Teaching Patterns Distilled From Heptabase¶

These are reusable patterns inferred from the historical Heptabase lessons. They are procedural guidance for Codex, not source authority.

Pattern 1 - Research First, Foundation Second¶

Start each topic by showing where it lives in the Conjecture 3 research map. Then teach the prerequisite.

Example: before GF(2), explain that parity-check matrices and CSS commutativity are written over GF(2). Before expander spectra, explain that expansion is what creates the 2D routing bottleneck.

Pattern 2 - Small Example Before General Definition¶

Use a small concrete object before formal language:

[7,4,3] Hamming code before general [n,k,d] codes.
[4,2,2] CSS code before quotient-space logical operators.
Petersen graph before spectral expansion and Ramanujan graphs.
Near-square grid before planar separator theorems.

Pattern 3 - Translate From Stabilizer Intuition¶

When introducing classical-code machinery, translate back to stabilizers:

row space of a parity-check matrix as stabilizer span
H_XH_Z^T=0 as commutativity
Tanner graph checks as stabilizer measurement constraints
logical operators as quotient representatives, not just Pauli strings

Pattern 4 - Keep The Bottleneck Visible¶

Every foundation should eventually point to one of these bottlenecks:

expansion creates large cross-cut demand
2D hardware has small balanced separators
syndrome extraction must service cross-cut stabilizer information
the remaining frontier is not the static 2D lower bound itself, but the compiler-native CD(T_n, G) interpretation

Pattern 5 - End With A Handoff¶

Each lesson should close with:

key takeaways
active recall
what has not yet been proven
the next concept and why it is needed