fix(agents): recursively decompose proof obligations

docs/ops/distributed-prefill-kv-network.md

@@ -349,11 +349,13 @@ and semantic fallback are forbidden. A global Critic score is valid only when
 `critic_omitted_tokens=0`. Long Prefill operations emit a heartbeat every 30
 seconds; on the 16GB allens worker, full-context Critic Prefill may take 15–25
 minutes.
-The Critic uses `adversarial_claim_audit_v1`: numeric scores and blanket
-approval are forbidden. It must reconstruct the thesis, quote and challenge
-each material claim, present the strongest objection, provide a corrected
-response, and state residual uncertainty. Epistemic honesty is evaluated
-separately from literal task completion.
+The Critic uses `recursive_proof_decomposition_v2`: numeric scores and blanket
+approval are forbidden. It ignores prizes, money, prestige, style, and other
+proof-irrelevant facts. It attacks the central stopping claim, recursively
+decomposes it into proof obligations, records arguments/counterarguments and
+dependencies for every node, and loops until every leaf is either explicitly
+derived or a precisely stated open lemma. It then reports the smallest
+unresolved frontier and next adversarial step.
 The worker reserves estimated final-snapshot capacity before model compute,
 prevents adaptive shrink from consuming active reservations, then atomically
 publishes and leases the final snapshot before adding optional intermediate

scripts/agent_gan_inference_demo.py

@@ -47,7 +47,7 @@ def build_critic_context(tokenizer, text: str) -> tuple[str, dict]:
         "critic_context_tokens": len(full_ids),
         "critic_omitted_tokens": 0,
         "review_scope": "full",
-        "critic_protocol": "adversarial_claim_audit_v1",
+        "critic_protocol": "recursive_proof_decomposition_v2",
     }
 
 
@@ -179,19 +179,22 @@ def main() -> int:
     critic_history = [{
         "role": "system",
         "content": (
-            "You are an adversarial peer reviewer, not a supportive grader. "
-            "Review the complete Generator response as one semantic argument. "
-            "Reconstruct its thesis and audit every material factual, logical, "
-            "and task-completion claim against the strongest counterargument. "
-            "Quote claims before challenging them. Distinguish an honest "
-            "boundary from literal task completion; unknown does not mean "
-            "impossible. Check numbers, quantifiers, awards, assumptions, and "
-            "claimed consequences. Never output a numeric score or blanket "
-            "approval without an explicit claim-by-claim audit. Return Thesis "
-            "Reconstruction, Claim-by-Claim Audit, Strongest Objection, "
-            "Corrected Response, and Residual Uncertainty. Claim truncation "
-            "only when completion_status is not EOS or syntax is cut off. "
-            "Do not sample, summarize, simplify, or use fallback review."
+            "You are a recursive adversarial proof analyst. Review the complete "
+            "Generator response as one semantic argument and focus only on the "
+            "central claim required by the task. Ignore prizes, money, prestige, "
+            "style, and facts that do not alter the proof chain. Attack any move "
+            "from unknown or unsolved to impossible. Recursively decompose the "
+            "central claim into minimal proof obligations. For every node give "
+            "its argument, strongest counterargument, dependencies, and status "
+            "as proved, disproved, or unresolved. Replace every broad unresolved "
+            "node with smaller obligations until each leaf has an explicit "
+            "derivation or is a precisely stated open lemma. Return Central "
+            "Claim, Decomposition Loop, Leaf Obligation Ledger, Smallest "
+            "Unresolved Frontier, and Next Adversarial Step. Never output a "
+            "numeric score or blanket approval, and never declare the theorem "
+            "proved unless every leaf is discharged. Claim truncation only when "
+            "completion_status is not EOS or syntax is cut off. Do not sample, "
+            "summarize, simplify, or use fallback review."
         ),
     }]
 

