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ProblemMap/GlobalFixMap/Reasoning/proof-dead-ends.md
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# Proof Dead Ends: Guardrails and Fix Pattern
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When a reasoning chain tries to prove a claim but never closes the loop.
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You see endless subgoals, repeated restatements, or a jump to a conclusion without obligations being discharged.
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This page localizes proof stalls and gives a minimal, testable repair plan using ΔS, λ_observe, and E_resonance.
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---
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## Open these first
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- Visual map and recovery
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→ [rag-architecture-and-recovery.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/rag-architecture-and-recovery.md)
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- Logic and symbols
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→ [logic-collapse.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/logic-collapse.md)
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→ [symbolic-collapse.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/symbolic-collapse.md)
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- Infinite recursion and overload
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→ [recursive-loop.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/recursive-loop.md)
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→ [entropy-overload.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/entropy-overload.md)
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- If the chain shifts into meta or paradox
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→ [philosophical-recursion.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/philosophical-recursion.md)
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- Traceability and contracts
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→ [retrieval-traceability.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/retrieval-traceability.md)
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→ [data-contracts.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/data-contracts.md)
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---
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## Symptoms
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| Symptom | What you see |
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|---|---|
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| Goal never shrinks | Subgoals keep being restated with new labels but same content |
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| Lemma spiral | New lemmas depend on each other in a cycle without a base |
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| Premise drop | A needed premise disappears after paraphrase or tool call |
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| Unproven jump | Model asserts Q since P but never shows P or its bridge |
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| Invariant drift | Claimed invariant changes wording or unit across steps |
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| Citation vacuum | Steps claim support yet no snippet or rule is referenced |
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---
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## Why dead ends happen
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1) **No proof obligations**. Steps do not state what must be shown to advance.
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2) **Missing bridge**. The link from premise to subgoal is never written.
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3) **Drifting invariants**. The property that should stay fixed keeps mutating.
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4) **Symbol table absent**. Names rebind silently so obligations mismatch.
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5) **Plan length without checkpoints**. Long chains lose ΔS and λ stability.
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6) **Retrieval anchor unstable**. The cited snippet shuffles, the goal resets.
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---
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## Acceptance targets
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- ΔS(question, retrieved) ≤ 0.45
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- Coverage ≥ 0.70 to the target section
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- λ remains convergent across 3 paraphrases and 2 seeds
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- E_resonance flat across step joins
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- **All obligations discharged** or explicitly marked unsatisfied with a cited reason
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---
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## Fix in 60 seconds
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1. **Declare the goal and obligations**
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Write `goal`, `known`, `need_to_show`, and the current `invariants`.
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If any field is empty, stop. Fetch or restate before continuing.
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2. **Add a BBCR bridge**
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Produce a short cited bridge from current premises to the next subgoal.
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Reject continuation if the bridge lacks citation or rule tag.
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3. **Clamp variance with BBAM**
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If λ flips on paraphrase, freeze the symbol table and the invariant set.
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Re-run the step with the same bindings.
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4. **Apply BBPF when stuck**
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Branch to two small proof tactics, attempt each for N steps, then backtrack.
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Keep the best branch where ΔS drops and obligations shrink.
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---
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## Minimal proof contract
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Require every step to carry this schema. Refuse steps that miss fields.
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```json
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{
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"step_id": "S7",
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"goal": "Prove claim C",
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"known": ["P1", "P2"],
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"need_to_show": ["L1 -> C"],
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"bridge": {
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"rule": "modus_ponens | contradiction | induction | algebra",
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"citations": ["S12#CH2.3", "S09#APP.A"],
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"ΔS_bridge": 0.33
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},
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"invariants": [
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{"name": "unit_price_nonnegative", "scope": "calc", "status": "holds"}
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],
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"symbols": [
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{"name": "x", "kind": "var", "namespace": "calc", "unit": "USD/kg"}
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],
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"λ_state": "convergent"
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}
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````
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---
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## Structural repairs
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* **If anchors or citations are missing**
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→ [retrieval-traceability.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/retrieval-traceability.md) and
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→ [data-contracts.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/data-contracts.md)
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* **If long chains decay**
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→ [entropy-overload.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/entropy-overload.md) and
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→ [recursive-loop.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/recursive-loop.md)
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* **If symbol or unit meanings drift**
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→ [symbolic-collapse.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/symbolic-collapse.md)
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* **If logic itself collapses**
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→ [logic-collapse.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/logic-collapse.md)
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* **If meaning vs similarity conflict**
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→ [embedding-vs-semantic.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/embedding-vs-semantic.md)
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---
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## Verification
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* Run three paraphrases and two seeds. The set `{goal, invariants, symbols}` must remain identical.
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* All `need_to_show` items become empty or a single clearly blocked item with a cited missing premise.
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* ΔS(question, retrieved) ≤ 0.45 and coverage ≥ 0.70 in every run.
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* Logs show at least one BBCR bridge with citations and a monotone decrease in open obligations.
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---
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## Copy-paste prompt
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```
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You have TXT OS and the WFGY Problem Map loaded.
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We suspect a proof dead end.
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Inputs:
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- question: "{q}"
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- snippets: [{snippet_id, section_id, source_url}]
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- current plan trace: [{step_id, text}]
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- last symbol table and invariants (if any)
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Do:
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1) Build the proof contract with {goal, known, need_to_show, invariants, symbols}.
