feat(instructions): add Method 3 Input Synthesis coaching knowledge (#653)

# Pull Request

## Description

Add `dt-method-03-synthesis.instructions.md` with method-tier coaching
knowledge for Design Thinking Method 3.

- Pattern recognition framework: data source integration and theme
development
- Systematic synthesis process: input organization, pattern recognition,
unified insight development
- Five-dimension synthesis validation: research fidelity, stakeholder
completeness, pattern robustness, actionability, team alignment
- Coaching patterns: multi-source validation, stakeholder balance,
context preservation, pattern honesty
- Human-AI collaboration sequence for synthesis work
- Problem-to-Solution Space transition readiness signals (critical
boundary)
- Method 2 input requirements and Method 4 output deliverables

## Related Issue(s)

Closes #578

## Type of Change

Select all that apply:

**Code & Documentation:**

- [ ] Bug fix (non-breaking change fixing an issue)
- [x] New feature (non-breaking change adding functionality)
- [ ] Breaking change (fix or feature causing existing functionality to
change)
- [ ] Documentation update

**Infrastructure & Configuration:**

- [ ] GitHub Actions workflow
- [ ] Linting configuration (markdown, PowerShell, etc.)
- [ ] Security configuration
- [ ] DevContainer configuration
- [ ] Dependency update

**AI Artifacts:**

- [ ] Reviewed contribution with `prompt-builder` agent and addressed
all feedback
- [x] Copilot instructions (`.github/instructions/*.instructions.md`)
- [ ] Copilot prompt (`.github/prompts/*.prompt.md`)
- [ ] Copilot agent (`.github/agents/*.agent.md`)
- [ ] Copilot skill (`.github/skills/*/SKILL.md`)

**Other:**

- [ ] Script/automation (`.ps1`, `.sh`, `.py`)
- [ ] Other (please describe):

## Testing

- Passes `npm run lint:md`
- `applyTo: '**/.copilot-tracking/dt/**/method-03*'` (method tier)

## Checklist

### Required Checks

- [ ] Documentation is updated (if applicable)
- [ ] Files follow existing naming conventions
- [ ] Changes are backwards compatible (if applicable)
- [ ] Tests added for new functionality (if applicable)

### Required Automated Checks

The following validation commands must pass before merging:

- [x] Markdown linting: `npm run lint:md`
- [x] Spell checking: `npm run spell-check`
- [x] Frontmatter validation: `npm run lint:frontmatter`
- [x] Skill structure validation: `npm run validate:skills`
- [x] Link validation: `npm run lint:md-links`
- [ ] PowerShell analysis: `npm run lint:ps`

## Security Considerations

- [x] This PR does not contain any sensitive or NDA information
- [ ] Any new dependencies have been reviewed for security issues
- [ ] Security-related scripts follow the principle of least privilege

## Additional Notes

<!-- Any additional information that reviewers should know -->

---------

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

Author: chaosdinosaur

.github/instructions/design-thinking/dt-method-03-synthesis.instructions.md

@@ -4,3 +4,4 @@ This collection includes instructions for:
 
 - **DT Coaching Identity** — Defines the coach's interaction philosophy (Think, Speak, Empower), progressive hint engine, psychological safety patterns, and hat-switching framework for consistent behavior across all nine methods
 - **DT Method 02: Design Research** — Interview techniques, research planning, environmental observation, and insight extraction patterns for systematic discovery of end-user needs through direct engagement across three phases: planning, execution, and documentation
+- **DT Method 03: Input Synthesis** — Pattern recognition, theme development, synthesis validation, and Problem-to-Solution Space transition readiness for transforming fragmented research data into unified problem understanding

collections/design-thinking.collection.md

@@ -14,5 +14,7 @@ items:
     kind: instruction
   - path: .github/instructions/design-thinking/dt-method-02-research.instructions.md
     kind: instruction
+  - path: .github/instructions/design-thinking/dt-method-03-synthesis.instructions.md
+    kind: instruction
 display:
   ordering: alpha

collections/design-thinking.collection.yml

@@ -159,6 +159,8 @@ items:
   kind: instruction
 - path: .github/instructions/design-thinking/dt-method-02-research.instructions.md
   kind: instruction
+- path: .github/instructions/design-thinking/dt-method-03-synthesis.instructions.md
+  kind: instruction
 - path: .github/instructions/design-thinking/dt-quality-constraints.instructions.md
   kind: instruction
 - path: .github/instructions/git-merge.instructions.md

collections/hve-core-all.collection.yml

@@ -16,6 +16,7 @@ copilot plugin install design-thinking@hve-core
 | dt-coaching-identity   | Required instructions when working with or doing any Design Thinking (DT); Contains instructions for the Design Thinking coach identity, philosophy, and user interaction and communication requirements for consistent coaching behavior. |
 | dt-quality-constraints | Quality constraints, fidelity rules, and output standards for Design Thinking coaching across all nine methods                                                                                                                             |
 | dt-method-02-research  | Method 2 Design Research coaching knowledge: interview techniques, research planning, environmental observation, and insight extraction patterns                                                                                           |
+| dt-method-03-synthesis | Method 3 Input Synthesis coaching knowledge: pattern recognition, theme development, synthesis validation, and Problem-to-Solution Space transition readiness                                                                              |
 
 ---
 

plugins/design-thinking/README.md

@@ -0,0 +1 @@
+../../../.github/instructions/design-thinking/dt-method-03-synthesis.instructions.md

plugins/design-thinking/instructions/dt-method-03-synthesis.md

@@ -96,6 +96,7 @@ copilot plugin install hve-core-all@hve-core
 | csharp                   | Required instructions for C# (CSharp) research, planning, implementation, editing, or creating - Brought to you by microsoft/hve-core                                                                                                                       |
 | dt-coaching-identity     | Required instructions when working with or doing any Design Thinking (DT); Contains instructions for the Design Thinking coach identity, philosophy, and user interaction and communication requirements for consistent coaching behavior.                  |
 | dt-method-02-research    | Method 2 Design Research coaching knowledge: interview techniques, research planning, environmental observation, and insight extraction patterns                                                                                                            |
+| dt-method-03-synthesis   | Method 3 Input Synthesis coaching knowledge: pattern recognition, theme development, synthesis validation, and Problem-to-Solution Space transition readiness                                                                                               |
 | dt-quality-constraints   | Quality constraints, fidelity rules, and output standards for Design Thinking coaching across all nine methods                                                                                                                                              |
 | git-merge                | Required protocol for Git merge, rebase, and rebase --onto workflows with conflict handling and stop controls.                                                                                                                                              |
 | github-backlog-discovery | Discovery protocol for GitHub backlog management - artifact-driven, user-centric, and search-based issue discovery                                                                                                                                          |

plugins/hve-core-all/README.md

@@ -0,0 +1 @@
+../../../.github/instructions/design-thinking/dt-method-03-synthesis.instructions.md