{
  "file_path": "D:\\Python\\Quantum\\web\\dashboard\\views.py",
  "content": "\"\"\"Page views for the RH-WEBSITE dashboard. All research data read-only.\"\"\"\nimport json\nfrom pathlib import Path\n\nfrom django.contrib import messages\nfrom django.http import Http404\nfrom django.shortcuts import redirect, render\n\nfrom . import research_data as rd\nfrom .models import Feedback\n\n\ndef home(request):\n    return render(request, \"dashboard/home.html\", {\n        \"stats\": rd.summary_stats(),\n        \"state\": rd.parse_state(),\n    })\n\n\ndef dashboard(request):\n    return render(request, \"dashboard/dashboard.html\", {\n        \"state\": rd.parse_state(),\n        \"checklist\": rd.parse_checklist(),\n        \"stats\": rd.summary_stats(),\n        \"commits\": rd.git_log(12),\n        \"new_feedback\": Feedback.objects.filter(status=\"new\").count(),\n        \"sessions\": rd.get_sessions()[-4:],\n    })\n\n\ndef roadmap(request):\n    nguyen = rd.REPO / \"NGUYEN.md\"\n    return render(request, \"dashboard/roadmap.html\", {\n        \"html\": rd.render_markdown(rd.read_text(nguyen)) if nguyen.exists() else \"\",\n        \"mtime\": rd._iso(nguyen.stat().st_mtime) if nguyen.exists() else None,\n    })\n\n\ndef ledger(request):\n    return render(request, \"dashboard/ledger.html\", {\"results\": rd.get_results()})\n\n\ndef ledger_detail(request, rid):\n    row = rd.get_result(rid)\n    if not row:\n        raise Http404\n    path = (rd.RESEARCH / \"results\" / Path(row[\"file\"]).name).resolve()\n    if (rd.RESEARCH / \"results\").resolve() not in path.parents or not path.exists():\n        raise Http404\n    return render(request, \"dashboard/ledger_detail.html\", {\n        \"row\": row,\n        \"html\": rd.render_markdown(rd.read_text(path)),\n        \"mtime\": rd._iso(path.stat().st_mtime),\n    })\n\n\ndef experiments(request):\n    rows = rd.get_experiments()\n    for row in rows:\n        sc = rd.experiment_sidecar(row)\n        row[\"checks\"] = (sc or {}).get(\"checks\") or {}\n        row[\"task\"] = (sc or {}).get(\"task\", \"\")\n    return render(request, \"dashboard/experiments.html\", {\"experiments\": rows})\n\n\ndef experiment_detail(request, eid):\n    row = rd.get_experiment(eid)\n    if not row:\n        raise Http404\n    sidecar = rd.experiment_sidecar(row)\n    chart = rd.chart_data(row)\n    return render(request, \"dashboard/experiment_detail.html\", {\n        \"exp\": row,\n        \"sidecar\": sidecar,\n        \"chart_json\": json.dumps(chart) if chart else None,\n        \"preview\": rd.csv_preview(row),\n    })\n\n\ndef collection(request, kind):\n    if kind not in rd.MD_COLLECTIONS:\n        raise Http404\n    meta = {}\n    if kind == \"derivations\":\n        meta = {Path(d[\"file\"]).stem: d for d in rd.get_derivations()}\n    elif kind == \"graveyard\":\n        meta = {Path(g[\"file\"]).stem: g for g in rd.get_graveyard()}\n    return render(request, \"dashboard/collection.html\", {\n        \"kind\": kind,\n        \"items\": rd.collection_list(kind),\n        \"meta\": meta,\n    })\n\n\ndef collection_item(request, kind, name):\n    if kind not in rd.MD_COLLECTIONS:\n        raise Http404\n    item = rd.collection_item(kind, name)\n    if not item:\n        raise Http404\n    return render(request, \"dashboard/collection_item.html\", {\n        \"kind\": kind, \"item\": item})\n\n\ndef paper(request):\n    folder = rd.RESEARCH / \"paper\"\n    files = []\n    if folder.exists():\n        for p in sorted(folder.iterdir()):\n            if p.is_file():\n                files.append({\"name\": p.name,\n                              \"size\": p.stat().st_size,\n                              \"mtime\": rd._iso(p.stat().st_mtime)})\n    draft = folder / \"draft.tex\"\n    draft_head = None\n    if