
Learn it right — a suggestion. These are professional-grade instructions, and most people need instructional help the first time through. Our suggestion: pair this edition with an AI tutor, such as Claude by Anthropic (claude.ai) — paste an instruction's 📜 origin line, its formula, and your numbers, and ask Claude to walk you through what it means, the units, and how to read the result before you rely on it. The calculator computes; a tutor explains.
Provenance — who and what
Formulas and laws of nature are unpatentable — no one owns them. Every calculation names its origin, in-app and in the shipped ledgers (PROVENANCE.md + PROVENANCE-CARBON.md). The ten CGB Mathematical Depositions are © Christopher Gabriel Brown; every borrowed formula credits its originator and year.
In the box
- The AlchemyCalc Carbon app — one file (185 KB), no install, no internet, phone-ready
- The Proof button — the calculator verifies itself against known values, live on your device
- The Professor button — composes a full lesson prompt for an AI tutor such as Claude (claude.ai)
- Plain-English guide (laymen notes), quick-start, license & IP notice
- Both provenance ledgers and a fictional demo dataset
Emission factors are standard averages — for reporting-grade carbon accounting, use your jurisdiction's official factors.
Christopher Gabriel Brown — Inventor · Author · Visionary
christopher@cri-one.com · crioneaka@outlook.com · 1341 Wellington Cove, Lawrenceville, GA 30043-5255, USA
© 2010–2026 Christopher Gabriel Brown, CRI-ONE. All rights reserved. Patents issued and pending.
Complete instruction list — all 95 functions
Every instruction in this edition, with its formula and its origin. Mathematical formulas and laws of nature are unpatentable; each borrowed formula credits its originator and year, and the ten CGB Mathematical Depositions are © Christopher Gabriel Brown.
CGB depositions (10)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| 1 · Dimensional Fold | V(n-sphere) = π^(n/2) / Γ(n/2+1) · rⁿ ⟹ peaks at n* = 5, → 0 as n → ∞ | CGB Deposition 1 © Christopher Gabriel Brown — builds on the classical n-sphere volume via Leonhard Euler's Gamma function (18th c.) |
| 2 · Entropic Bridge | S = −k_B Σ pᵢ ln pᵢ ≥ ∮dQ/T (Shannon = Clausius = Helmholtz) | CGB Deposition 2 © Christopher Gabriel Brown — builds on Claude Shannon (1948), Ludwig Boltzmann & Rudolf Clausius (19th c.), Rolf Landauer (1961) |
| 3 · Golden Spiral Convergence | lim F(n+1)/F(n) = φ = (1+√5)/2 ⟹ r_opt = φ⁻² ≈ 0.382 wire/gate area | CGB Deposition 3 © Christopher Gabriel Brown — builds on Leonardo of Pisa “Fibonacci” (1202) and Euclid's extreme-and-mean ratio (~300 BC) |
| 4 · Harmonic Decay | Σ 1/n² = π²/6 ⊗ ∫₀^∞ e^(−λt)cos(ωt)dt = λ/(λ²+ω²) | CGB Deposition 4 © Christopher Gabriel Brown — builds on Leonhard Euler's Basel solution (1734) and Pierre-Simon Laplace's transform (c. 1785) |
| 5 · Photon Chromosome Encoding | C = ⌊log₂(Δλ/δλ)⌋ + ⌊log₂(2π/δθ)⌋ + ⌊log₂(I_max/I_min)⌋ bits/photon | CGB Deposition 5 © Christopher Gabriel Brown — builds on Claude Shannon's information theory (1948) and Max Planck's quantum (1900) |
| 6 · Quantum Counting Paradox | 2ⁿ states ≠ 2ⁿ computations ⟹ P = sin²((2k+1)θ), k* = ⌊(π/4)√N⌋ | CGB Deposition 6 © Christopher Gabriel Brown — builds on Lov Grover's quantum search algorithm (1996) |
| 7 · Recursive Growth Bound | T(n) = a·T(n/b) + n^c ⟹ compare c against log_b(a) | CGB Deposition 7 © Christopher Gabriel Brown — builds on the Master Theorem of Jon Bentley, Dorothea Haken & James B. Saxe (1980) |
