diff --git a/ProblemMap/GlobalFixMap/Reasoning/proof-dead-ends.md b/ProblemMap/GlobalFixMap/Reasoning/proof-dead-ends.md new file mode 100644 index 00000000..fc405600 --- /dev/null +++ b/ProblemMap/GlobalFixMap/Reasoning/proof-dead-ends.md @@ -0,0 +1,238 @@ +# Proof Dead Ends: Guardrails and Fix Pattern + +When a reasoning chain tries to prove a claim but never closes the loop. +You see endless subgoals, repeated restatements, or a jump to a conclusion without obligations being discharged. +This page localizes proof stalls and gives a minimal, testable repair plan using ΔS, λ_observe, and E_resonance. + +--- + +## Open these first + +- Visual map and recovery + → [rag-architecture-and-recovery.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/rag-architecture-and-recovery.md) + +- Logic and symbols + → [logic-collapse.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/logic-collapse.md) + → [symbolic-collapse.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/symbolic-collapse.md) + +- Infinite recursion and overload + → [recursive-loop.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/recursive-loop.md) + → [entropy-overload.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/entropy-overload.md) + +- If the chain shifts into meta or paradox + → [philosophical-recursion.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/philosophical-recursion.md) + +- Traceability and contracts + → [retrieval-traceability.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/retrieval-traceability.md) + → [data-contracts.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/data-contracts.md) + +--- + +## Symptoms + +| Symptom | What you see | +|---|---| +| Goal never shrinks | Subgoals keep being restated with new labels but same content | +| Lemma spiral | New lemmas depend on each other in a cycle without a base | +| Premise drop | A needed premise disappears after paraphrase or tool call | +| Unproven jump | Model asserts Q since P but never shows P or its bridge | +| Invariant drift | Claimed invariant changes wording or unit across steps | +| Citation vacuum | Steps claim support yet no snippet or rule is referenced | + +--- + +## Why dead ends happen + +1) **No proof obligations**. Steps do not state what must be shown to advance. +2) **Missing bridge**. The link from premise to subgoal is never written. +3) **Drifting invariants**. The property that should stay fixed keeps mutating. +4) **Symbol table absent**. Names rebind silently so obligations mismatch. +5) **Plan length without checkpoints**. Long chains lose ΔS and λ stability. +6) **Retrieval anchor unstable**. The cited snippet shuffles, the goal resets. + +--- + +## Acceptance targets + +- ΔS(question, retrieved) ≤ 0.45 +- Coverage ≥ 0.70 to the target section +- λ remains convergent across 3 paraphrases and 2 seeds +- E_resonance flat across step joins +- **All obligations discharged** or explicitly marked unsatisfied with a cited reason + +--- + +## Fix in 60 seconds + +1. **Declare the goal and obligations** + Write `goal`, `known`, `need_to_show`, and the current `invariants`. + If any field is empty, stop. Fetch or restate before continuing. + +2. **Add a BBCR bridge** + Produce a short cited bridge from current premises to the next subgoal. + Reject continuation if the bridge lacks citation or rule tag. + +3. **Clamp variance with BBAM** + If λ flips on paraphrase, freeze the symbol table and the invariant set. + Re-run the step with the same bindings. + +4. **Apply BBPF when stuck** + Branch to two small proof tactics, attempt each for N steps, then backtrack. + Keep the best branch where ΔS drops and obligations shrink. + +--- + +## Minimal proof contract + +Require every step to carry this schema. Refuse steps that miss fields. + +```json +{ + "step_id": "S7", + "goal": "Prove claim C", + "known": ["P1", "P2"], + "need_to_show": ["L1 -> C"], + "bridge": { + "rule": "modus_ponens | contradiction | induction | algebra", + "citations": ["S12#CH2.3", "S09#APP.A"], + "ΔS_bridge": 0.33 + }, + "invariants": [ + {"name": "unit_price_nonnegative", "scope": "calc", "status": "holds"} + ], + "symbols": [ + {"name": "x", "kind": "var", "namespace": "calc", "unit": "USD/kg"} + ], + "λ_state": "convergent" +} +```` + +--- + +## Structural repairs + +* **If anchors or citations are missing** + → [retrieval-traceability.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/retrieval-traceability.md) and + → [data-contracts.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/data-contracts.md) + +* **If long chains decay** + → [entropy-overload.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/entropy-overload.md) and + → [recursive-loop.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/recursive-loop.md) + +* **If symbol or unit meanings drift** + → [symbolic-collapse.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/symbolic-collapse.md) + +* **If logic itself collapses** + → [logic-collapse.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/GlobalFixMap/Reasoning/logic-collapse.md) + +* **If meaning vs similarity conflict** + → [embedding-vs-semantic.