Skip to content

Heptabase Source Map

This file is a distilled read-only map of the Heptabase AI Tutor material used to seed the Codex-native course. It stores provenance and progress state, not raw Heptabase prose.

Goal

  • Goal title: Master QLDPC Barrier Research
  • Goal ID: f02a4f8f-b271-4ebb-8498-9376b96591ae
  • Description: develop expertise in quantum LDPC codes, expander lower bounds, and matroid-theoretic compiler barriers for constrained-hardware compilation.

Course

  • Course title: Coding and Expansion Foundations
  • Course ID: 1fc215df-fc80-44f7-abb5-794147341438
  • Purpose: build the mathematical language of linear codes over GF(2), Tanner graphs, expander graphs, QLDPC constructions, and Conjecture 3 hardware barriers.

Section Versus Lesson-Part Mismatch

The Heptabase UI shows seven AI Tutor sections:

  1. GF(2) and Linear Codes
  2. Generator and Parity-Check Matrices
  3. CSS Codes and Tanner Graphs
  4. Girth, Local Views, and Tanner Codes
  5. CSS Tanner Graphs and Spectral Expansion
  6. Expansion, Cuts, and Grids
  7. CSS and QLDPC Codes

Those sections are not the same granularity as the syllabus bullets. Each section contains multiple lesson parts. For example, section 1 contains research orientation, GF(2) arithmetic, vector spaces, and the Hamming code; section 6 contains Cheeger, Ramanujan graphs, bisection width, the 2D grid bottleneck, and the expansion mismatch.

The repo-native course therefore uses nine fresh-start lessons:

  • the seven historical sections rewritten as coherent Codex lessons
  • one new syndrome-extraction lesson for Topic 5
  • one new research-map integration lesson for Topic 6

This preserves all Heptabase-covered topics while making the local Markdown course complete and easier to restart from Lesson 01.

Source Cards

  • ffdd92fc-dd7f-4bb9-bdaa-f1c0eedc32cb: Conjecture 3 full statement and definitions.
  • cf1810f9-7d6d-48ca-a916-59cb496f8bd3: Conjecture 3 Research Map.
  • a804be96-fbb5-418f-9543-49806231db84: Quantum Tanner Expander Anchor.
  • ad376936-066f-4a16-a84f-2ea3bae39a79: Quantum Tanner Diagonal Expansion Structure.
  • a10f7347-056d-41ba-86df-fd8aade747b7: 2D Grid Bisection Width.
  • e04d8298-51de-4e5a-8251-bb22416d7ffc: 2D Grid Routing Tightness.
  • 5d8399e7-9647-4944-b4be-a27e88fcd0e0: 2D Local Clifford Syndrome Space-Depth Tradeoff.
  • 689b04fd-7f6f-4f66-9d57-8516719d23c8: Expansion Cut To Syndrome Depth.

Heptabase Section Map

Lesson 1 - GF(2) and Linear Codes

  • Lesson ID: 3a3ada78-da42-4bc0-806c-1ba01e7cd5b5
  • Status: ended
  • Covered parts:
    • ecd8f8cb-8afd-4ea0-a80c-0c6213990af6: Research Orientation
    • 141c5431-59b6-42f3-889c-9c462c346e77: GF(2) Arithmetic
    • bac9c02f-0d52-4209-8dfd-6bd3a4906984: Vector Spaces over GF(2)
    • dd142616-8985-4861-a869-117a04317ac4: The [7,4,3] Hamming Code
  • Teaching pattern: start from the Conjecture 3 barrier, then build GF(2) foundations using small binary examples.

Lesson 2 - Generator and Parity-Check Matrices

  • Lesson ID: 89c9fa70-f458-4598-92ca-496abf972396
  • Status: ended
  • Covered parts:
    • da6608db-de8c-4093-bba2-13ba16c90f68: Systematic Form and Row Spaces
    • 9327f11f-164d-402b-8545-a5c2a237b796: Dual Codes and CSS Preview
    • f2197435-5dee-40c8-b8c1-c3eecdf54d2a: Code Parameters and Bounds
    • 0bbf13bc-7961-445e-9380-07f8bc8f7ca3: Puncturing, Shortening, and Local Structure
  • Teaching pattern: generalize the Hamming-code example into matrix and dual-code language.

Lesson 3 - CSS Codes and Tanner Graphs

  • Lesson ID: 52d28312-6db0-4092-ac61-dd031a01fe62
  • Status: ended
  • Covered parts:
    • 982f7c09-42b0-43ba-84bf-2077e455ccc2: Classical Codes in CSS
    • bdb37c16-250c-495e-b394-6e50ed2e6bfa: Tanner Graphs from Matrices
    • fdfddac9-c167-485f-93a5-080fa6179f32: Degree, LDPC, and Locality
  • Teaching pattern: translate the learner's stabilizer knowledge into GF(2) matrix and Tanner-graph language.