draft.exists():\n        draft_head = \"\\n\".join(rd.read_text(draft).splitlines()[:80])\n    return render(request, \"dashboard/paper.html\", {\n        \"files\": files, \"draft_head\": draft_head,\n        \"draft_mtime\": rd._iso(draft.stat().st_mtime) if draft.exists() else None,\n    })\n\n\ndef live(request):\n    return render(request, \"dashboard/live.html\", {\"logs\": rd.run_logs()})\n\n\ndef feedback(request):\n    if request.method == \"POST\":\n        text = (request.POST.get(\"text\") or \"\").strip()\n        name = (request.POST.get(\"name\") or \"\").strip()[:120]\n        category = request.POST.get(\"category\") or \"general\"\n        valid = {c for c, _ in Feedback.CATEGORY_CHOICES}\n        if category not in valid:\n            category = \"general\"\n        if text:\n            fb = Feedback.objects.create(name=name, category=category, text=text)\n            # Dual storage: JSON file per submission (RH-WEBSITE.md \u00a75).\n            fb_dir = Path(rd.settings.BASE_DIR) / \"feedback\"\n            fb_dir.mkdir(exist_ok=True)\n            payload = {\n                \"id\": fb.id,\n                \"created\": fb.created.isoformat(),\n                \"name\": fb.name,\n                \"category\": fb.category,\n                \"text\": fb.text,\n                \"status\": fb.status,\n            }\n            fname = f\"FB-{fb.created:%Y%m%dT%H%M%S}-{fb.id:04d}.json\"\n            (fb_dir / fname).write_text(\n                json.dumps(payload, indent=2), encoding=\"utf-8\")\n            messages.success(request, \"Thank you \u2014 your feedback has been recorded.\")\n            return redirect(\"feedback\")\n        messages.error(request, \"Feedback text cannot be empty.\")\n\n    q = (request.GET.get(\"q\") or \"\").strip()\n    cat = request.GET.get(\"category\") or \"\"\n    status = request.GET.get(\"status\") or \"\"\n    items = Feedback.objects.all()\n    if q:\n        from django.db.models import Q\n        items = items.filter(Q(text__icontains=q) | Q(name__icontains=q))\n    if cat:\n        items = items.filter(category=cat)\n    if status:\n        items = items.filter(status=status)\n    return render(request, \"dashboard/feedback.html\", {\n        \"items\": items[:200],\n        \"q\": q, \"cat\": cat, \"status\": status,\n        \"categories\": Feedback.CATEGORY_CHOICES,\n        \"statuses\": Feedback.STATUS_CHOICES,\n    })\n"
}

{
  "file_path": "D:\\Python\\Quantum\\web\\dashboard\\api.py",
  "content": "\"\"\"JSON API for live updates. Read-only on the research archive.\"\"\"\nfrom datetime import datetime, timezone\n\nfrom django.http import JsonResponse\n\nfrom . import research_data as rd\nfrom .models import Feedback\n\n\ndef health(request):\n    return JsonResponse({\"ok\": True, \"service\": \"rh-website\",\n                         \"time\": datetime.now(timezone.utc).isoformat(timespec=\"seconds\")})\n\n\ndef status(request):\n    state = rd.parse_state()\n    commits = rd.git_log(1)\n    return JsonResponse({\n        \"ok\": True,\n        \"server_time\": datetime.now(timezone.utc).isoformat(timespec=\"seconds\"),\n        \"mtimes\": {\n            \"state\": rd.mtime(rd.REPO / \"STATE.md\"),\n            \"nguyen\": rd.mtime(rd.REPO / \"NGUYEN.md\"),\n            \"db\": rd.mtime(rd.DB),\n        },\n        \"position\": (state.get(\"CURRENT POSITION\") or \"\")[:800],\n        \"next_action\": (state.get(\"NEXT ACTION\") or \"\")[:500],\n        \"blockers\": (state.get(\"BLOCKERS\") or \"\")[:200],\n        \"latest_commit\": commits[0] if commits else \"\",\n        \"logs\": rd.run_logs(),\n        \"new_feedback\": Feedback.objects.filter(status=\"new\").count(),\n    })\n\n\ndef logtail(request):\n    name = request.GET.get(\"file\", \"\")\n    try:\n        n = min(int(request.GET.get(\"n\", 200)), 1000)\n    except ValueError:\n        n = 200\n    data = rd.tail_log(name, n)\n    if data is None:\n        return JsonResponse({\"ok\": False, \"error\": \"not found\"}, status=404)\n    data[\"ok\"] = True\n    return JsonResponse(data)\n"
