Merge branch 'copilot/explore-taxicab-number-concept' into copilot/merge-open-pull-requests (conflicts resolved)

equations/README.md

@@ -23,6 +23,7 @@ All equations from the notebook, organized by category.
 | [`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 | — |
 | [`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 |
 
@@ -50,5 +51,7 @@ The claims in [`CLAIMS.md`](../CLAIMS.md) introduce two additional equations not
 - **5 machine learning equations** (from issue #40)
 - **Total: ~32 equations** across the framework
 
+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.