Lesson 4 - Girth, Local Views, and Tanner Codes

  • Lesson ID: f6732ad7-1c8f-40b4-aa05-bb1c74376923
  • Status: ended
  • Covered parts:
    • 3158579e-360d-4f3c-bda2-6393731bd0be: Girth and Tree Structure
    • 2d06b825-04a6-48bd-965d-c487f3ea8de6: Local Views and Neighborhoods
    • 453c470d-5717-40d1-992a-1addebbcd63c: Tanner Code Construction
    • 4ae66de6-b51f-4d58-9d29-3eca7eb9187b: Small-Set Expansion
  • Teaching pattern: use local neighborhoods to motivate local testability and Tanner-code structure.

Lesson 5 - CSS Tanner Graphs and Spectral Expansion

  • Lesson ID: 522a7430-2dd1-4dec-876c-200f63397af5
  • Status: ended
  • Covered parts:
    • 166f872d-8814-4d06-97c5-0fa59956abdc: Tanner Graph of a CSS Code
    • d0da2a30-a77d-451e-8284-724a7a26fe3a: Adjacency Spectra of Regular Graphs
    • 6b25ba4b-f98d-46ee-83cf-e5e825174ec9: The Petersen Graph as a Small Expander
  • Teaching pattern: bridge CSS Tanner graphs to spectral graph theory with a concrete expander example.

Lesson 6 - Expansion, Cuts, and Grids

  • Lesson ID: eede0316-fe47-4eec-83ce-0356628ac9c2
  • Status: ended
  • Covered parts:
    • f48d2c43-c160-403c-b331-093b963f709a: Edge Expansion and Cheeger
    • 92f9c374-544f-4432-9f31-4ee081047af6: Ramanujan Graphs
    • 70abbcdf-efe0-48b0-bb81-eec9be9336a4: Bisection Width
    • 176f5266-cbd7-4919-b284-7f6a57d8bda9: The 2D Grid Bottleneck
    • 41e0fae0-ecf9-4522-a6b2-5101f9ce492d: The Expansion Mismatch
  • Teaching pattern: turn spectral/combinatorial expansion into a hardware-capacity bottleneck.

Lesson 7 - CSS and QLDPC Codes

  • Lesson ID: 5f11785a-5fbb-4434-9c0b-504b0a8e0aca
  • Status: not ended
  • Covered/in-progress parts:
    • 26c6621a-2a83-4774-953a-1e8074db75a9: CSS Construction Revisited - covered
    • a564919d-0866-4c33-9928-ded22ed4812c: Logical Operators and Distance - in progress
  • Planned parts:
    • Good Parameters and the LDPC Tension
    • Why Linear Distance Requires Expansion
    • Left-Right Cayley Complexes
    • Quantum Tanner Codes
    • Spectral Expansion and the Anchor Gap
    • Other QLDPC Families
  • Teaching pattern: use the learner's CSS foundation to build toward quantum Tanner codes and the anchor gap.

Repo Lesson Coverage Map

  • Lesson 01: Roadmap introduction, GF(2) arithmetic, GF(2) vector spaces, and the [7,4,3] Hamming code.
  • Lesson 02: Generator matrices, parity-check matrices, dual codes, code parameters, puncturing, and shortening.
  • Lesson 03: CSS bridge, Tanner graphs from matrices, degree constraints, LDPC, and locality.
  • Lesson 04: Girth, local views, Tanner codes, and small-set expansion.
  • Lesson 05: CSS Tanner graphs, regular graph spectra, spectral gap, and Petersen graph intuition.
  • Lesson 06: Edge expansion, Cheeger, Ramanujan graphs, bisection width, 2D grids, planar separators, expansion mismatch, and routing tightness.
  • Lesson 07: CSS logical operators, good QLDPC parameters, expansion for distance, left-right Cayley complexes, quantum Tanner codes, diagonal spectral expansion, anchor gap, and QLDPC family context.
  • Lesson 08: Stabilizer measurement circuits, hardware locality, SWAP routing, congestion, dilation, CD, static 2D lower bound, expansion cut to syndrome depth, space-depth tradeoff, and proved-versus-open boundaries.
  • Lesson 09: Lower-bound proof chain, open gaps, congestion-dilation versus stabilizer cut rank, research-card reading practice, and positioning toward a matroid/cut-rank course.

Known Corrections Applied During Regeneration

  • Markdown tables with math pipes were avoided; the new lessons use paragraphs and lists instead.
  • CSS distance is treated as a relative/quotient logical-distance question, not simply as the raw distance of one classical code.
  • Girth and spectral expansion are kept distinct; spectral gap alone is not claimed to force large girth.
  • Good QLDPC parameters are not claimed to automatically imply every exact Tanner-expansion hypothesis needed by the Conjecture 3 route.
  • The static 2D syndrome-depth theorem is distinguished from the broader compiler-native CD(T_n,G) frontier.