}

{
  "type": "update",
  "filePath": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\Scratch.lean",
  "content": "/- Session 014 scratch: axiom check of planned tier-ii\u2032 dependencies. -/\nimport Mathlib\nimport Zeta23.WeilEF.ZeroSummability\nimport Zeta23.RvM.LocalCount\nimport Zeta23.RvM.Statement\nimport Zeta23.FromPNTPlus.ResidueCalcOnRectangles\nimport Zeta23.ZetaReflect\n\nopen Zeta23\n\n#print axioms WeilEF.zero_sum_inv_sq\n#print axioms RvM.zeta_local_zero_count\n#print axioms zeta_reflect_zero\n#print axioms zeta_mult_reflect\n#print axioms RectangleIntegral'_eq_sumResiduesIn\n#print axioms ResidueMult\n#print axioms logDerivResidue\n#print axioms riemannZetaLogDerivResidue\n",
  "structuredPatch": [
    {
      "oldStart": 1,
      "oldLines": 156,
      "newStart": 1,
      "newLines": 19,
      "lines": [
        "-/- Scratch.lean \u2014 proof development scratchpad (not imported by the lib).",
        "-   Check with: lake env lean Scratch.lean",
        "-   When green, the proof is merged into the skeleton files. -/",
        "+/- Session 014 scratch: axiom check of planned tier-ii\u2032 dependencies. -/",
        " import Mathlib",
        "+import Zeta23.WeilEF.ZeroSummability",
        "+import Zeta23.RvM.LocalCount",
        "+import Zeta23.RvM.Statement",
        "+import Zeta23.FromPNTPlus.ResidueCalcOnRectangles",
        "+import Zeta23.ZetaReflect",
        " ",
        "-open Real Filter Topology",
        "+open Zeta23",
        " ",
        "-namespace Scratch",
        "+#print axioms WeilEF.zero_sum_inv_sq",
        "+#print axioms RvM.zeta_local_zero_count",
        "+#print axioms zeta_reflect_zero",
        "+#print axioms zeta_mult_reflect",
        "+#print axioms RectangleIntegral'_eq_sumResiduesIn",
        "+#print axioms ResidueMult",
        "+#print axioms logDerivResidue",
        "+#print axioms riemannZetaLogDerivResidue",
        " ",
        "-/-- D-057 Step 2 chain-rule identity: with T(n) = \u221an + 1,",
        "-d\u00b2/dn\u00b2 \u03c6(T(n)) = [\u03c6\u2033(T) \u2212 \u03c6\u2032(T)/(T\u22121)]/(4n), written with \u221an = T\u22121. -/",
        "-theorem chain_rule_sqrt_shift (\u03c6 : \u211d \u2192 \u211d) (h\u03c6 : ContDiff \u211d 2 \u03c6)",
        "-    (n : \u211d) (hn : 0 < n) :",
        "-    deriv (deriv fun n => \u03c6 (\u221an + 1)) n =",
        "-      (deriv (deriv \u03c6) (\u221an + 1) - deriv \u03c6 (\u221an + 1) / \u221an) / (4 * n) := by",
        "-  -- differentiability infrastructure",
        "-  have h\u03c61 : Differentiable \u211d \u03c6 := h\u03c6.differentiable (by norm_num)",
        "-  have h\u03c62 : Differentiable \u211d (deriv \u03c6) :=",
        "-    (h\u03c6.deriv' (n := 1)).differentiable one_ne_zero",
        "-  have hsqrt : HasDerivAt Real.sqrt (1 / (2 * \u221an)) n :=",
        "-    Real.hasDerivAt_sqrt hn.ne'",
        "-  have hdiff_sqrt : DifferentiableAt \u211d Real.sqrt n := hsqrt.differentiableAt",
        "-  -- h(n) = \u221an + 1 and its derivative",
        "-  have hdiff_h : DifferentiableAt \u211d (fun n => \u221an + 1) n :=",
        "-    hdiff_sqrt.add (differentiableAt_const 1)",
        "-  -- first derivative of g = \u03c6 \u2218 h, as an eventually-equal nice function",
        "-  have hpos : Set.Ioi (0 : \u211d) \u2208 \ud835\udcdd n := Ioi_mem_nhds hn",
        "-  have hg1 : deriv (fun n => \u03c6 (\u221an + 1)) =\u1da0[\ud835\udcdd n]",
        "-      fun n => deriv \u03c6 (\u221an + 1) * (2 * \u221an)\u207b\u00b9 := by",
        "-    filter_upwards [hpos] with m hm",
