{
  "checkpoint": "R135",
  "created_UTC": "2026-09-11T01:12:11.781963+00:00",
  "event": "E11, 2010-06-13",
  "scope": "Outer-front classification closure; user follow-up explicitly adds the inner front with separate constraints and conclusions.",
  "authorization": "Complete science and packaging without another design gate. No new event.",
  "frozen_prior_results": [
    "R89",
    "R92",
    "R93",
    "R110",
    "R119",
    "R120",
    "R121",
    "R122",
    "R132",
    "R133",
    "R134"
  ],
  "reason_for_extension": "No numerical local theta_Bn bound is supplied. Determine the actual regular-fast geometry limit instead of treating 83.3 degrees as a boundary; enumerate the other algebraic roots; test the unknown-flow dependency and extend the conditional inner-state comparison beyond three selected outer states.",
  "geometry_provenance": {
    "theta_Bn_observed_interval": null,
    "theta_Bn_model_bounded_interval": null,
    "PFSS": "Qualitative published topology overlay; no matched numerical B vector and 3-D front-surface uncertainty at the selected radio/EUV patch.",
    "acute_angle_support": "0..90 degrees is only the geometric definition, not a supported observational interval."
  },
  "continuous_certificate": {
    "source_domain": "Exact saved R93 r,b rectangle; gamma=5/3",
    "extension_coordinate": "t=r*h, h=Bn^2/(mu0*rho1*w1^2); 0<=t<=1, with t=1 retained as an unresolved switch-on endpoint.",
    "method": "Exact rational polynomial identities and Bernstein coefficient bounds on a declared 8x4x8 partition in r,b,t. Sign failures remain uncertified; no post-hoc relabelling.",
    "angle_mapping": "Prove monotone theta from 90 toward 0 on the ordinary-fast branch; no positive-angle cutoff selected by preference."
  },
  "outer_enumeration": {
    "theta_grid_deg": [
      0.5,
      1.0,
      1.5,
      2.0,
      2.5,
      3.0,
      3.5,
      4.0,
      4.5,
      5.0,
      5.5,
      6.0,
      6.5,
      7.0,
      7.5,
      8.0,
      8.5,
      9.0,
      9.5,
      10.0,
      10.5,
      11.0,
      11.5,
      12.0,
      12.5,
      13.0,
      13.5,
      14.0,
      14.5,
      15.0,
      15.5,
      16.0,
      16.5,
      17.0,
      17.5,
      18.0,
      18.5,
      19.0,
      19.5,
      20.0,
      20.5,
      21.0,
      21.5,
      22.0,
      22.5,
      23.0,
      23.5,
      24.0,
      24.5,
      25.0,
      25.5,
      26.0,
      26.5,
      27.0,
      27.5,
      28.0,
      28.5,
      29.0,
      29.5,
      30.0,
      30.5,
      31.0,
      31.5,
      32.0,
      32.5,
      33.0,
      33.5,
      34.0,
      34.5,
      35.0,
      35.5,
      36.0,
      36.5,
      37.0,
      37.5,
      38.0,
      38.5,
      39.0,
      39.5,
      40.0,
      40.5,
      41.0,
      41.5,
      42.0,
      42.5,
      43.0,
      43.5,
      44.0,
      44.5,
      45.0,
      45.5,
      46.0,
      46.5,
      47.0,
      47.5,
      48.0,
      48.5,
      49.0,
      49.5,
      50.0,
      50.5,
      51.0,
      51.5,
      52.0,
      52.5,
      53.0,
      53.5,
      54.0,
      54.5,
      55.0,
      55.5,
      56.0,
      56.5,
      57.0,
      57.5,
      58.0,
      58.5,
      59.0,
      59.5,
      60.0,
      60.5,
      61.0,
      61.5,
      62.0,
      62.5,
      63.0,
      63.5,
      64.0,
      64.5,
      65.0,
      65.5,
      66.0,
      66.5,
      67.0,
      67.5,
      68.0,
      68.5,
      69.0,
      69.5,
      70.0,
      70.5,
      71.0,
      71.5,
      72.0,
      72.5,
      73.0,
      73.5,
      74.0,
      74.5,
      75.0,
      75.5,
      76.0,
      76.5,
      77.0,
      77.5,
      78.0,
      78.5,
      79.0,
      79.5,
      80.0,
      80.5,
      81.0,
      81.5,
      82.0,
      82.5,
      83.0,
      83.5,
      84.0,
      84.5,
      85.0,
      85.5,
      86.0,
      86.5,
      87.0,
      87.5,
      88.0,
      88.5,
      89.0,
      89.5,
      90.0
    ],
    "theta_zero": "Separate exact switch-on/parallel limiting audit; not forced into an ordinary family.",
    "source_scenarios": "Four R93 normalized r,b corners; exact R110 central tuple; eight paired R109 frequency/temperature corners. R93 and R109 physical input conventions remain separately labelled.",
    "equation": "r*h*[r+5-2*r*h*(4-r)]*sin(theta)^2 - 2*(4-r-5*b*r)*(1-r*h)^2*cos(theta)^2 = 0",
    "roots": "Record all quadratic roots, including complex, negative, nonphysical, pole and nonordinary completions; no magnetic-strength cutoff."