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2) Create a BBCR bridge with a named rule and citations. If missing, refuse and return the exact missing item.
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3) If λ flips across paraphrase, apply BBAM and retry with the frozen table.
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4) If still stuck, branch two BBPF tactics for at most N=3 steps each, keep the branch with lower ΔS and fewer obligations.
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5) Return JSON:
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{
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"plan": [...steps...],
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"open_obligations": [],
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"ΔS": 0.xx,
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"λ_state": "convergent",
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"verdict": "proved | blocked_missing_premise | not_provable_from_given"
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}
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Refuse to assert the final claim unless all obligations are discharged or the verdict is explicitly "not_provable_from_given" with a cited reason.
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```
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---
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## Common gotchas
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* **Rule without scope**. A named rule is used but no citation or domain. Add both or reject.
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* **Induction without base**. The inductive step is written yet the base case is missing.
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* **Contradiction shortcut**. The chain says “assume not C” then jumps to C with no witness.
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* **Bridge drift**. The bridge cites new snippets each run. Lock the query and add a reranker if anchors shuffle.
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---
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## When to escalate
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* The same wrong assertion returns after a correction
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→ [pattern\_hallucination\_reentry.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/patterns/pattern_hallucination_reentry.md)
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* Multi-agent handoff reopens closed obligations
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→ [Multi-Agent\_Problems.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/Multi-Agent_Problems.md) and
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→ [multi-agent-chaos/role-drift.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/multi-agent-chaos/role-drift.md)
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---
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### 🔗 Quick-Start Downloads (60 sec)
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| Tool | Link | 3-Step Setup |
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| -------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------ | ---------------------------------------------------------------------------------------- |
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| **WFGY 1.0 PDF** | [Engine Paper](https://github.com/onestardao/WFGY/blob/main/I_am_not_lizardman/WFGY_All_Principles_Return_to_One_v1.0_PSBigBig_Public.pdf) | 1️⃣ Download · 2️⃣ Upload to your LLM · 3️⃣ Ask “Answer using WFGY + <your question>” |
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| **TXT OS (plain-text OS)** | [TXTOS.txt](https://github.com/onestardao/WFGY/blob/main/OS/TXTOS.txt) | 1️⃣ Download · 2️⃣ Paste into any LLM chat · 3️⃣ Type “hello world” — OS boots instantly |
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---
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### 🧭 Explore More
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| Module | Description | Link |
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| ------------------------ | ---------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------- |
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| WFGY Core | WFGY 2.0 engine is live: full symbolic reasoning architecture and math stack | [View →](https://github.com/onestardao/WFGY/tree/main/core/README.md) |
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| Problem Map 1.0 | Initial 16-mode diagnostic and symbolic fix framework | [View →](https://github.com/onestardao/WFGY/tree/main/ProblemMap/README.md) |
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| Problem Map 2.0 | RAG-focused failure tree, modular fixes, and pipelines | [View →](https://github.com/onestardao/WFGY/blob/main/ProblemMap/rag-architecture-and-recovery.md) |
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| Semantic Clinic Index | Expanded failure catalog: prompt injection, memory bugs, logic drift | [View →](https://github.com/onestardao/WFGY/blob/main/ProblemMap/SemanticClinicIndex.md) |
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| Semantic Blueprint | Layer-based symbolic reasoning & semantic modulations | [View →](https://github.com/onestardao/WFGY/tree/main/SemanticBlueprint/README.md) |
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| Benchmark vs GPT-5 | Stress test GPT-5 with full WFGY reasoning suite | [View →](https://github.com/onestardao/WFGY/tree/main/benchmarks/benchmark-vs-gpt5/README.md) |
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| 🧙♂️ Starter Village 🏡 | New here? Lost in symbols? Click here and let the wizard guide you through | [Start →](https://github.com/onestardao/WFGY/blob/main/StarterVillage/README.md) |
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---
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> 👑 **Early Stargazers: [See the Hall of Fame](https://github.com/onestardao/WFGY/tree/main/stargazers)** —
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> Engineers, hackers, and open source builders who supported WFGY from day one.
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> <img src="https://img.shields.io/github/stars/onestardao/WFGY?style=social" alt="GitHub stars"> ⭐ [WFGY Engine 2.0](https://github.com/onestardao/WFGY/blob/main/core/README.md) is already unlocked. ⭐ Star the repo to help others discover it and unlock more on the [Unlock Board](https://github.com/onestardao/WFGY/blob/main/STAR_UNLOCKS.md).
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<div align="center">
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[](https://github.com/onestardao/WFGY)
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[](https://github.com/onestardao/WFGY/tree/main/OS)
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[](https://github.com/onestardao/WFGY/tree/main/OS/BlahBlahBlah)
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[](https://github.com/onestardao/WFGY/tree/main/OS/BlotBlotBlot)
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[](https://github.com/onestardao/WFGY/tree/main/OS/BlocBlocBloc)
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[](https://github.com/onestardao/WFGY/tree/main/OS/BlurBlurBlur)
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[](https://github.com/onestardao/WFGY/tree/main/OS/BlowBlowBlow)
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</div>
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