| 8 · Thermal Noise Floor | E_bit ≥ k_B·T·ln2 ⟹ FLOPS_max = P_budget / (k_B·T·ln2) | CGB Deposition 8 © Christopher Gabriel Brown — builds on Rolf Landauer's limit (1961) |
| 9 · Voxel Resonance | Ψ(v) = Π[αₖ sin(2πfₖ/Nₖ) + βₖ e^(−γₖd²)] · det(M_seed) | CGB Deposition 9 © Christopher Gabriel Brown — original composite formulation |
| 10 · Zero-Point Fabrication | Σ ½ħω → ∞ ⟹ ζ(−1) = −1/12 ⟹ E_reg = −ħcπ²/(720d³) | CGB Deposition 10 © Christopher Gabriel Brown — builds on Hendrik Casimir (1948) and Euler–Riemann zeta regularization ζ(−1) = −1/12 |
Mathematics (8)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Quadratic roots | ax² + bx + c = 0 ⟹ x = (−b ± √(b²−4ac)) / 2a | Classical mathematics — Babylonian tablets (~1800 BC); general solution tradition of al-Khwarizmi (c. 820). Unpatentable, public domain |
| Combinations & permutations | C(n,k) = n! / k!(n−k)! · P(n,k) = n!/(n−k)! (log-gamma — no overflow) | Classical combinatorics — Pingala (~200 BC), Blaise Pascal (1654); computed via Cornelius Lanczos's log-gamma approximation (1964). Public domain |
| Bayes' theorem | P(A|B) = P(B|A)·P(A) / [P(B|A)·P(A) + P(B|¬A)·P(¬A)] | Rev. Thomas Bayes (published 1763), generalized by Pierre-Simon Laplace (1774). Public domain |
| Normal distribution | φ(x) = e^(−(x−μ)²/2σ²) / σ√2π · Φ(x) via erf | Abraham de Moivre (1733), Carl Friedrich Gauss (1809); erf approximation from Abramowitz & Stegun's Handbook 7.1.26 (Hastings, 1964, US-Gov public domain) |
| Logistic growth | P(t) = K / (1 + ((K−P₀)/P₀)·e^(−rt)) | Pierre François Verhulst (1838). Public domain |
| Compound & continuous growth | A = P(1 + r/n)^(nt) · A = P·e^(rt) | Classical finance mathematics; continuous compounding via Jacob Bernoulli (1683) and Euler's e. Public domain |
| Shannon channel capacity | C = B · log₂(1 + S/N) | Claude Shannon (1948), with Ralph Hartley (1928) — the Shannon–Hartley theorem. Public domain |
| Prime counting estimate | π(n) ≈ n/ln n · sharper: n/(ln n − 1) | Carl Friedrich Gauss & Adrien-Marie Legendre (1790s); Prime Number Theorem proved by Hadamard & de la Vallée Poussin (1896). Public domain |
Physics & Energy (12)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Mass–energy E = mc² | E = m·c² | Albert Einstein (1905). A law of nature — unpatentable, public domain |
| Kinetic energy & momentum | KE = ½mv² · p = mv | Classical mechanics — Isaac Newton (1687), Gottfried Leibniz's vis viva; modern ½mv² formalized 19th c. Public domain |
| Ohm's law solver | V = I·R · P = V·I (leave exactly one of V/I/R blank) | Georg Simon Ohm (1827); electrical power after James Prescott Joule. Public domain |
| Coulomb's law | F = k·q₁·q₂ / r² | Charles-Augustin de Coulomb (1785). Public domain |
| Ideal gas PV = nRT | P·V = n·R·T (leave exactly one blank) | Émile Clapeyron (1834), combining Robert Boyle (1662), Jacques Charles, Joseph Gay-Lussac and Amedeo Avogadro. Public domain |
| Carnot efficiency | η = 1 − T_cold / T_hot | Sadi Carnot (1824). Public domain |
| Battery C-rate & runtime | E = Ah·V · I = C·Ah · runtime = 1/C | Standard electrical-engineering C-rate convention (20th c. industry practice). No single originator; unpatentable arithmetic |
| Solar PV yield | E = A · η · H_sun · PR | Standard photovoltaic yield estimation (industry practice, late 20th c.). Unpatentable arithmetic |
| Wind turbine power | P = ½·ρ·A·v³·Cp (Betz limit Cp ≤ 16/27 ≈ 0.593) | Kinetic flux ½ρAv³ (classical); Betz limit — Albert Betz (1919), independently Frederick Lanchester (1915). Public domain |
