anentrypoint Fifth-Dimension Engine
WFGY 5.0's core problem-solving tool. Lifts a target into a higher problem-coordinate, then returns a route that can be inspected, attacked, expanded, and tested.
Before you decide, shoot first.
What This Is
The Fifth-Dimension Engine does not just answer. It transforms a target into a route.
| Input | Engine Action |
|---|---|
| Theorem | Produces proof-route structure |
| Frontier problem | Produces research kernel |
| Strange theme | Produces mathematical skeleton |
| Life decision | Produces route map |
| Product idea | Produces positioning route |
| Engineering failure | Produces repair path |
| Meme or absurd target | Produces hidden structure |
The output is not a direct answer. It is a route: an inspectable, attackable, expandable structure you can verify, challenge, and refine.
When to Use
Use this skill when you have:
- A well-specified problem (use Goal Compiler first if unclear)
- A target worth spending time on (trivial problems don't need shooting)
- An appetite for structured reasoning (prefer depth over speed)
Use especially for:
- Theorem work (formal proofs, mathematical problems)
- Strategic decisions (career, startup, major choices)
- Research questions (turning ideas into research kernels)
- Engineering failures (root cause analysis, repair paths)
- Product/positioning work (audience, launch strategy)
- Mixed-theme problems (combining unrelated ideas into research)
How to Use
Basic Command
shoot + [your problem]
The Engine Returns
A structured route containing:
- Route: The core strategy or path forward
- Structure: Decomposition into sub-problems
- Candidate Lemmas: Supporting proofs, insights, or evidence
- Objections: What could go wrong, counterarguments
- Open Debt: What remains unresolved
- Next Command: What to do next (for theorem work: a new Lean line; for other work: next investigative step)
Why This Matters
Instead of:
- A flat answer (right or wrong, you can't inspect it)
You get:
- A structure you can examine
- Sub-claims you can verify independently
- Attack surfaces (where to challenge it)
- Expansion points (where to dig deeper)
- Clear open questions (what's not yet resolved)
Interaction with Other Skills
With Polaris Goal Compiler
- Goal Compiler specifies and atomizes the problem
- Fifth-Dimension Engine produces the route
- Goal Compiler's verification gates validate the engine's output
Integration: After Goal Compiler breaks work into atoms, use the engine on each atom that requires structured reasoning.
Workflow:
- Goal Compiler compiles the problem into task atoms
- For each atom, ask: "Do I need to shoot this, or is it routine?"
- If routine: execute directly
- If complex: shoot it with Fifth-Dimension Engine
- Use Goal Compiler's verification gate to check the output
- Move to next atom
With WFGY-Method (Drift Control)
- Fifth-Dimension Engine produces structured reasoning
- WFGY-Method keeps that reasoning aligned with the original goal
Integration: While the engine explores the route, WFGY-Method checks: "Are we still solving the original problem, or have we drifted into a different one?"
Use the engine for depth, WFGY-Method for direction.
Modes
Theorem and Formal Work
Shoot a theorem or formal problem; the engine returns a proof-route structure that can be checked against a formal verification standard.
Mixing Themes
Give the engine two unrelated themes and let it find the mathematical skeleton underneath them:
shoot + [theme 1] + [theme 2]
See references/research-kernel-extraction.md for how mixed themes become research kernels.
Everyday Problems
The same engine works on ordinary decisions, work problems, product questions, and engineering failures — any well-specified target benefits from being shot into a route rather than answered directly.
Verification
The engine output is inspectable, which means verifiable. See references/route-inspection-guide.md for how to inspect, attack, and verify a route.
This is not: a black box. You can (and should) inspect, attack, and refine.
What This Is Not
This skill does not:
- Specify the problem (that's Goal Compiler)
- Control drift during execution (that's WFGY-Method)
- Produce a final answer (it produces a route, which you then verify and decide on)
- Guarantee the route is correct (inspection and verification are your job)
- Claim every shoot becomes a final theorem (a shoot creates a structured route; final proof, empirical truth, or real-world correctness depends on verification, review, formalization, or testing)
References
See references/ directory for:
route-structure.md— what a route is and how it is structuredresearch-kernel-extraction.md— turning ideas into research kernelsroute-inspection-guide.md— how to verify and attack a routeskills/polaris-protocol/SKILL.md— the Polaris Protocol tree root and state machine