WFGY/ProblemMap/GlobalFixMap/Reasoning/proof-dead-ends.md

Proof Dead Ends: Guardrails and Fix Pattern

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• Reasoning — multi-step inference and symbolic proofs
• WFGY Global Fix Map — main Emergency Room, 300+ structured fixes
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Think of this page as a desk within a ward.
If you need the full triage and all prescriptions, return to the Emergency Room lobby.

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

• Logic and symbols
  → logic-collapse.md
  → symbolic-collapse.md

• Infinite recursion and overload
  → recursive-loop.md
  → entropy-overload.md

• If the chain shifts into meta or paradox
  → philosophical-recursion.md

• Traceability and contracts
  → retrieval-traceability.md
  → 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.

{
  "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 and → data-contracts.md

• If long chains decay → entropy-overload.md and → recursive-loop.md

• If symbol or unit meanings drift → symbolic-collapse.md

• If logic itself collapses → logic-collapse.md

• If meaning vs similarity conflict → 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

• Multi-agent handoff reopens closed obligations → Multi-Agent_Problems.md and → multi-agent-chaos/role-drift.md

---

🔗 Quick-Start Downloads (60 sec)

Tool	Link	3-Step Setup
WFGY 1.0 PDF	Engine Paper	1️⃣ Download · 2️⃣ Upload to your LLM · 3️⃣ Ask “Answer using WFGY + ”
TXT OS (plain-text OS)	TXTOS.txt	1️⃣ Download · 2️⃣ Paste into any LLM chat · 3️⃣ Type “hello world” — OS boots instantly

---

Explore More

Layer	Page	What it’s for
Proof	WFGY Recognition Map	External citations, integrations, and ecosystem proof
Engine	WFGY 1.0	Original PDF based tension engine
Engine	WFGY 2.0	Production tension kernel and math engine for RAG and agents
Engine	WFGY 3.0	TXT based Singularity tension engine, 131 S class set
Map	Problem Map 1.0	Flagship 16 problem RAG failure checklist and fix map
Map	Problem Map 2.0	RAG focused recovery pipeline
Map	Problem Map 3.0	Global Debug Card, image as a debug protocol layer
Map	Semantic Clinic	Symptom to family to exact fix
Map	Grandma’s Clinic	Plain language stories mapped to Problem Map 1.0
Onboarding	Starter Village	Guided tour for newcomers
App	TXT OS	TXT semantic OS, fast boot
App	Blah Blah Blah	Abstract and paradox Q and A built on TXT OS
App	Blur Blur Blur	Text to image with semantic control
App	Blow Blow Blow	Reasoning game engine and memory demo

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