scripts/agent_gan_repl.py

@@ -51,10 +51,12 @@ def build_generator_messages(prompt: str) -> list[dict[str, str]]:
         {
             "role": "system",
             "content": (
-                "Answer rigorously. For open problems, state the accepted "
-                "boundary and never fabricate a proof. Distinguish unknown "
-                "from impossible; qualify awards, quantities, and claimed "
-                "downstream consequences precisely."
+                "Pursue the requested mathematical argument constructively and "
+                "rigorously. For an open problem, do not fabricate a proof, but "
+                "do not stop at 'unsolved': identify the exact global claim, "
+                "derive known reductions, recursively decompose missing proof "
+                "obligations, and state the smallest unresolved frontier. "
+                "Distinguish unknown from impossible."
             ),
         },
         {"role": "user", "content": prompt},
@@ -72,20 +74,26 @@ def build_critic_messages(
         {
             "role": "system",
             "content": (
-                "Act as an adversarial peer reviewer, not a supportive grader. "
-                "Read the complete response as one semantic argument. Rebuild "
-                "its thesis and audit every material factual, logical, and "
-                "task-completion claim against the strongest counterargument. "
-                "Quote the exact claim before challenging it. Distinguish "
-                "epistemic honesty from literal task completion: unknown or "
-                "unsolved does not mean impossible, and an honest refusal does "
-                "not complete a requested proof. Check numbers, awards, "
-                "quantifiers, and claimed consequences. Never output a numeric "
-                "score. Never issue blanket approval unless every material "
-                "claim has been explicitly audited. Use exactly these sections: "
-                "Thesis Reconstruction; Claim-by-Claim Audit; Strongest "
-                "Objection; Corrected Response; Residual Uncertainty. Do not "
-                "sample, summarize, simplify, or use a fallback review."
+                "Act as a recursive adversarial proof analyst. Read the complete "
+                "response as one semantic argument and focus exclusively on the "
+                "central mathematical claim required by the task. Ignore prizes, "
+                "money, prestige, style, and other facts that do not change the "
+                "proof chain. If the response stops at 'unknown', 'unsolved', or "
+                "'impossible', attack that stopping claim rather than accepting "
+                "it as an answer. Build a proof-obligation tree: decompose the "
+                "central claim into minimal necessary subclaims; for each node "
+                "give the argument, strongest counterargument, dependencies, and "
+                "status as proved, disproved, or unresolved. Recursively replace "
+                "every broad unresolved node with smaller obligations until each "
+                "leaf is either discharged by an explicit derivation or is a "
+                "precisely stated open lemma. Then identify the smallest "
+                "unresolved frontier and the next lemma that must be proved. "
+                "Never output a numeric score or blanket approval. Never claim "
+                "the original theorem is proved unless every leaf is discharged. "
+                "Use exactly these sections: Central Claim; Decomposition Loop; "
+                "Leaf Obligation Ledger; Smallest Unresolved Frontier; Next "
+                "Adversarial Step. Do not sample, summarize, simplify, or use a "
+                "fallback review."
             ),
         },
         {

tests/inference_engine/bridge/test_agent_gan_demo.py

@@ -120,4 +120,4 @@ def test_critic_context_preserves_complete_generator_response():
     assert metrics["critic_context_tokens"] == 10
     assert metrics["critic_omitted_tokens"] == 0
     assert metrics["review_scope"] == "full"
-    assert metrics["critic_protocol"] == "adversarial_claim_audit_v1"
+    assert metrics["critic_protocol"] == "recursive_proof_decomposition_v2"

tests/inference_engine/bridge/test_agent_gan_repl.py

@@ -140,13 +140,13 @@ def test_stage_includes_full_context_metrics():
             "critic_context_tokens": 100,
             "critic_omitted_tokens": 0,
             "review_scope": "full",
-            "critic_protocol": "adversarial_claim_audit_v1",
+            "critic_protocol": "recursive_proof_decomposition_v2",
         },
     )
     assert stage["critic_context_tokens"] == 100
     assert stage["critic_omitted_tokens"] == 0
     assert stage["review_scope"] == "full"
-    assert stage["critic_protocol"] == "adversarial_claim_audit_v1"
+    assert stage["critic_protocol"] == "recursive_proof_decomposition_v2"
 
 
 def test_telemetry_timeout_warns_without_stopping_inference(
@@ -195,8 +195,11 @@ def test_interactive_prompts_are_deterministic_for_kv_reuse():
     combined = repr(generator_a + critic_a)
     assert "Internal run" not in combined
     assert "open problem" in combined
-    assert "adversarial peer reviewer" in combined
+    assert "recursive adversarial proof analyst" in combined
     assert "Never output a numeric score" in combined
-    assert "Claim-by-Claim Audit" in combined
-    assert "unknown or unsolved does not mean impossible" in combined
+    assert "Decomposition Loop" in combined
+    assert "If the response stops at" in combined
+    assert "attack that stopping claim" in combined
+    assert "Ignore prizes, money, prestige" in combined
+    assert "smallest unresolved frontier" in combined
     assert "sample, summarize, simplify" in combined