| Radioactive decay | N(t) = N₀·e^(−λt), λ = ln2 / t½ | Ernest Rutherford & Frederick Soddy (1902). A law of nature — public domain |
| Photon energy E = hc/λ | E = h·c / λ | Max Planck (1900) and Albert Einstein (1905). Public domain |
| Faraday electrolysis | m = Q·M / (z·F), Q = I·t | Michael Faraday's laws of electrolysis (1834). Public domain |
Chemistry & Carbon (10)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Dilution C₁V₁ = C₂V₂ | C₁·V₁ = C₂·V₂ (leave exactly one blank) | Standard laboratory chemistry (C₁V₁ = C₂V₂ conservation). No single originator; unpatentable arithmetic |
| pH / pOH | pH = −log₁₀[H⁺] · pH + pOH = 14 | Søren Peder Lauritz Sørensen (1909). Public domain |
| Henderson–Hasselbalch | pH = pKa + log₁₀([A⁻]/[HA]) | Lawrence Joseph Henderson (1908) and Karl Albert Hasselbalch (1917). Public domain |
| Arrhenius rate | k = A·e^(−Ea/RT) | Svante Arrhenius (1889). Public domain |
| Gibbs free energy | ΔG = ΔH − T·ΔS · K = e^(−ΔG/RT) | Josiah Willard Gibbs (1873–1878); equilibrium link after Jacobus van 't Hoff. Public domain |
| Nernst equation | E = E° − (RT/zF)·ln Q | Walther Nernst (1889). Public domain |
| Beer–Lambert | A = ε·l·c | Pierre Bouguer (1729), Johann Heinrich Lambert (1760), August Beer (1852). Public domain |
| Hydrocarbon combustion — CO₂ ledger | CₓHᵧ + (x+y/4)O₂ → xCO₂ + (y/2)H₂O | Stoichiometry on Antoine Lavoisier's conservation of mass (1770s–80s). Public domain |
| Carbon-14 dating | t = (t½/ln2)·ln(N₀/N), t½ = 5,730 yr | Willard Libby (1946–49, Nobel 1960); 5,730-yr “Cambridge half-life” (1962). Public domain |
| Percent yield & atom economy | yield% = actual/theoretical · 100 · AE% = M(product)/ΣM(reactants) · 100 | Standard chemistry; atom economy after Barry Trost (1991, concept — the arithmetic is unpatentable). Public domain |
Medicine (10)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Body mass index | BMI = kg / m² | Adolphe Quetelet (1832); the name “body mass index” after Ancel Keys (1972); WHO bands. Public domain |
| Body surface area (Mosteller) | BSA = √(cm·kg / 3600) | R. D. Mosteller (1987, NEJM). A published clinical formula — unpatentable |
| Creatinine clearance (Cockcroft–Gault) | CrCl = (140−age)·kg·(0.85 if female) / (72·SCr) | Donald Cockcroft & Matthew Gault (1976, Nephron). Public domain |
| Half-life & steady state | t½ = 0.693/k · steady state ≈ 5·t½ | Standard pharmacokinetics, foundational work of Torsten Teorell (1937). Public domain |
| Loading dose | LD = C_target · Vd · kg / F | Standard clinical pharmacokinetics (Rowland & Tozer convention). Unpatentable arithmetic |
| Maintenance dosing | rate = Cl · C_ss / F | Standard clinical pharmacokinetics (Rowland & Tozer convention). Unpatentable arithmetic |
| Clearance ↔ Vd ↔ t½ | Cl = k·Vd · t½ = 0.693·Vd/Cl | Standard pharmacokinetics — clearance/volume/half-life identities. Public domain |
| Mass dose → molar dose | n = dose / M(formula) — molar mass from the built-in engine | Standard chemistry applied to dosing; molar masses from IUPAC values. Unpatentable arithmetic |
| IV drip rate | gtt/min = volume·dropFactor / minutes | Standard clinical/nursing formula. No single originator; unpatentable arithmetic |
| Cardiac output (Fick) | CO = VO₂ / [(CaO₂ − CvO₂) · 10] | Adolf Eugen Fick's principle (1870). Public domain |
Combustion & Fuels (11)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Oxygenated-fuel combustion CₓHᵧO₂ | CₓHᵧO_z + (x + y/4 − z/2)·O₂ → x·CO₂ + (y/2)·H₂O | Stoichiometry on Antoine Lavoisier's conservation of mass (1770s–80s). Public domain |
