From f04430079fa20ee5ef94995ff8e44ee397df4972 Mon Sep 17 00:00:00 2001 From: Allaun Silverfox <28494262+allaunthefox@users.noreply.github.com> Date: Thu, 2 Jul 2026 03:37:11 +0200 Subject: [PATCH] Remove BREAKGLASS_NR_BRACKET_PROPOSAL.md --- .../reviews/BREAKGLASS_NR_BRACKET_PROPOSAL.md | 356 ------------------ 1 file changed, 356 deletions(-) delete mode 100644 docs/reviews/BREAKGLASS_NR_BRACKET_PROPOSAL.md diff --git a/docs/reviews/BREAKGLASS_NR_BRACKET_PROPOSAL.md b/docs/reviews/BREAKGLASS_NR_BRACKET_PROPOSAL.md deleted file mode 100644 index c6aafa0e..00000000 --- a/docs/reviews/BREAKGLASS_NR_BRACKET_PROPOSAL.md +++ /dev/null @@ -1,356 +0,0 @@ -# Breakglass Proposal — Fusion of Fusions: The NR Bracket Unifies Six Layers - -**Status:** REAL-DATA VALIDATED — d_CE μ = 0 confirmed on 10 RRC candidates - ---- - -## 1. What this is - -**Execution model (three-layer fusion):** This breakglass runs on a fused -combination of LLMs. "Fusion" here means **three independent fusion -layers stacked on top of each other**: - -1. **Provider fusion (Free → Subscription → Paid).** Primary inference - is free or subscription-tier (whatever models are available without - per-token cost). When those models are not up to a task — e.g. - generating a complex Lean proof that a small or quantized model - cannot produce — inference falls through to paid OpenRouter tokens. - The FreeLLMAPI proxy auto-router on qfox-1 manages this: it tries - the available pool, and OpenRouter's "fusion" mode (parallel - multi-model dispatch → first complete response wins) is the escape - hatch for hard problems. I buy tokens only for the cases the free - tier can't handle. - -2. **Tool fusion (OpenCode → Hermes → Lean REPL).** The agent stack - is also fused — each layer covers what the previous one can't: - - **OpenCode (this session)** — edits files, runs builds, writes shims. - - **DeepSeek V4 Flash (via FreeLLMAPI/OpenRouter)** — generates formal - Lean proofs (`generate_lean_proof` tool), classifies via RRC - alignment gates. Used only when smaller models can't close a proof. - - **Hermes Agent v0.14.0 (neon-64gb, netcup ARM64)** — orchestrates - multi-step pipelines, hosts the remote Lean REPL (port 3904) and - Python LSP (port 3905) for zero-/low-token compile checks. - - **Human (me)** — owns the research direction, pays the bills when - the machine ceiling is hit. - -3. **Mathematical fusion.** The single algebraic lemma - \([\mu,\mu]_{\mathrm{NR}} = 0\) unifies six formerly separate layers - (2b–2f, PIST, VCN) under one Sidon-support-separation mechanism. - -The fused model means: no single provider is the bottleneck. Free cache -hits do 90% of the work; paid tokens cover the tail. The breakglass is -not a proposal — it's a running system that burns small money on hard -proofs and near-zero on everything else. - ---- - -The Nijenhuis–Richardson bracket \([\mu,\mu]_{\mathrm{NR}} = 0\) is **not** -just an algebraic lemma for one module. It is the **same structural -mechanism** appearing in six formerly separate layers of the stack: - -``` - ┌──────────────────────────────────────────────┐ - │ [μ,μ]_{NR} = 0 │ - │ ↓ Sidon support separation ↓ │ - ├──────────────────────────────────────────────┤ - │ Layer 1: Four discrete invariants I₁–I₄ │ - │ Layer 2: Crossing matrix C + J² = J+I │ - │ Layer 2b: Eigensolid convergence (analytic) │ - │ Layer 2c: NR bracket MC equation (algebraic) │ ✓ PROVEN + VALIDATED - │ Layer 2d: Yang-Baxter integrability │ ← EXPOSED - │ Layer 2e: TL quotient factorization │ ← EXPOSED - ├──────────────────────────────────────────────┤ - │ PIST classification: same support separation │ - │ VCN substrate: zero-gap = vanishing NR term │ - └──────────────────────────────────────────────┘ -``` - -**The core insight:** The Sidon address map \((i,j) \mapsto 2^i + 2^j\) -does four independent jobs simultaneously, and the NR bracket vanishing -is where all four converge. - ---- - -## 2. The six connections (showing my work) - -### 2a. Core: [μ,μ]_{NR} = 0 (the new code) - -**What is proven:** The 2-cochain \(\mu \in C^2(V,V)\) induced by the -Sidon crossing matrix satisfies the Maurer–Cartan equation: - -\[ -d_{\mathrm{CE}}\mu + \tfrac12[\mu, \mu]_{\mathrm{NR}} = 0, -\qquad \mu \in \mathrm{MC}(\mathcal{O}_{\mathrm{split}} \subset C^\bullet(V,V)). -\] - -**Why it holds (three-step proof):** - -| Step | Argument | Source | -|------|----------|--------| -| 1. Internal | Each \(\mu_i\) has 1D \(\lambda_-\) eigenspace → Jacobiator vanishes → \([\mu_i,\mu_i]_{\mathrm{NR}} = 0\) | I₂ (\(\sigma-\tau > 0\)) | -| 2. Cross | Sidon-disjoint supports → no operadic contraction path → \([\mu_i,\mu_j]_{\mathrm{NR}} = 0\) | I₄ (binary uniqueness) | -| 3. Sum | \([\mu,\mu]_{\mathrm{NR}} = \sum_i [\mu_i,\mu_i]_{\mathrm{NR}} + 2\sum_{i