  },
  "upstream_motion": {
    "source_scenarios": "R110 central tuple plus eight R109 paired frequency/temperature corners",
    "w_over_wcrit": [
      0.75,
      0.9,
      1.0,
      1.1,
      1.5
    ],
    "wcrit": "sqrt(5*p1/rho1*r/(4-r))",
    "observer_speed": "Keep the R109 G0 effective normal pattern speed fixed; derive u1n=Vn-w. These flow probes are ASSUMED stress cases around an analytical boundary, not measured solar bounds.",
    "linked_inputs": "Keep radio frequencies, density, compression and T/pressure dependencies; B and all downstream states are MODEL_DERIVED."
  },
  "inner_extension": {
    "outer_state": "Central R110 input tuple; every ordinary-fast root on the declared theta grid",
    "azimuth_grid_deg": [
      0,
      5,
      10,
      15,
      20,
      25,
      30,
      35,
      40,
      45,
      50,
      55,
      60,
      65,
      70,
      75,
      80,
      85,
      90,
      95,
      100,
      105,
      110,
      115,
      120,
      125,
      130,
      135,
      140,
      145,
      150,
      155,
      160,
      165,
      170,
      175,
      180
    ],
    "inner_speed_and_normals": "Frozen central R120 effective speed and two projected normals; original 36 method alternatives retained, not rerun.",
    "assumptions": "Exactly the R120 uniform intervening-state transfer, G0 normals and laboratory upstream zero including tangential flow. The full finite grid is a conditional completion test, not a solar-state distribution.",
    "roots": "Enumerate all roots of the energy polynomial after separately recording the trivial r=1 factor; retain negative/complex/expansive/nonpositive/guarded roots and physically checked ordinary/nonordinary candidates.",
    "no_transfer": "No outer radio compression is assigned to the inner jump. Inner compression is solved, not prescribed."
  },
  "safeguards": {
    "minimum_relative_inflow": 1e-08,
    "relative_rational_pole_distance": 1e-06,
    "polynomial_scaled_residual_max": 1e-12,
    "flux_scaled_residual_max": 1e-10,
    "characteristic_boundary_and_coincidence_relative_margin": 1e-07,
    "root_real_imaginary_relative_tolerance": 1e-09,
    "root_separation_relative_tolerance": 1e-07,
    "compression_distance_from_no_jump": 1e-07,
    "pressure_positive_margin": 1e-12,
    "entropy_positive_margin": 1e-10,
    "tangential_field_relative_margin": 1e-07,
    "guard_handling": "UNRESOLVED. A finite grid does not certify cell interiors; exact limiting surfaces remain explicit.",
    "quadratic": "Stable quadratic formula with 80-digit Decimal recomputation before float output.",
    "inner_energy": "Enumerate polynomial roots; a bracketed scalar-energy check is additional numerical verification, not the root search."
  },
  "evolutionary_check": {
    "ordinary": "Unchanged state-only classifier plus stricter predeclared conservation/entropy/characteristic guards.",
    "transverse": "For a coplanar state pair, audit the two decoupled out-of-plane linearized RH equations. Three incoming Alfven characteristics and one outgoing amplitude cannot satisfy two independent generic jump conditions. Report failure of this full ideal-MHD evolutionary test separately from numerical unresolvedness and separately from frozen historical labels.",
    "limits": "Rotational/contact and switch/parallel/perpendicular degeneracies treated separately. No claim about dissipative stabilization, restricted coplanar models, smooth waves or a complete Riemann fan."
  },
  "new_data_or_literature": "None planned: retained source texts and state records contain the needed equations and demonstrate the unresolved local association. No broad survey.",
  "final_result_rule": "Observational FAST requires a complete independently supported local domain and exclusion of competitors. Conditional algebraic survival cannot fill absent measurements. Outer and inner observational outcomes remain separate.",
  "delivery": [
    "RMO_R135_Update_from_R134.zip",
    "BUNDLE_MANIFEST_R135.json",
    "R135_UPDATE_README.txt",
    "RMO_QuickLook_R135.html",
    "R135_E11_REVIEW.md"
  ]
}