diff --git a/scripts/prove.py b/scripts/prove.py
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+++ b/scripts/prove.py
@@ -0,0 +1,381 @@
+#!/usr/bin/env python3
+"""
+prove.py — Lean proof-filling loop with 5-check verification pipeline.
+
+Adapted from Peng et al. (2026) pipeline-math verify.sh:
+  1. SHA pin check    — frozen theorem stubs haven't drifted
+  2. Banned keywords  — no sorry/native_decide/admit/axiom in proof files
+  3. lake build clean — 0 errors, 0 unexpected warnings
+  4. #print axioms    — proof depends only on {propext, Classical.choice, Quot.sound}
+  5. Discharge gate   — @Frozen = @Proof := rfl (proof matches theorem type)
+
+Metric: build_errors * 1000 + sorries (lower = better, 0 = perfect).
+"""
+import os, sys, time, json, subprocess, re, hashlib, shutil
+from pathlib import Path
+import urllib.request
+
+# ── Config ──────────────────────────────────────────────────────────────
+
+SILVERSIGHT_DIR = os.path.expanduser("~/SilverSight")
+LEAN_FILE = os.environ.get("TARGET_FILE", "formal/CoreFormalism/Bind.lean")
+LLM_MODEL = os.environ.get("LLM_MODEL", "phi4:14b")
+LLM_BASE_URL = os.environ.get("LLM_BASE_URL", "http://100.92.88.64:11434/v1")
+LLM_API_KEY = os.environ.get("LLM_API_KEY", "sk-local")
+TIME_BUDGET_S = int(os.environ.get("TIME_BUDGET_S", "600"))
+
+BANNED_KEYWORDS = ["sorryAx", "native_decide", "admit", "unsafe",
+                   "implemented_by", "ofReduceBool"]
+ALLOWED_AXIOMS = {"propext", "Classical.choice", "Quot.sound"}
+
+# ── LLM client ─────────────────────────────────────────────────────────
+
+def llm_complete(prompt, system="You are a Lean 4 proof engineer."):
+    body = json.dumps({
+        "model": LLM_MODEL,
+        "messages": [
+            {"role": "system", "content": system},
+            {"role": "user", "content": prompt},
+        ],
+        "temperature": 0.3,
+        "max_tokens": 4096,
+    }).encode()
+    req = urllib.request.Request(
+        f"{LLM_BASE_URL}/chat/completions",
+        data=body,
+        headers={"Content-Type": "application/json",
+                 "Authorization": f"Bearer {LLM_API_KEY}"},
+        method="POST",
+    )
+    try:
+        resp = urllib.request.urlopen(req, timeout=120)
+        data = json.loads(resp.read())
+        return data["choices"][0]["message"]["content"]
+    except Exception as e:
+        print(f"LLM error: {e}")
+        return None
+
+# ─── Check 1: SHA pins ────────────────────────────────────────────────
+
+def check_sha_pins(lean_file):
+    """Check SHA-256 of file against pinned hash in scripts/frozen.sha256."""
+    pins_path = Path(SILVERSIGHT_DIR) / "scripts" / "frozen.sha256"
+    if not pins_path.exists():
+        return True, "no pins file (SKIP)"
+    rel_path = os.path.relpath(
+        os.path.join(SILVERSIGHT_DIR, lean_file),
+        SILVERSIGHT_DIR
+    )
+    content = pins_path.read_text()
+    for line in content.splitlines():
+        line = line.strip()
+        if not line or line.startswith("#"):
+            continue
+        parts = line.split(None, 1)
+        if len(parts) == 2 and parts[1] == rel_path:
+            pinned = parts[0]
+            actual = sha256_of(os.path.join(SILVERSIGHT_DIR, lean_file))
+            if pinned == actual:
+                return True, f"SHA pin match: {rel_path}"
+            else:
+                return False, f"SHA pin MISMATCH {rel_path}: pinned={pinned[:16]} actual={actual[:16]}"
+    return True, "no pin for this file (SKIP)"
+
+def sha256_of(path):
+    h = hashlib.sha256()
+    with open(path, "rb") as f:
+        h.update(f.read())
+    return h.hexdigest()
+
+# ─── Check 2: Banned keywords ─────────────────────────────────────────
+
+def check_banned_keywords(text, allow_sorry=False):
+    """Check for banned keywords in Lean code. Returns (pass, message)."""
