research(B-0562): QG isomorphism Step 2 — cube + Adinkra + Cayley-Dickson → HaPPY-like QECC#3941
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AceHack merged 3 commits intoMay 16, 2026
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…kson → HaPPY-like QECC Step 2 of the 4-step QG isomorphism proof path opened in B-0543 / PR #3614. Step 1 (B-0544, PR #3614) formalized Zeta_{RA} = (Zeta, M, A) with an internal monad M for memory and modal operator A for attention. Step 2 unfolds the two axioms into a 4-axis cube (Remember × When × Pay × Attention), grafts the Adinkra-Gates supermultiplet layer onto cube vertices, lifts the cube through a Cayley-Dickson tower (R → C → H → O → S → T), and proposes the algebraic shape that matches HaPPY (holographic perfect-tensor) QEC codes. Originally allocated as B-0545; collided with PR #3619's renumber-sweep that re-took B-0545 for Riven's cursor-terminal loop work. Renumbered to B-0562 (next free above all merged-on-main + in-flight #3878's B-0561) per the multi-Otto ID-allocation discipline in .claude/rules/otto-channels-reference-card.md. Crash-recovery note: this row + research file were the only artifacts from the pre-crash Otto session that hadn't already shipped via concurrent PRs (rule landed via #3935, B-0507 follow-on via #3937, Lior tick via #3936). Per-artifact refresh-before-decide caught the duplications before pushing. Co-Authored-By: Claude <noreply@anthropic.com>
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Pull request overview
This PR adds two history-surface artifacts for Step 2 of the B-0543 QG isomorphism proof path: a P2 backlog row and a research seed describing a proposed mapping from a 4-axis cube + Adinkra layer + Cayley-Dickson tower onto a HaPPY-like quantum error-correcting code structure. It is documentation/research-only, with no code or tooling changes.
Changes:
- Adds backlog row
B-0562(P2, in_progress, depends_on B-0543/B-0544) describing the Step 2 research scope, effort (XL), and open questions. - Adds a research seed sketching the cube-face → boundary, edges → entanglement, vertices → bulk operators, and Adinkra → SUSY-generators mapping toward HaPPY-style entanglement-wedge reconstruction.
- Notes the B-0545 → B-0562 renumber to avoid collision with #3619 / #3878 in-flight allocations.
Reviewed changes
Copilot reviewed 2 out of 2 changed files in this pull request and generated no comments.
| File | Description |
|---|---|
docs/backlog/P2/B-0562-qg-isomorphism-step-2-cube-adinkra-cayley-dickson-to-happylike-qecc-2026-05-16.md |
New P2 backlog row with frontmatter (id, depends_on, last_updated) and scope/effort/open-questions for Step 2. |
docs/research/2026-05-15-qg-isomorphism-step-2-cube-adinkra-cayley-dickson-to-happylike-qecc.md |
New research seed laying out the cube/Adinkra/Cayley-Dickson → HaPPY mapping strategy and open technical gaps. |
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CI failures on PR #3941: - markdownlint MD029 line 22 (blockquote ordered list starting at "2." preserves source numbering from B-0543's 4-step proof strategy; added <!-- markdownlint-disable-next-line MD029 --> + clarifying intro) - markdownlint MD047 line 102 (missing trailing newline) - BACKLOG.md generated-index drift (B-0562 row added; incidentally sweeps up pre-existing B-0507/B-0508 [ ] → [x] flip that should have landed with PR #3937 but didn't trigger a regen) Co-Authored-By: Claude <noreply@anthropic.com>
Resolves Copilot review threads on PR #3941: - L22: ordered-list `> 2.` in blockquote → bold `> **Step 2.**` (MD029) - L102: missing trailing newline (MD047) Co-Authored-By: Claude <noreply@anthropic.com>
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| # Step 2 of 4 — From cube + Adinkra + Cayley-Dickson to HaPPY-like QEC | ||
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| **Date:** 2026-05-16 |
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| - [ ] **[B-0551](backlog/P2/B-0551-qg-isomorphism-step-2-infinite-game-topos-qecc-structure-2026-05-16.md)** QG isomorphism step 2 — formalize infinite-game extension topos and QECC algebraic structure | ||
| - [ ] **[B-0562](backlog/P2/B-0562-qg-isomorphism-step-2-cube-adinkra-cayley-dickson-to-happylike-qecc-2026-05-16.md)** QG isomorphism Step 2 — Cube + Adinkra + Cayley-Dickson → HaPPY-like QEC structure |
| effort: XL | ||
| tags: [research, category-theory, quantum-error-correction, adinkra, cayley-dickson, happy-code] | ||
| depends_on: [B-0543, B-0544] | ||
| composes_with: [] |
This was referenced May 16, 2026
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Summary
Step 2 of the 4-step QG isomorphism proof path opened in B-0543 / #3614. Unfolds the two axioms (Remember-When + Pay-Attention) into a 4-axis cube, grafts the Adinkra-Gates supermultiplet layer on cube vertices, lifts through a Cayley-Dickson tower (R → C → H → O → S → T), and proposes the algebraic shape that matches HaPPY (holographic perfect-tensor) QEC codes.
Why this is Step 2
Step 1 (B-0544, shipped via #3614) formalized
Zeta_{RA} = (Zeta, M, A)— a toposZetawith internal monadMfor memory and modal operatorAfor attention. The Step 2 question is: what's the algebraic structure of the extension when you let the two axioms factor through richer carriers (Adinkra symmetry + division-algebra tower)? This research seed identifies HaPPY-style holographic perfect tensors as the candidate algebraic shape.Files
docs/backlog/P2/B-0562-qg-isomorphism-step-2-cube-adinkra-cayley-dickson-to-happylike-qecc-2026-05-16.md(101 lines — backlog row, P2, depends_on [B-0543, B-0544])docs/research/2026-05-15-qg-isomorphism-step-2-cube-adinkra-cayley-dickson-to-happylike-qecc.md(173 lines — research seed)ID-allocation note (B-0545 → B-0562 renumber)
Originally allocated as B-0545. Collided with #3619's renumber-sweep that re-took B-0545 for Riven's cursor-terminal loop work. Renumbered to B-0562 — the next free above all merged-on-main (highest B-0560) plus in-flight #3878's B-0561 allocation. Discipline per
.claude/rules/otto-channels-reference-card.md's multi-Otto ID-allocation section.Crash-recovery context
This row + research file were authored by the pre-crash Otto session and were the only artifacts that hadn't already shipped via concurrent PRs:
premise-flagged-unverified-...) landed via #3935Per-artifact
git show origin/main:<path>checks caught all four duplications BEFORE this push.Test plan
depends_ononce they're filed🤖 Generated with Claude Code