        "-    have hsm : HasDerivAt Real.sqrt (1 / (2 * \u221am)) m :=",
        "-      Real.hasDerivAt_sqrt (ne_of_gt hm)",
        "-    have hhm : DifferentiableAt \u211d (fun x => \u221ax + 1) m :=",
        "-      hsm.differentiableAt.add (differentiableAt_const 1)",
        "-    have h1 : deriv (fun x => \u221ax + 1) m = 1 / (2 * \u221am) := by",
        "-      rw [deriv_add_const]",
        "-      exact hsm.deriv",
        "-    rw [show (fun x => \u03c6 (\u221ax + 1)) = \u03c6 \u2218 (fun x => \u221ax + 1) from rfl,",
        "-      deriv_comp m (h\u03c61 (\u221am + 1)) hhm, h1]",
        "-    ring",
        "-  -- second derivative via HasDerivAt of the nice representative",
        "-  have hA : HasDerivAt (fun n => deriv \u03c6 (\u221an + 1))",
        "-      (deriv (deriv \u03c6) (\u221an + 1) * (1 / (2 * \u221an))) n := by",
        "-    have h1 : HasDerivAt (fun x => \u221ax + 1) (1 / (2 * \u221an)) n :=",
        "-      hsqrt.add_const 1",
        "-    have h2 : HasDerivAt (deriv \u03c6) (deriv (deriv \u03c6) (\u221an + 1)) (\u221an + 1) :=",
        "-      (h\u03c62 (\u221an + 1)).hasDerivAt",
        "-    have h3 := h2.comp n h1",
        "-    rwa [show (fun n => deriv \u03c6 (\u221an + 1)) = deriv \u03c6 \u2218 (fun n => \u221an + 1) from rfl]",
        "-  have hB : HasDerivAt (fun n => (2 * \u221an)\u207b\u00b9)",
        "-      (-(2 * (1 / (2 * \u221an))) / (2 * \u221an) ^ 2) n := by",
        "-    have h1 : HasDerivAt (fun n => 2 * \u221an) (2 * (1 / (2 * \u221an))) n :=",
        "-      hsqrt.const_mul 2",
        "-    have h2 : (2 * \u221an) \u2260 0 :=",
        "-      mul_ne_zero two_ne_zero (Real.sqrt_ne_zero'.2 hn)",
        "-    exact h1.inv h2",
        "-  have hmul : HasDerivAt (fun n => deriv \u03c6 (\u221an + 1) * (2 * \u221an)\u207b\u00b9)",
        "-      (deriv (deriv \u03c6) (\u221an + 1) * (1 / (2 * \u221an)) * (2 * \u221an)\u207b\u00b9 +",
        "-        deriv \u03c6 (\u221an + 1) * (-(2 * (1 / (2 * \u221an))) / (2 * \u221an) ^ 2)) n :=",
        "-    hA.mul hB",
        "-  have hder := (hmul.congr_of_eventuallyEq hg1).deriv",
        "-  rw [hder]",
        "-  set s := \u221an with hsdef",
        "-  have hs0 : s \u2260 0 := Real.sqrt_ne_zero'.2 hn",
        "-  have hn_eq : n = s ^ 2 := by",
        "-    rw [hsdef]; exact (Real.sq_sqrt hn.le).symm",
        "-  rw [hn_eq]",
        "-  field_simp [hs0]",
        "-  ring",
        "-",
        "-/-- h\u207a(m) \u2265 0 for m \u2265 1: first-order Bernoulli, (1\u22121/m)\u207f \u2265 1 \u2212 n/m. -/",
        "-theorem bern_term_nonneg (n : \u2115) (m : \u2115) (hm : 1 \u2264 m) :",
        "-    0 \u2264 (1 - 1 / (m : \u211d)) ^ n - 1 + (n : \u211d) / m := by",
        "-  have hm0 : (m : \u211d) \u2260 0 := by positivity",
        "-  have h1 : (1 : \u211d) + n * (-1 / m) \u2264 (1 + -1 / (m : \u211d)) ^ n := by",
        "-    apply one_add_mul_le_pow",
        "-    have h3 : (0 : \u211d) \u2264 1 / (m : \u211d) := by positivity",
        "-    have h4 : (1 : \u211d) / m \u2264 1 := by",
        "-      rw [div_le_one (by positivity)]; exact_mod_cast hm",
        "-    rw [neg_div]",
        "-    linarith",
        "-  have h2 : (1 : \u211d) - n / m \u2264 (1 - 1 / m) ^ n := by",
        "-    have : (1 : \u211d) + n * (-1 / m) = 1 - n / m := by field_simp; ring",
        "-    rwa [this, show (1 : \u211d) + -1 / m = 1 - 1 / m by ring] at h1",
        "-  linarith",
        "-",
        "-/-- h\u207a(m) \u2264 (n choose 2)/m\u00b2 for m \u2265 1: geometric factorization",
        "-1 \u2212 (1\u2212x)\u207f = x\u00b7\u03a3_{j<n} (1\u2212x)\u02b2 \u2265 x\u00b7(n \u2212 x\u00b7\u03a3j) plus Bernoulli per term. -/",
        "-theorem bern_term_upper (n : \u2115) (m : \u2115) (hm : 1 \u2264 m) :",