+    cleaned = strip_comments(text)
+    for kw in BANNED_KEYWORDS:
+        if re.search(r'\b' + re.escape(kw) + r'\b', cleaned):
+            return False, f"banned keyword: {kw}"
+    if not allow_sorry:
+        if re.search(r'\bsorry\b', cleaned):
+            return False, "banned keyword: sorry (not allowed in proof files)"
+    return True, "no banned keywords"
+
+def strip_comments(s):
+    """Strip Lean comments (-- line, /- ... -/ block)."""
+    out = []
+    i, n = 0, len(s)
+    depth = 0
+    while i < n:
+        two = s[i:i+2]
+        if depth == 0 and two == "--":
+            j = s.find("\n", i)
+            i = j if j != -1 else n
+        elif two == "/-":
+            depth += 1
+            i += 2
+        elif depth > 0 and two == "-/":
+            depth -= 1
+            i += 2
+        elif depth > 0:
+            i += 1
+        else:
+            out.append(s[i])
+            i += 1
+    return "".join(out)
+
+# ─── Check 3: lake build ──────────────────────────────────────────────
+
+def lake_build(target=None, timeout=120):
+    """Run `lake build` and return (error_count, output)."""
+    cmd = ["lake", "build"]
+    if target:
+        cmd.append(target)
+    try:
+        result = subprocess.run(
+            cmd, cwd=SILVERSIGHT_DIR, capture_output=True, text=True,
+            timeout=timeout,
+        )
+        output = result.stdout + result.stderr
+        errors = output.count("error:")
+        warnings = output.count("warning:") - output.count("declaration uses .sorry.")
+        return errors, warnings, output
+    except subprocess.TimeoutExpired:
+        return 999, 0, "TIMEOUT"
+    except Exception as e:
+        return 999, 0, str(e)
+
+# ─── Check 4: #print axioms ───────────────────────────────────────────
+
+def check_axioms(module_name):
+    """Check that a module's axioms are within the allowed set."""
+    ax_file = os.path.join(SILVERSIGHT_DIR, ".lake", "tmp_ax_check.lean")
+    os.makedirs(os.path.dirname(ax_file), exist_ok=True)
+    with open(ax_file, "w") as f:
+        f.write(f"import {module_name}\n")
+        f.write(f"#print axioms {module_name}\n")
+
+    try:
+        result = subprocess.run(
+            ["lake", "env", "lean", ax_file],
+            cwd=SILVERSIGHT_DIR, capture_output=True, text=True, timeout=60,
+        )
+        output = result.stdout + result.stderr
+        os.remove(ax_file)
+        # Parse axiom line
+        m = re.search(r"'([^']+)' depends on axioms:\s*\[([^\]]+)\]", output)
+        if m:
+            axioms = set(a.strip() for a in m.group(2).split(",") if a.strip())
+            bad = axioms - ALLOWED_AXIOMS
+            if bad:
+                return False, f"unexpected axioms: {bad}"
+            return True, f"axioms OK: {axioms}"
+        return True, "no axiom line (module might be empty)"
+    except Exception as e:
+        return False, f"axiom check error: {e}"
+
+# ─── Check 5: Discharge gate ──────────────────────────────────────────
+
+def check_discharge_gate(lean_file):
+    """Check that Discharge.lean compiles — proof ↔ theorem type gate."""