| Stoichiometric air–fuel ratio | AFR = (x + y/4 − z/2) × 137.9 / M_fuel (mass air per mass fuel) | Standard combustion engineering (stoichiometric air requirement). Public domain |
| Excess air & lambda | λ = AFR_actual / AFR_stoich · %EA = (λ−1)×100 | Standard combustion engineering (lambda convention). Unpatentable arithmetic |
| Higher heating value (Dulong) | HHV ≈ 0.338·C% + 1.428·(H% − O%/8) + 0.095·S% MJ/kg | Pierre Louis Dulong's heating-value formula (19th c.). Public domain |
| LHV from HHV | LHV = HHV − 2.442 × 9·H%/100 (water-of-combustion penalty) | Standard calorimetry — latent-heat correction. Public domain |
| Combustion air volume | V_air = mol_fuel × (x+y/4−z/2) × 4.76 × 22.414 L (STP) | Standard combustion stoichiometry. Public domain |
| Biogas energy content | E = CH₄% × 35.8 MJ/m³ | Standard fuel-gas calorimetry. Unpatentable arithmetic |
| Grid emission factor from fuel | kgCO₂/kWh = CO₂-per-kg ÷ (MJ/kg ÷ 3.6 × η) | Standard power-plant emission arithmetic. Unpatentable |
| Wood fuel vs moisture | LHV_as-received = LHV_dry·(1−M) − 2.442·M | Standard biomass-fuel calorimetry. Public domain |
| Volumetric energy density | MJ/L = MJ/kg × density | Arithmetic on published fuel properties. Unpatentable |
| Fuel cost per useful kWh | $/kWh = price ÷ (kWh-per-unit × η) | Billing arithmetic. Unpatentable |
C_CC (12)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Carbon ↔ CO₂ mass | CO₂ = C × 44.009/12.011 = C × 3.664 | Molecular mass ratio 44.009/12.011 — a fact of chemistry. Public domain |
| Tree biomass → CO₂ stored | CO₂ = green mass × (1−moisture) × C-fraction × 3.664 | Standard forestry carbon accounting (IPCC-style default fractions). Public domain |
| Forest sequestration rate | annual = area × rate | Standard forestry accounting arithmetic. Unpatentable |
| ppm ↔ gigatonnes | 1 ppm CO₂ = 2.13 GtC = 7.81 GtCO₂ | Standard carbon-cycle conversion (2.13 GtC per ppm). Public domain |
| Emissions → atmospheric rise | Δppm = GtCO₂ × AF / 7.81 | Standard carbon-cycle bookkeeping (airborne fraction after Keeling-era studies). Public domain |
| CO₂ radiative forcing | ΔF = 5.35 × ln(C/C₀) W/m² | Myhre, Highwood, Shine & Stordal (1998, GRL) simplified forcing expression. Published formula — unpatentable |
| Doubling forcing & warming | ΔF₂ₓ = 5.35·ln2 ≈ 3.71 W/m² · ΔT = λ·ΔF | Svante Arrhenius (1896) lineage; modern coefficient after Myhre et al. (1998). Public domain |
| CO₂ concentration projection | C(t) = C₀ + rate × years (linear trend) | Linear projection on the record begun by Charles David Keeling (1958). Public domain |
| Dissolved CO₂ (Henry's law) | [CO₂(aq)] = k_H × pCO₂ | William Henry (1803). Public domain |
| Carbonate speciation vs pH | pK₁ = 6.35, pK₂ = 10.33 — fractions of H₂CO₃*/HCO₃⁻/CO₃²⁻ | Standard aquatic chemistry (Bjerrum speciation, after Niels Bjerrum). Public domain |
| Greenhouse gases → CO₂e | CO₂e = mass × GWP₁₀₀ (CH₄ 27.9 · N₂O 273) | GWP₁₀₀ factors per IPCC Sixth Assessment Report (2021) — public scientific record |
| Per-capita emissions | t/person = national MtCO₂ × 10⁶ / population | Arithmetic. Unpatentable |
C_CM (13)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Fullerene C₆₀ arithmetic | M(C₆₀) = 60 × 12.011 = 720.66 g/mol | Buckminsterfullerene discovered by Kroto, Curl & Smalley (1985, Nobel 1996); arithmetic on molar mass. Public domain |
| Graphene sheet mass | mass = area × 0.77 mg/m² (single layer) | Graphene isolated by Geim & Novoselov (2004, Nobel 2010); areal density from graphite lattice — a material fact |