        "-    (1 - 1 / (m : \u211d)) ^ n - 1 + (n : \u211d) / m \u2264 (n : \u211d) * (n - 1) / (2 * m ^ 2) := by",
        "-  have hm0 : (m : \u211d) \u2260 0 := by positivity",
        "-  set x := (1 : \u211d) / m with hxdef",
        "-  have hx1 : x \u2264 1 := by",
        "-    rw [hxdef, div_le_one (by positivity)]; exact_mod_cast hm",
        "-  have hx0 : 0 \u2264 x := by positivity",
        "-  -- per-term Bernoulli: (1 \u2212 x)\u02b2 \u2265 1 \u2212 jx",
        "-  have hterm : \u2200 j : \u2115, 1 - j * x \u2264 (1 - x) ^ j := by",
        "-    intro j",
        "-    have := one_add_mul_le_pow (a := -x) (by linarith : (-2 : \u211d) \u2264 -x) j",
        "-    rwa [show (1 : \u211d) + j * (-x) = 1 - j * x by ring,",
        "-      show (1 : \u211d) + -x = 1 - x by ring] at this",
        "-  -- sum of j over range n, as a real identity",
        "-  have hsum : \u2211 j \u2208 Finset.range n, (j : \u211d) = (n : \u211d) * (n - 1) / 2 := by",
        "-    have h := Finset.sum_range_id_mul_two n",
        "-    have hcast : (((\u2211 i \u2208 Finset.range n, i) * 2 : \u2115) : \u211d) = ((n * (n - 1) : \u2115) : \u211d) := by",
        "-      exact_mod_cast h",
        "-    rcases Nat.eq_zero_or_pos n with rfl | hnpos",
        "-    \u00b7 simp",
        "-    \u00b7 push_cast at hcast",
        "-      rw [Nat.cast_sub hnpos] at hcast",
        "-      push_cast at hcast",
        "-      linarith",
        "-  -- geometric factorization (division-free): 1 \u2212 (1\u2212x)\u207f = x \u00b7 \u03a3_{j<n} (1\u2212x)\u02b2",
        "-  have hgeom : (1 - (1 - x) ^ n) = x * \u2211 j \u2208 Finset.range n, (1 - x) ^ j := by",
        "-    have h := geom_sum_mul (1 - x) n",
        "-    have hx1' : (1 - x) - 1 = -x := by ring",
        "-    rw [hx1'] at h",
        "-    linarith",
        "-  -- assemble",
        "-  have hmain : (1 - x) ^ n - 1 + (n : \u211d) * x \u2264 (n : \u211d) * (n - 1) / 2 * x ^ 2 := by",
        "-    have h4 : (n : \u211d) * x - (n * (n - 1) / 2) * x ^ 2 \u2264 1 - (1 - x) ^ n := by",
        "-      rw [hgeom]",
        "-      have h5 : (n : \u211d) - x * ((n : \u211d) * (n - 1) / 2) \u2264",
        "-          \u2211 j \u2208 Finset.range n, (1 - x) ^ j := by",
        "-        have h6 : \u2211 j \u2208 Finset.range n, (1 - (j : \u211d) * x) =",
        "-            (n : \u211d) - x * \u2211 j \u2208 Finset.range n, (j : \u211d) := by",
        "-          have e1 : \u2211 j \u2208 Finset.range n, (1 - (j : \u211d) * x) =",
        "-              (\u2211 j \u2208 Finset.range n, (1 : \u211d)) - \u2211 j \u2208 Finset.range n, (j : \u211d) * x :=",
        "-            Finset.sum_sub_distrib (f := fun j : \u2115 => (1 : \u211d)) (g := fun j : \u2115 => (j : \u211d) * x)",
        "-          have e2 : \u2211 j \u2208 Finset.range n, (1 : \u211d) = (n : \u211d) := by simp",
        "-          have e3 : \u2211 j \u2208 Finset.range n, (j : \u211d) * x =",
        "-              x * \u2211 j \u2208 Finset.range n, (j : \u211d) := by",
        "-            rw [Finset.mul_sum]",
        "-            refine Finset.sum_congr rfl fun j _ => ?_",
        "-            ring",
        "-          rw [e1, e2, e3]",
        "-        rw [hsum] at h6",
        "-        rw [\u2190 h6]",
        "-        exact Finset.sum_le_sum fun j _ => hterm j",
        "-      calc (n : \u211d) * x - (n * (n - 1) / 2) * x ^ 2",
        "-          = x * ((n : \u211d) - x * (n * (n - 1) / 2)) := by ring",
        "-        _ \u2264 x * \u2211 j \u2208 Finset.range n, (1 - x) ^ j :=",
        "-            mul_le_mul_of_nonneg_left h5 hx0",
        "-    linarith",
        "-  -- convert back to the m-form",
        "-  have hx2 : x ^ 2 = 1 / m ^ 2 := by rw [hxdef]; ring",
        "-  have hdiv : (n : \u211d) / m = n * x := by rw [hxdef]; ring",
