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…trate formalization (Aaron 2026-05-01) Aaron 2026-05-01: "we should do all of those backlog and start with 1 i think if you agree" — referring to the formalization roadmap Otto laid out in long-form writeup after Claude.ai's critique that Zeta substrate is "not yet, strictly speaking, a formal system." Aaron's "not yet" is the move. Eight rows filed: P2 (tractable, prioritize start): B-0131: Z-set retraction algebra in Lean (TRACTABLE START) B-0132: CRDT-composition for BFT propagation B-0133: Sequent calculus for claim/retraction/attribution B-0134: Type-theoretic encoding of orthogonality discipline P3 (research-grade, deferred): B-0135: Modal logic for retractability (Quantum-Rodney's-Razor in S4 / dynamic logic) B-0136: Category-theoretic compositional structure (operads + monoidal cats) B-0137: Tarski-stratification proof (requires substrate to be formal-system-grade first) B-0138: BFT-resistance theorem for Aurora (composed-CRDT-plus-consensus) Each row cites the load-bearing source (Budiu et al. for DBSP, Shapiro et al. for CRDTs, Troelstra & Schwichtenberg for proof theory, Blackburn et al. for modal logic, Mac Lane / Milewski for category theory). Each composes-with chain references concrete substrate files. Each acceptance criteria includes academic-mathematician review per the lattice-capture corrective discipline (B-0130 / feedback_lattice_capture_*). Aaron's "high school graduate, this is where you could really help" framing acknowledged: formalization is a path. Otto's role is bridge between architectural intuition + formal-systems literature. Specific learning paths cited in B-0131 for Aaron to follow alongside if he chooses (Theorem Proving in Lean 4, Mathlib, Shapiro CRDT paper, Troelstra & Schwichtenberg). Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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Pull request overview
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Adds eight new backlog entries (B-0131..B-0138) describing a formalization roadmap for the Zeta substrate (P2 “tractable” through P3 “research-grade”), and updates the main backlog index to reference them.
Changes:
- Added new P2 backlog docs for Lean Z-set formalization, CRDT composition, sequent calculus, and a type-theoretic orthogonality judgment.
- Added new P3 backlog docs for modal logic, category theory framing, a Tarski-stratification claim, and an Aurora BFT-resistance theorem effort.
- Updated
docs/BACKLOG.mdto include the new items under P2 and P3.
Reviewed changes
Copilot reviewed 9 out of 9 changed files in this pull request and generated 4 comments.
Show a summary per file
| File | Description |
|---|---|
| docs/backlog/P2/B-0131-formalize-zset-retraction-algebra-in-lean-aaron-2026-05-01.md | New backlog row for Lean formalization of Z-set/retraction algebra and DBSP theorems |
| docs/backlog/P2/B-0132-crdt-composition-for-bft-propagation-aaron-2026-05-01.md | New backlog row mapping substrate events to CRDTs and composing with BFT |
| docs/backlog/P2/B-0133-sequent-calculus-for-claim-retraction-attribution-aaron-2026-05-01.md | New backlog row for sequent calculus / labeled deductive systems framing |
| docs/backlog/P2/B-0134-type-theoretic-orthogonality-discipline-encoding-aaron-2026-05-01.md | New backlog row for decidable “extension vs new class” orthogonality judgment |
| docs/backlog/P3/B-0135-modal-logic-for-retractability-quantum-rodney-razor-aaron-2026-05-01.md | New backlog row for modal/dynamic logic semantics for retractability |
| docs/backlog/P3/B-0136-category-theoretic-compositional-structure-aaron-2026-05-01.md | New backlog row for categorical invariants (operads/monoidal categories) |
| docs/backlog/P3/B-0137-tarski-stratification-proof-aaron-2026-05-01.md | New backlog row for investigating a Tarski-style stratification theorem |
| docs/backlog/P3/B-0138-bft-resistance-theorem-aurora-composed-crdt-plus-consensus-aaron-2026-05-01.md | New backlog row for an Aurora BFT-resistance theorem composed from CRDT+consensus |
| docs/BACKLOG.md | Index updates to include B-0131..B-0138 under P2/P3 |
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| | Substrate event | CRDT type | Notes | | ||
| |---|---|---| | ||
| | Claim creation | G-Set add | Add-only is monotone | | ||
| | Claim revision | LWW-Register or Multi-Value-Register | LWW or branch-and-merge | | ||
| | Claim retraction | OR-Set remove | Observed-Remove preserves causal history | | ||
| | Candidate promotion | State machine on monotone semi-lattice | Rank/level transitions | | ||
| | Consensus formation | PBFT / HotStuff / Tendermint family | Where BFT proper lives | |
| Specific scope: | ||
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| - **Z-set semi-ring algebra**: formalize Z-sets as multisets-with-multiplicity (positive and negative), with operations {+, -, ⋈, π, σ, ρ, distinct}. Already partially formal in DBSP papers; mechanize. | ||
| - **Retraction operator semantics**: prove that retractions form a group (every operation invertible) and compose monotonically with other Z-set operations. |
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| 1. **Lean 4 project structure** under `tools/lean4/` extending the existing setup, with explicit dependence on Mathlib. | ||
| 2. **Z-set type definition** with explicit positive/negative multiplicity. `ZSet α : Type` with operations as instances of typeclasses (`AddGroup`, `MulZeroClass`, etc. where applicable). | ||
| 3. **Retraction-operator theorems** mechanized: idempotence on retractions, group-inversion property, monotone composition with other operators. |
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| - `feedback_aaron_pirate_not_priest_expand_prune_pedagogical_framework_quantum_rodney_razor_parallel_worlds_aaron_2026_05_01.md` — parallel-worlds-pruning metaphysics. | ||
| - `feedback_retraction_native_paraconsistent_set_theory_candidate_quantum_bp.md` — Quantum-Rodney's-Razor + paraconsistent set theory. |
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Eight backlog rows for Zeta substrate formalization. P2 (tractable): Z-set Lean (B-0131 START), CRDT-composition BFT (B-0132), sequent calculus (B-0133), orthogonality type-theory (B-0134). P3 (research-grade): modal logic (B-0135), category theory (B-0136), Tarski-stratification proof (B-0137), Aurora BFT-resistance theorem (B-0138). Aaron's 'not yet' framing: formalization is a path.