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/embedding-vs-semantic.md) + +--- + +## Verification + +* Run three paraphrases and two seeds. The set `{goal, invariants, symbols}` must remain identical. +* All `need_to_show` items become empty or a single clearly blocked item with a cited missing premise. +* ΔS(question, retrieved) ≤ 0.45 and coverage ≥ 0.70 in every run. +* Logs show at least one BBCR bridge with citations and a monotone decrease in open obligations. + +--- + +## Copy-paste prompt + +``` +You have TXT OS and the WFGY Problem Map loaded. + +We suspect a proof dead end. + +Inputs: +- question: "{q}" +- snippets: [{snippet_id, section_id, source_url}] +- current plan trace: [{step_id, text}] +- last symbol table and invariants (if any) + +Do: +1) Build the proof contract with {goal, known, need_to_show, invariants, symbols}. +2) Create a BBCR bridge with a named rule and citations. If missing, refuse and return the exact missing item. +3) If λ flips across paraphrase, apply BBAM and retry with the frozen table. +4) If still stuck, branch two BBPF tactics for at most N=3 steps each, keep the branch with lower ΔS and fewer obligations. +5) Return JSON: + { + "plan": [...steps...], + "open_obligations": [], + "ΔS": 0.xx, + "λ_state": "convergent", + "verdict": "proved | blocked_missing_premise | not_provable_from_given" + } +Refuse to assert the final claim unless all obligations are discharged or the verdict is explicitly "not_provable_from_given" with a cited reason. +``` + +--- + +## Common gotchas + +* **Rule without scope**. A named rule is used but no citation or domain. Add both or reject. +* **Induction without base**. The inductive step is written yet the base case is missing. +* **Contradiction shortcut**. The chain says “assume not C” then jumps to C with no witness. +* **Bridge drift**. The bridge cites new snippets each run. Lock the query and add a reranker if anchors shuffle. + +--- + +## When to escalate + +* The same wrong assertion returns after a correction + → [pattern\_hallucination\_reentry.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/patterns/pattern_hallucination_reentry.md) + +* Multi-agent handoff reopens closed obligations + → [Multi-Agent\_Problems.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/Multi-Agent_Problems.md) and + → [multi-agent-chaos/role-drift.md](https://github.com/onestardao/WFGY/blob/main/ProblemMap/multi-agent-chaos/role-drift.md) + +--- + +### 🔗 Quick-Start Downloads (60 sec) + +| Tool | Link | 3-Step Setup | +| -------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------ | ---------------------------------------------------------------------------------------- | +| **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 + ” | +| **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 | + +--- + +### 🧭 Explore More + +| Module | Description | Link | +| ------------------------ | ---------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------- | +| 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) | +| Problem Map 1.0 | Initial 16-mode diagnostic and symbolic fix framework | [View →](https://github.com/onestardao/WFGY/tree/main/ProblemMap/README.md) | +| 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) | +| Semantic Clinic Index | Expanded failure catalog: prompt injection, memory bugs, logic drift | [View →](https://github.com/onestardao/WFGY/blob/main/ProblemMap/SemanticClinicIndex.md) | +| Semantic Blueprint | Layer-based symbolic reasoning & semantic modulations | [View →](https://github.com/onestardao/WFGY/tree/main/SemanticBlueprint/README.md) | +| 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) | +| 🧙‍♂️ 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) | + +--- + +> 👑 **Early Stargazers: [See the Hall of Fame](https://github.com/onestardao/WFGY/tree/main/stargazers)** — +> Engineers, hackers, and open source builders who supported WFGY from day one. + +> 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). + +
+ +[![WFGY Main](https://img.shields.io/badge/WFGY-Main-red?style=flat-square)](https://github.com/onestardao/WFGY) +  +[![TXT OS](https://img.shields.io/badge/TXT%20OS-Reasoning%20OS-orange?style=flat-square)](https://github.com/onestardao/WFGY/tree/main/OS) +  +[![Blah](https://img.shields.io/badge/Blah-Semantic%20Embed-yellow?style=flat-square)](https://github.com/onestardao/WFGY/tree/main/OS/BlahBlahBlah) +  +[![Blot](https://img.shields.io/badge/Blot-Persona%20Core-green?style=flat-square)](https://github.com/onestardao/WFGY/tree/main/OS/BlotBlotBlot) +  +[![Bloc](https://img.shields.io/badge/Bloc-Reasoning%20Compiler-blue?style=flat-square)](https://github.com/onestardao/WFGY/tree/main/OS/BlocBlocBloc) +  +[![Blur](https://img.shields.io/badge/Blur-Text2Image%20Engine-navy?style=flat-square)](https://github.com/onestardao/WFGY/tree/main/OS/BlurBlurBlur) +  +[![Blow](https://img.shields.io/badge/Blow-Game%20Logic-purple?style=flat-square)](https://github.com/onestardao/WFGY/tree/main/OS/BlowBlowBlow) +  + +