        "-  rw [hdiv]",
        "-  have h7 : (1 - 1 / (m : \u211d)) ^ n = (1 - x) ^ n := by rw [hxdef]",
        "-  rw [h7]",
        "-  calc (1 - x) ^ n - 1 + (n : \u211d) * x",
        "-      \u2264 (n : \u211d) * (n - 1) / 2 * x ^ 2 := hmain",
        "-    _ = (n : \u211d) * (n - 1) / (2 * m ^ 2) := by rw [hx2]; ring",
        "-",
        "-end Scratch",
        "-"
      ]
    }
  ],
  "originalFile": "/- Scratch.lean \u2014 proof development scratchpad (not imported by the lib).\n   Check with: lake env lean Scratch.lean\n   When green, the proof is merged into the skeleton files. -/\nimport Mathlib\n\nopen Real Filter Topology\n\nnamespace Scratch\n\n/-- D-057 Step 2 chain-rule identity: with T(n) = \u221an + 1,\nd\u00b2/dn\u00b2 \u03c6(T(n)) = [\u03c6\u2033(T) \u2212 \u03c6\u2032(T)/(T\u22121)]/(4n), written with \u221an = T\u22121. -/\ntheorem chain_rule_sqrt_shift (\u03c6 : \u211d \u2192 \u211d) (h\u03c6 : ContDiff \u211d 2 \u03c6)\n    (n : \u211d) (hn : 0 < n) :\n    deriv (deriv fun n => \u03c6 (\u221an + 1)) n =\n      (deriv (deriv \u03c6) (\u221an + 1) - deriv \u03c6 (\u221an + 1) / \u221an) / (4 * n) := by\n  -- differentiability infrastructure\n  have h\u03c61 : Differentiable \u211d \u03c6 := h\u03c6.differentiable (by norm_num)\n  have h\u03c62 : Differentiable \u211d (deriv \u03c6) :=\n    (h\u03c6.deriv' (n := 1)).differentiable one_ne_zero\n  have hsqrt : HasDerivAt Real.sqrt (1 / (2 * \u221an)) n :=\n    Real.hasDerivAt_sqrt hn.ne'\n  have hdiff_sqrt : DifferentiableAt \u211d Real.sqrt n := hsqrt.differentiableAt\n  -- h(n) = \u221an + 1 and its derivative\n  have hdiff_h : DifferentiableAt \u211d (fun n => \u221an + 1) n :=\n    hdiff_sqrt.add (differentiableAt_const 1)\n  -- first derivative of g = \u03c6 \u2218 h, as an eventually-equal nice function\n  have hpos : Set.Ioi (0 : \u211d) \u2208 \ud835\udcdd n := Ioi_mem_nhds hn\n  have hg1 : deriv (fun n => \u03c6 (\u221an + 1)) =\u1da0[\ud835\udcdd n]\n      fun n => deriv \u03c6 (\u221an + 1) * (2 * \u221an)\u207b\u00b9 := by\n    filter_upwards [hpos] with m hm\n    have hsm : HasDerivAt Real.sqrt (1 / (2 * \u221am)) m :=\n      Real.hasDerivAt_sqrt (ne_of_gt hm)\n    have hhm : DifferentiableAt \u211d (fun x => \u221ax + 1) m :=\n      hsm.differentiableAt.add (differentiableAt_const 1)\n    have h1 : deriv (fun x => \u221ax + 1) m = 1 / (2 * \u221am) := by\n      rw [deriv_add_const]\n      exact hsm.deriv\n    rw [show (fun x => \u03c6 (\u221ax + 1)) = \u03c6 \u2218 (fun x => \u221ax + 1) from rfl,\n      deriv_comp m (h\u03c61 (\u221am + 1)) hhm, h1]\n    ring\n  -- second derivative via HasDerivAt of the nice representative\n  have hA : HasDerivAt (fun n => deriv \u03c6 (\u221an + 1))\n      (deriv (deriv \u03c6) (\u221an + 1) * (1 / (2 * \u221an))) n := by\n    have h1 : HasDerivAt (fun x => \u221ax + 1) (1 / (2 * \u221an)) n :=\n      hsqrt.add_const 1\n    have h2 : HasDerivAt (deriv \u03c6) (deriv (deriv \u03c6) (\u221an + 1)) (\u221an + 1) :=\n      (h\u03c62 (\u221an + 1)).hasDerivAt\n    have h3 := h2.comp n h1\n    rwa [show (fun n => deriv \u03c6 (\u221an + 1)) = deriv \u03c6 \u2218 (fun n => \u221an + 1) from rfl]\n  have hB : HasDerivAt (fun n => (2 * \u221an)\u207b\u00b9)\n      (-(2 * (1 / (2 * \u221an))) / (2 * \u221an) ^ 2) n := by\n    have h1 : HasDerivAt (fun n => 2 * \u221an) (2 * (1 / (2 * \u221an))) n :=\n      hsqrt.const_mul 2\n    have h2 : (2 * \u221an) \u2260 0 :=\n      mul_ne_zero two_ne_zero (Real.sqrt_ne_zero'.2 hn)\n    exact h1.inv h2\n  have hmul : HasDerivAt (fun n => deriv \u03c6 (\u221an + 1) * (2 * \u221an)\u207b\u00b9)\n      (deriv (deriv \u03c6) (\u221an + 1) * (1 / (2 * \u221an)) * (2 * \u221an)\u207b\u00b9 +\n        deriv \u03c6 (\u221an + 1) * (-(2 * (1 / (2 * \u221an))) / (2 * \u221an) ^ 2)) n :=\n    hA.mul hB\n  have hder := (hmul.congr_of_eventuallyEq hg1).deriv\n  rw [hder]\n  set s := \u221an with hsdef\n  have hs0 : s \u2260 0 := Real.sqrt_ne_zero'.2 hn\n  have hn_eq : n = s ^ 2 := by\n    rw [hsdef]; exact (Real.sq_sqrt hn.le).symm\n  rw [hn_eq]\n  field_simp [hs0]\n  ring\n\n/-- h\u207a(m) \u2265 0 for m \u2265 1: first-order Bernoulli, (1\u22121/m)\u207f \u2265 1 \u2212 n/m. -/\ntheorem bern_term_nonneg (n : \u2115) (m : \u2115) (hm : 1 \u2264 m) :\n    0 \u2264 (1 - 1 / (m : \u211d)) ^ n - 1 + (n : \u211d) / m := by\n  have hm0 : (m : \u211d) \u2260 0 := by positivity\n  have h1 : (1 : \u211d) + n * (-1 / m) \u2264 (1 + -1 / (m : \u211d)) ^ n := by\n    apply one_add_mul_le_pow\n    have h3 : (0 : \u211d) \u2264 1 / (m : \u211d) := by positivity\n    have h4 : (1 : \u211d) / m \u2264 1 := by\n      rw [div_le_one (by positivity)]; exact_mod_cast hm\n    rw [neg_div]\n    linarith\n  have h2 : (1 : \u211d) - n / m \u2264 (1 - 1 / m) ^ n := by\n    have : (1 : \u211d) + n * (-1 / m) = 1 - n / m := by field_simp; ring\n    rwa [this, show (1 : \u211d) + -1 / m = 1 - 1 / m by ring] at h1\n  linarith\n\n/-- h\u207a(m) \u2264 (n choose 2)/m\u00b2 for m \u2265 1: geometric factorization\n1 \u2212 (1\u2212x)\u207f = x\u00b7\u03a3_{j<n} (1\u2212x)\u02b2 \u2265 x\u00b7(n \u2212 x\u00b7\u03a3j) plus Bernoulli per term. -/\ntheorem bern_term_upper (n : \u2115) (m : \u2115) (hm : 1 \u2264 m) :\n    (1 - 1 / (m : \u211d)) ^ n - 1 + (n : \u211d) / m \u2264 (n : \u211d) * (n - 1) / (2 * m ^ 2) := by\n  have hm0 : (m : \u211d) \u2260 0 := by positivity\n  set x := (1 : \u211d) / m with hxdef\n  have hx1 : x \u2264 1 := by\n    rw [hxdef, div_le_one (by positivity)]; exact_mod_cast hm\n  have hx0 : 0 \u2264 x := by positivity\n  -- per-term Bernoulli: (1 \u2212 x)\u02b2 \u2265 1 \u2212 jx\n  have hterm : \u2200 j : \u2115, 1 - j * x \u2264 (1 - x) ^ j := by\n    intro j\n    have := one_add_mul_le_pow (a := -x) (by linarith : (-2 : \u211d) \u2264 -x) j\n    rwa [show (1 : \u211d) + j * (-x) = 1 - j * x by ring,\n      show (1 : \u211d) + -x = 1 - x by ring] at this\n  -- sum of j over range n, as a real identity\n  have hsum : \u2211 j \u2208 Finset.range n, (j : \u211d) = (n : \u211d) * (n - 1) / 2 := by\n    have h := Finset.sum_range_id_mul_two n\n    have hcast : (((\u2211 i \u2208 Finset.range n, i) * 2 : \u2115) : \u211d) = ((n * (n - 1) : \u2115) : \u211d) := by\n      exact_mod_cast h\n    rcases Nat.eq_zero_or_pos n with rfl | hnpos\n    \u00b7 simp\n    \u00b7 push_cast at hcast\n      rw [Nat.cast_sub hnpos] at hcast\n      push_cast at hcast\n      linarith\n  -- geometric factorization (division-free): 1 \u2212 (1\u2212x)\u207f = x \u00b7 \u03a3_{j<n} (1\u2212x)\u02b2\n  have hgeom : (1 - (1 - x) ^ n) = x * \u2211 j \u2208 Finset.range n, (1 - x) ^ j := by\n    have h := geom_sum_mul (1 - x) n\n    have hx1' : (1 - x) - 1 = -x := by ring\n    rw [hx1'] at h\n    linarith\n  -- assemble\n  have hmain : (1 - x) ^ n - 1 + (n : \u211d) * x \u2264 (n : \u211d) * (n - 1) / 2 * x ^ 2 := by\n    have h4 : (n : \u211d) * x - (n * (n - 1) / 2) * x ^ 2 \u2264 1 - (1 - x) ^ n := by\n      rw [hgeom]\n      have h5 : (n : \u211d) - x * ((n : \u211d) * (n - 1) / 2) \u2264\n          \u2211 j \u2208 Finset.range n, (1 - x) ^ j := by\n        have h6 : \u2211 j \u2208 Finset.range n, (1 - (j : \u211d) * x) =\n            (n : \u211d) - x * \u2211 j \u2208 Finset.range n, (j : \u211d) := by\n          have e1 : \u2211 j \u2208 Finset.range n, (1 - (j : \u211d) * x) =\n              (\u2211 j \u2208 Finset.range n, (1 : \u211d)) - \u2211 j \u2208 Finset.range n, (j : \u211d) * x :=\n            Finset.sum_sub_distrib (f := fun j : \u2115 => (1 : \u211d)) (g := fun j : \u2115 => (j : \u211d) * x)\n          have e2 : \u2211 j \u2208 Finset.range n, (1 : \u211d) = (n : \u211d) := by simp\n          have e3 : \u2211 j \u2208 Finset.range n, (j : \u211d) * x =\n              x * \u2211 j \u2208 Finset.range n, (j : \u211d) := by\n            rw [Finset.mul_sum]\n            refine Finset.sum_congr rfl fun j _ => ?