Research-Stack/obsidian-vault/08-TOOLS/01-Templates/Formal Proof.md
Brandon Schneider 54004abe71 Setup Obsidian Knowledge Base for Research Stack
Created comprehensive Obsidian vault for managing Research Stack knowledge:

Core Structure:
- 00-MAP/ - Navigation, Dashboard, Core Concepts, Glossary, Getting Started
- 01-LAYERS/ - All 7 USTSM layers (L0-L6) with formal proofs, docs, receipts, hardware
- 07-RESEARCH/ - Milestones, Attack Plans, Conjectures, Experiments
- 08-TOOLS/ - Templates, Workflows, Scripts
- 09-REFERENCES/ - External resources
- 10-ARCHIVE/ - Completed items

Configuration Files:
- .obsidian/app.json - Vault settings
- .obsidian/community-plugins.json - Plugin configuration
- .obsidian/snippets/research-stack.css - Custom theme with layer colors
- .obsidian/plugins/ - Templater, QuickAdd, Dataview settings
- .obsidian/workspaces.json - Pre-configured workspaces

Templates Created:
- Formal Proof - For Lean theorem documentation
- Attack Plan - For research initiatives
- Milestone - For project milestones
- Receipt - For validation receipts
- Daily Standup - For daily progress tracking

Features:
- Dataview dashboard queries for system health
- Layer-specific color coding (L0-L6)
- Receipt styling and validation status
- Graph view customization
- QuickAdd commands for rapid note creation
- Templater automation with research helpers
- Pre-configured workspaces for different activities

Documentation:
- README.md - Complete vault guide
- Getting Started.md - Step-by-step tutorial
- Core Concepts.md - Fundamental principles
- Glossary.md - Research Stack terminology

Burgers 4-Theorem Attack Plan documented:
- Energy Dissipation theorem
- CFL Stability theorem
- Mass Conservation theorem
- Complexity Regularization theorem

Generated with [Devin](https://cli.devin.ai/docs)

Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>
2026-05-19 14:40:41 +00:00

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Markdown

---
title: "<% tp.file.title %>"
type: "formal-proof"
layer: "<% tp.system.suggester(['L0', 'L1', 'L2', 'L3', 'L4', 'L5', 'L6'], ['L0 - Primordial', 'L1 - Geometric', 'L2 - Biological', 'L3 - Thermodynamic', 'L4 - Security', 'L5 - Semantic', 'L6 - Meta']) %>"
status: "<% tp.system.suggester(['draft', 'in-progress', 'proven', 'verified'], ['Draft', 'In Progress', 'Proven', 'Verified']) %>"
created: "<% tp.date.now('YYYY-MM-DD') %>"
modified: "<% tp.date.now('YYYY-MM-DD') %>"
lean-module: ""
dependencies: []
related-theorems: []
receipts: []
---
# <% tp.file.title %>
## Overview
<!-- Brief description of the formal proof -->
## Layer Context
**Layer:** <% tp.system.suggester(['L0', 'L1', 'L2', 'L3', 'L4', 'L5', 'L6'], ['L0 - Primordial', 'L1 - Geometric', 'L2 - Biological', 'L3 - Thermodynamic', 'L4 - Security', 'L5 - Semantic', 'L6 - Meta']) %>
## Formal Statement
```lean
theorem <% tp.file.title %> [hypotheses] : conclusion :=
sorry
```
## Proof Strategy
<!-- High-level proof approach -->
### Key Lemmas
- [[Lemma 1]]
- [[Lemma 2]]
### Dependencies
- [[Dependency 1]]
- [[Dependency 2]]
## Lean Implementation
<!-- Link to actual Lean code -->
```lean
-- Path: 0-Core-Formalism/lean/Semantics/
```
## Receipt Generation
<!-- Receipt functions and validation -->
```lean
def <% tp.file.title %>Receipt (state : State) : String :=
"<% tp.file.title %>:" ++ toString state.val ++ ","
```
## Verification Status
- **Formal Verification:** <% tp.system.suggester(['pending', 'in-progress', 'complete'], ['Pending', 'In Progress', 'Complete']) %>
- **Code Review:** <% tp.system.suggester(['pending', 'in-progress', 'complete'], ['Pending', 'In Progress', 'Complete']) %>
- **Testing:** <% tp.system.suggester(['pending', 'in-progress', 'complete'], ['Pending', 'In Progress', 'Complete']) %>
## Related Work
- [[Related Proof 1]]
- [[Related Proof 2]]
## Notes
<!-- Additional notes, TODOs, and open questions -->
## Tags
#formal-proof #layer-<% tp.system.suggester(['L0', 'L1', 'L2', 'L3', 'L4', 'L5', 'L6'], ['L0', 'L1', 'L2', 'L3', 'L4', 'L5', 'L6']) %> #status-<% tp.system.suggester(['draft', 'in-progress', 'proven', 'verified'], ['draft', 'in-progress', 'proven', 'verified']) %>