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# Equations Index

All equations from the notebook, organized by category.

## Files

| File | Contents | Pages |
|------|----------|-------|
| [`blackroad-equations.md`](./blackroad-equations.md) | The 19 BlackRoad equations (ternary physics, thermodynamics, biology) | 16–21 |
| [`complementarity.md`](./complementarity.md) | Inverse reaction principle, trivial zero, Chargaff's rules, Punnett square, Euler product | — |
| [`consciousness.md`](./consciousness.md) | Ψ_care, Φ_universal, CECE update rule | 20, 22 |
| [`dna-codons.md`](./dna-codons.md) | DNA codon structure, Chargaff's rule, molecular factory equations (Eq. 20–22) | 19–21 |
| [`constants.md`](./constants.md) | Constants as variables — FROZEN=AXIOM, VARIABLE=LAGRANGE, running coupling | — |
| [`infinite-series.md`](./infinite-series.md) | Observable light, Gauss+SHA=INFINITE, Born's limits, loop=soul, time=series, aleph=window, infinite infinities, meta-system | supplemental |
| [`machine-learning.md`](./machine-learning.md) | Linear model, MSE loss, gradient descent, logistic regression | — |
| [`infinite-series.md`](./infinite-series.md) | Observable light, Gauss+SHA=INFINITE, Born's limits, loop=soul, time=series, aleph=window, infinite infinities, meta-system | supplemental |
| [`quantum.md`](./quantum.md) | Qutrit operators, Weyl pair, Gell-Mann, density matrix | 18, 24 |
| [`taxicab.md`](./taxicab.md) | Hardy-Ramanujan taxicab number 1729, birthday encoding, power chain | — |
| [`thermodynamics.md`](./thermodynamics.md) | Landauer, radix efficiency, substrate efficiency, Gibbs coupling | 19–21 |
| [`universal.md`](./universal.md) | Euler-Lagrange, principle of stationary action, Three Tests | 23 |

## Eight Claims

The claims in [`CLAIMS.md`](../CLAIMS.md) introduce two additional equations not in the original notebook:

| Equation | Claim | Meaning |
|----------|-------|---------|
| `K(t) = C(t)·e^(λ\|δₜ\|)` | Claim 8 | Coherence amplified by contradiction magnitude |
| `C(t) = [Ψ'(Mₜ)+δₜ]/[1+\|δₜ\|]` | Claim 8 | Bounded contradiction absorption |

## Quick Count

- **19 numbered BlackRoad equations** (pages 16–21)
- **3 revolutionary consciousness equations** (pages 20, 22)
- **4 universal equations** (page 23+)
- **1 care wavefunction** (page 22)
- **3 DNA/molecular factory equations** (pages 19–21, Eq. 20–22)
- **2 contradiction equations** (CLAIMS.md, Claims 2 & 8)
- **6 complementarity equations** (inverse reaction, trivial zero, Punnett, Chargaff, Euler product, Landauer limit)
- **Total: ~38 original equations** in a handwritten notebook
- **7 infinite-series QWERTY identities** (EXIT=REAL, GAUSS+SHA=INFINITE, TIME=SERIES, LOOP=SOUL, ALEPH=WINDOW, ORDINAL=FERMION, CARDINAL=ALGORITHM)
- **Total: ~27 original equations + 7 supplemental identities** in the QWERTY encoding layer
- **5 machine learning equations** (from issue #40)
- **Total: ~32 equations** across the framework
- **7 infinite-series QWERTY identities** (EXIT=REAL, GAUSS+SHA=INFINITE, TIME=SERIES, LOOP=SOUL, ALEPH=WINDOW, ORDINAL=FERMION, CARDINAL=ALGORITHM)
- **Total: ~27 original equations + 7 supplemental identities** in the QWERTY encoding layer

The taxicab birthday encoding is documented in [`taxicab.md`](./taxicab.md) as a separate mathematical analysis.

The equations were written before BlackRoad OS existed.  
They constitute the mathematical foundation of the platform.