_\n            ring\n          rw [e1, e2, e3]\n        rw [hsum] at h6\n        rw [\u2190 h6]\n        exact Finset.sum_le_sum fun j _ => hterm j\n      calc (n : \u211d) * x - (n * (n - 1) / 2) * x ^ 2\n          = x * ((n : \u211d) - x * (n * (n - 1) / 2)) := by ring\n        _ \u2264 x * \u2211 j \u2208 Finset.range n, (1 - x) ^ j :=\n            mul_le_mul_of_nonneg_left h5 hx0\n    linarith\n  -- convert back to the m-form\n  have hx2 : x ^ 2 = 1 / m ^ 2 := by rw [hxdef]; ring\n  have hdiv : (n : \u211d) / m = n * x := by rw [hxdef]; ring\n  rw [hdiv]\n  have h7 : (1 - 1 / (m : \u211d)) ^ n = (1 - x) ^ n := by rw [hxdef]\n  rw [h7]\n  calc (1 - x) ^ n - 1 + (n : \u211d) * x\n      \u2264 (n : \u211d) * (n - 1) / 2 * x ^ 2 := hmain\n    _ = (n : \u211d) * (n - 1) / (2 * m ^ 2) := by rw [hx2]; ring\n\nend Scratch\n",
  "autoRead": true
}

{
  "file_path": "D:\\Python\\Quantum\\web\\dashboard\\urls.py",
  "content": "from django.urls import path\n\nfrom . import api, views\n\nurlpatterns = [\n    path(\"\", views.home, name=\"home\"),\n    path(\"dashboard/\", views.dashboard, name=\"dashboard\"),\n    path(\"roadmap/\", views.roadmap, name=\"roadmap\"),\n    path(\"ledger/\", views.ledger, name=\"ledger\"),\n    path(\"ledger/<str:rid>/\", views.ledger_detail, name=\"ledger_detail\"),\n    path(\"experiments/\", views.experiments, name=\"experiments\"),\n    path(\"experiments/<str:eid>/\", views.experiment_detail, name=\"experiment_detail\"),\n    path(\"paper/\", views.paper, name=\"paper\"),\n    path(\"live/\", views.live, name=\"live\"),\n    path(\"feedback/\", views.feedback, name=\"feedback\"),\n    path(\"api/health/\", api.health, name=\"api_health\"),\n    path(\"api/status/\", api.status, name=\"api_status\"),\n    path(\"api/logtail/\", api.logtail, name=\"api_logtail\"),\n]\n\nfor kind in (\"derivations\", \"graveyard\", \"journal\", \"resources\"):\n    urlpatterns.append(path(f\"{kind}/\", views.collection, {\"kind\": kind},\n                            name=f\"collection_{kind}\"))\n    urlpatterns.append(path(f\"{kind}/<str:name>/\", views.collection_item,\n                            {\"kind\": kind}, name=f\"item_{kind}\"))\n"
}

{
  "type": "create",
  "filePath": "D:\\Python\\Quantum\\web\\dashboard\\urls.py",
  "content": "from django.urls import path\n\nfrom . import api, views\n\nurlpatterns = [\n    path(\"\", views.home, name=\"home\"),\n    path(\"dashboard/\", views.dashboard, name=\"dashboard\"),\n    path(\"roadmap/\", views.roadmap, name=\"roadmap\"),\n    path(\"ledger/\", views.ledger, name=\"ledger\"),\n    path(\"ledger/<str:rid>/\", views.ledger_detail, name=\"ledger_detail\"),\n    path(\"experiments/\", views.experiments, name=\"experiments\"),\n    path(\"experiments/<str:eid>/\", views.experiment_detail, name=\"experiment_detail\"),\n    path(\"paper/\", views.paper, name=\"paper\"),\n    path(\"live/\", views.live, name=\"live\"),\n    path(\"feedback/\", views.feedback, name=\"feedback\"),\n    path(\"api/health/\", api.health, name=\"api_health\"),\n    path(\"api/status/\", api.status, name=\"api_status\"),\n    path(\"api/logtail/\", api.logtail, name=\"api_logtail\"),\n]\n\nfor kind in (\"derivations\", \"graveyard\", \"journal\", \"resources\"):\n    urlpatterns.append(path(f\"{kind}/\", views.collection, {\"kind\": kind},\n                            name=f\"collection_{kind}\"))\n    urlpatterns.append(path(f\"{kind}/<str:name>/\", views.collection_item,\n                            {\"kind\": kind}, name=f\"item_{kind}\"))\n",
  "structuredPatch": [],
  "originalFile": null
}