+    discharge_path = os.path.join(
+        os.path.dirname(os.path.join(SILVERSIGHT_DIR, lean_file)),
+        "Discharge.lean"
+    )
+    if not os.path.exists(discharge_path):
+        return True, "no Discharge.lean (SKIP)"
+    discharge_module = "Discharge"
+    err, warn, out = lake_build(target=discharge_module, timeout=60)
+    if err == 0:
+        return True, "Discharge gate PASS"
+    return False, f"Discharge gate FAIL ({err} errors)"
+
+# ── Proof filling ──────────────────────────────────────────────────────
+
+def count_sorries(text):
+    cleaned = strip_comments(text)
+    return len(re.findall(r'\bsorry\b', cleaned))
+
+def get_sorry_context(filepath):
+    path = Path(os.path.join(SILVERSIGHT_DIR, filepath))
+    if not path.exists():
+        return None, None, 0, "file not found"
+    text = path.read_text()
+    n = count_sorries(text)
+    if n == 0:
+        return text, None, 0, "no sorries found"
+    # Find the first theorem/lemma that contains a sorry
+    blocks = list(re.finditer(
+        r'(theorem\s+\w+|lemma\s+\w+|def\s+\w+)[\s\S]*?(?=\b(theorem|lemma|def)\b|\Z)',
+        text
+    ))
+    for m in blocks:
+        block = m.group(0)
+        if 'sorry' in block:
+            return text, block, n, None
+    return text, None, n, "could not find sorry block"
+
+def fill_sorry(filepath, proof_text):
+    path = Path(os.path.join(SILVERSIGHT_DIR, filepath))
+    text = path.read_text()
+    new_text = text.replace("sorry", proof_text.strip(), 1)
+    path.write_text(new_text)
+    return new_text
+
+def restore_file(filepath, original):
+    path = Path(os.path.join(SILVERSIGHT_DIR, filepath))
+    path.write_text(original)
+
+# ── Main experiment loop ────────────────────────────────────────────────
+
+def experiment():
+    print("=" * 60)
+    print("  AutoResearch: Lean Proof Filling (5-check pipeline)")
+    print(f"  Model: {LLM_MODEL}")
+    print(f"  File: {LEAN_FILE}")
+    print(f"  Budget: {TIME_BUDGET_S}s")
+    print("=" * 60)
+
+    t_start = time.time()
+    t_end = t_start + TIME_BUDGET_S
+    results = []
+    best_score = 999999
+
+    initial_sorries = count_sorries(Path(os.path.join(SILVERSIGHT_DIR, LEAN_FILE)).read_text())
+    print(f"  Initial sorries: {initial_sorries}")
+    print()
+
+    while time.time() < t_end:
+        iteration = len(results) + 1
+        t_iter = time.time()
+
+        text, context, n, err = get_sorry_context(LEAN_FILE)
+        if err:
+            current = count_sorries(Path(os.path.join(SILVERSIGHT_DIR, LEAN_FILE)).read_text())
+            if current == 0:
+                print(f"\n*** All {initial_sorries} sorries filled! ***")
+                break
+            print(f"\n[{iteration}] {err}")
+            break
+
+        # Ask LLM to fill the sorry
+        sys_prompt = "You are a Lean 4 proof engineer. Write complete, compilable proofs."
+        prompt = f"""Fill the `sorry` in this Lean 4 theorem.
+Write ONLY the proof body — the text that replaces `sorry` after `:= by`.
+Do NOT repeat the theorem header. Use `by` block syntax, not `begin`/`end`.
+Output raw Lean code only, no markdown.