| Carbon allotrope volume | V = m/ρ (graphite 2.266, diamond 3.514 g/cm³) | Arithmetic on published densities. Unpatentable |
| CO₂ gas density | ρ = P·M / (R·T) | Ideal-gas density (Clapeyron 1834 applied). Public domain |
| Dry-ice cooling | Q = m × 571 kJ/kg (sublimation) | Standard thermophysical constants. Public domain |
| Limestone calcination CO₂ | CaCO₃ → CaO + CO₂ (44.01/100.09 by mass) | Standard industrial chemistry (lime burning, ancient practice; stoichiometry after Lavoisier). Public domain |
| Bicarbonate buffer pH | pH = 6.35 + log₁₀([HCO₃⁻]/[H₂CO₃*]) | Henderson–Hasselbalch (1908/1917) applied to carbonic acid. Public domain |
| Adsorption — Freundlich | q = K·C^(1/n) | Herbert Freundlich (1907). Public domain |
| Adsorption — Langmuir | q = q_m·K·C / (1 + K·C) | Irving Langmuir (1918, Nobel 1932). Public domain |
| CO₂ compression work (isothermal) | W = n·R·T·ln(P₂/P₁) | Classical thermodynamics — isothermal ideal-gas work (Boyle/Clapeyron lineage). Public domain |
| δ¹³C isotope signature | δ¹³C = (R_sample/R_VPDB − 1) × 1000 ‰ · R_VPDB = 0.011180 | Standard isotope geochemistry on the VPDB scale (program of Harold Urey's school, 1950s). Public domain |
| Photosynthesis energy ledger | 6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂ · ΔG ≈ +2,870 kJ/mol | Standard biochemistry; carbon-fixation pathway after Melvin Calvin (1950s, Nobel 1961). Public domain |
| Carbon-fiber composite modulus | E = V_f·E_f + V_m·E_m (rule of mixtures) | Rule of mixtures after Woldemar Voigt (1889). Public domain |
C_CA (9)
| Instruction | Formula | Origin — who and what |
|---|---|---|
| Driving CO₂ from fuel economy | kg = L/100km × km/100 × 2.31 (petrol) / 2.68 (diesel) | Stoichiometric fuel factors (2.31/2.68 kg per liter) — standard emission arithmetic. Public domain |
| Flight CO₂ estimate | kg ≈ km × factor × class multiplier | Standard aviation emission-factor averages. Unpatentable arithmetic |
| Electricity CO₂ | kg = kWh × grid factor / 1000 | Standard grid-factor arithmetic. Unpatentable |
| Fuel volume → CO₂ (stoichiometric) | petrol 2.31 · diesel 2.68 kg CO₂ per liter | Stoichiometric fuel factors — standard. Public domain |
| Natural gas → CO₂ (computed) | CH₄: 16.04 g/mol at 22.414 L/mol → ×44.009/16.043 CO₂ | Computed from molecular ratios (CH₄ → CO₂). Public domain |
| Carbon price cost | cost = tCO₂ × price | Arithmetic. Unpatentable |
| Tree-planting offset estimate | trees = annual tCO₂ ÷ ~0.021 t/tree/yr (rough average) | Common forestry average — arithmetic on published estimates. Unpatentable |
| Linear net-zero pathway | annual cut = current ÷ (target year − now) | Arithmetic. Unpatentable |
| Carbon-capture energy penalty | extra fuel = p / (1 − p) | Standard carbon-capture engineering arithmetic. Public domain |
Image SHA-256 — emb_CRIONE-ALCHEMY-V3-C-101_1.png
c46bd0c47eeb2550192343e2506efa64021c80602cfe622809939f98a742918aAlchemyCalc Carbon V3
$12K
In stock
SKU
CRIONE-ALCHEMY-V3-C-101
Leave blank to use the product price.
Themed edition on the AlchemyCalc G2 core: 95 live functions — the G2 base plus a 45-instruction combustion, climate & carbon-chemistry pack. Proof & Professor buttons, instruction editor, math accelerator, Fractal Lab. Emission factors are averages — use official factors for reporting. Guide included.
First to market
Publicly online since 2010 · U.S. patent applications since 2012 · inventions offered since 2014. The work of Christopher Gabriel Brown, independently documented.
First posted:
Related Products
Check items to add to the cart or