+
+{context}
+
+Proof body to replace `sorry`:"""
+
+        proof = llm_complete(prompt, sys_prompt)
+        if not proof:
+            print(f"  [{iteration}] LLM returned nothing, skipping")
+            results.append({"iteration": iteration, "error": "no response"})
+            continue
+
+        # Post-process LLM output
+        proof = proof.strip()
+        if proof.startswith("```"):
+            proof = proof.split("```")[1] if "```" in proof[3:] else proof
+            if proof.startswith("lean"):
+                proof = proof[4:]
+        proof = proof.strip().rstrip("`").strip()
+        if proof.startswith("theorem") or proof.startswith("lemma") or proof.startswith("def"):
+            lines = proof.split("\n")
+            for i, line in enumerate(lines):
+                if line.strip().startswith(":= by"):
+                    proof = "\n".join(lines[i+1:])
+                    break
+            else:
+                proof = lines[-1]
+
+        # Apply proof
+        original = Path(os.path.join(SILVERSIGHT_DIR, LEAN_FILE)).read_text()
+        fill_sorry(LEAN_FILE, proof)
+
+        # ── 5-check pipeline ────────────────────────────────────────
+        checks_passed = True
+        new_text = Path(os.path.join(SILVERSIGHT_DIR, LEAN_FILE)).read_text()
+
+        # Check 1: SHA pins
+        pin_ok, pin_msg = check_sha_pins(LEAN_FILE)
+        if not pin_ok:
+            print(f"  [{iteration}] CHECK 1 FAIL: {pin_msg}")
+            checks_passed = False
+
+        # Check 2: Banned keywords
+        kw_ok, kw_msg = check_banned_keywords(new_text, allow_sorry=False)
+        if not kw_ok:
+            print(f"  [{iteration}] CHECK 2 FAIL: {kw_msg}")
+            checks_passed = False
+
+        # Check 3: lake build
+        build_errors, build_warnings, build_out = lake_build(timeout=120)
+        current_sorries = count_sorries(new_text)
+        elapsed = time.time() - t_iter
+
+        score = build_errors * 1000 + current_sorries
+        status = "KEEP" if checks_passed and score < best_score else "DISCARD"
+
+        if status == "KEEP":
+            # Check 4: #print axioms (only if build passed)
+            if build_errors == 0:
+                module_name = LEAN_FILE.replace("/", ".").replace(".lean", "")
+                ax_ok, ax_msg = check_axioms(module_name)
+                if not ax_ok:
+                    print(f"  [{iteration}] CHECK 4 FAIL: {ax_msg}")
+                    checks_passed = False
+                    status = "DISCARD"
+
+            # Check 5: Discharge gate
+            if checks_passed:
+                dg_ok, dg_msg = check_discharge_gate(LEAN_FILE)
+                if not dg_ok:
+                    print(f"  [{iteration}] CHECK 5 FAIL: {dg_msg}")
+                    checks_passed = False
+                    status = "DISCARD"
+
+        if status == "KEEP":
+            best_score = score
+            subprocess.run(
+                ["git", "add", "-f", LEAN_FILE],
+                cwd=SILVERSIGHT_DIR, capture_output=True
+            )
+            subprocess.run(
+                ["git", "commit", "-m",
+                 f"autoresearch: {build_errors} err/{current_sorries} sorries (iter {iteration})"],
+                cwd=SILVERSIGHT_DIR, capture_output=True
+            )
+
+        if status == "DISCARD":
+            restore_file(LEAN_FILE, original)
+
+        checks_str = ""
+        if not checks_passed:
+            checks_str = " CHECKS FAILED"
+        print(f"  [{iteration:3d}] build_err={build_errors} sorries={current_sorries:3d}"
+              f" elapsed={elapsed:.1f}s [{status}]{checks_str}")
+
+        results.append({
+            "iteration": iteration,
+            "sorries": current_sorries,
+            "build_errors": build_errors,
+            "status": status,
+            "checks_passed": checks_passed,
+            "elapsed_s": round(elapsed, 1),
+        })
+
+        if current_sorries == 0 and build_errors == 0:
+            print(f"\n*** ALL PROOFS COMPLETE! ***")
+            break
+
+    total = time.time() - t_start
+    print(f"\n{'='*60}")
+    print(f"  Summary: {len(results)} iterations, {total:.0f}s")
+    print(f"  Best score (errors*1000+sorries): {best_score}")
+    print(f"  Model: {LLM_MODEL}")
+    print(f"{'='*60}")
+
+if __name__ == "__main__":
+    experiment()