[
  {
    "name": "Dark Energy Density",
    "channel": "static",
    "quantum_input": "Spectral norm ||A||/||Γ|| = √(1+γ²) on S² horizon",
    "classical_output": "ρ_Λ, Ω_Λ = 0.6970",
    "constants": [
      "γ²",
      "1+γ²"
    ],
    "prediction": "Ω_Λ = 0.6970",
    "observation": "Ω_Λ = 0.685 ± 0.013 (Planck 2018)",
    "residual": "+0.92σ",
    "status": "DERIVED",
    "papers": [
      8,
      9
    ],
    "zenodo": "https://zenodo.org/records/18895980/latest",
    "summary": "Dark energy is the spectral weight of the Ashtekar-Barbero connection projected into the bulk through the Holst action.",
    "formula": "Omega_Lambda = rho_Lambda / rho_crit = 0.6970 (Holst/Ashtekar-Barbero spectral-weight row)",
    "formula_class": "sourced_display_pending_closed_form_audit"
  },
  {
    "name": "Baryon Fraction",
    "channel": "static",
    "quantum_input": "SU(2) topological vacuum scalarization",
    "classical_output": "f_b = 2γ/x = 0.30576",
    "constants": [
      "γ",
      "x"
    ],
    "prediction": "f_b = 0.30576 (gauge-coupling inventory; active x)",
    "observation": "Not directly comparable to a single CMB ω_b/ω_m. Active branch slots are ω_b,geom = 0.020996 (α=1, sound speed/BBN), ω_b,eff = 0.028989 (acoustic effective slot), and ω_b,clustering = 0.017035 (α=3/2, clustering).",
    "residual": "Observable-class dependent; see the active Paper 19/29 slot map",
    "status": "DERIVED",
    "papers": [
      12,
      19
    ],
    "zenodo": "https://zenodo.org/records/18936508/latest",
    "summary": "Baryons are the gauge-coupled subset of OS dust. The fraction is set by the SU(2) gauge topology of the horizon. Different observable classes probe different projected values.",
    "formula": "f_b = 2 gamma / x",
    "formula_class": "closed_form"
  },
  {
    "name": "Rosetta Identity",
    "channel": "static",
    "quantum_input": "Quaternionic SU(2) Casimir norm Q(q_γ) = 1+γ²",
    "classical_output": "O(η) = x^(2α)(1+γ²)^(α/2)",
    "constants": [
      "γ²",
      "x",
      "α"
    ],
    "prediction": "Exact algebraic identity",
    "observation": "N/A (structural theorem)",
    "residual": "N/A",
    "status": "THEOREM",
    "papers": [
      15
    ],
    "zenodo": "https://zenodo.org/records/19026431/latest",
    "summary": "The master identity organizing all observable classes by their form degree on the α-ladder.",
    "formula": "O(eta) = x^(2 alpha) (1 + gamma^2)^(alpha/2)",
    "formula_class": "closed_form_symbolic"
  },
  {
    "name": "Spatial Decoupling Δ",
    "channel": "static",
    "quantum_input": "Ashtekar-Barbero connection projection",
    "classical_output": "Δ = x⁴(1+γ²) = 6.15266",
    "constants": [
      "γ²",
      "x"
    ],
    "prediction": "6.15266",
    "observation": "N/A (framework constant)",
    "residual": "N/A",
    "status": "DERIVED",
    "papers": [
      2,
      8,
      9
    ],
    "zenodo": "https://zenodo.org/records/18868612/latest",
    "summary": "The master geometric scale combining compactness and gauge weight.",
    "formula": "Delta = x^4 (1 + gamma^2)",
    "formula_class": "closed_form"
  },
  {
    "name": "Generating Potential V(α)",
    "channel": "static",
    "quantum_input": "Fubini-Study Kähler potential on reduced gauge center",
    "classical_output": "V(α) = −2 ln(cos α)",
    "constants": [
      "γ"
    ],
    "prediction": "Exact functional form",
    "observation": "N/A (structural theorem)",
    "residual": "N/A",
    "status": "THEOREM",
    "papers": [
      18
    ],
    "zenodo": "https://zenodo.org/records/19054258/latest",
    "summary": "The unique generating potential on the reduced gauge center organizing all observable classes.",
    "formula": "V(alpha) = -2 ln(cos alpha)",
    "formula_class": "closed_form_symbolic"
  },
  {
    "name": "Deuterium Abundance (D/H)",
    "channel": "dynamic",
    "quantum_input": "Rate-dressing via (1+γ²) at α=1 rung of V(α)",
    "classical_output": "D/H = 2.509 × 10⁻⁵",
    "constants": [
      "1+γ²"
    ],
    "prediction": "2.509 × 10⁻⁵",
    "observation": "2.547 ± 0.025 × 10⁻⁵ (Cooke 2018)",
    "residual": "−0.61σ",
    "status": "DERIVED",
    "papers": [
      24
    ],
    "zenodo": "https://zenodo.org/records/19219282/latest",
    "summary": "Deuterium abundance from geometric dressing of BBN rates. This is the quantum gravity fingerprint at the nuclear scale.",
    "formula": "numeric PRyMordial/BBN network solution for D/H on the Paper-24/Paper-26 banked branch",
    "formula_class": "numeric_pipeline"
  },
  {
    "name": "Helium-4 Abundance (Y_p)",
    "channel": "dynamic",
    "quantum_input": "Weak freeze-out thermal covariance, (1+γ²) dressing",
    "classical_output": "Y_p = 0.2477",
    "constants": [
      "1+γ²"
    ],
    "prediction": "0.2477",
    "observation": "0.2449 ± 0.0040 (Aver 2021)",
    "residual": "+0.68σ",
    "status": "DERIVED",
    "papers": [
      25
    ],
    "zenodo": "https://zenodo.org/records/19242682/latest",
    "summary": "Primordial helium from geometric dressing of the weak freeze-out rate.",
    "formula": "numeric PRyMordial/BBN network solution for Y_p on the Paper-24/Paper-26 banked branch",
    "formula_class": "numeric_pipeline"
  },
  {
    "name": "Lithium-7 Abundance",
    "channel": "dynamic",
    "quantum_input": "Isovector transport J_(I=1)/J_(I=0) = 1+γ²",
    "classical_output": "Li-7/H = 1.75 × 10⁻¹⁰",
    "constants": [
      "1+γ²"
    ],
    "prediction": "1.75 × 10⁻¹⁰",
    "observation": "1.6 ± 0.3 × 10⁻¹⁰ (Sbordone 2010)",
    "residual": "+0.55σ",
    "status": "DERIVED",
    "papers": [
      24
    ],
    "zenodo": "https://zenodo.org/records/19219282/latest",
    "summary": "The cosmological lithium problem resolved. The same (1+γ²) dressing is channel-resolved on the I=1 adjoint branch.",
    "formula": "K_gauge=ln(1+gamma_BI^2); q_scale=sqrt(B(E2)_down)/100; q_trans,ex=q_scale <F0>_amp,ex; R_ex(T9)=exp[-epsilon_n((q_trans,ex/x)/Q_d)nu_34(T9)]; R_34,tot=f_gs R_gs+(1-f_gs)R_ex",
    "formula_class": "numeric_pipeline"
  },
  {
    "name": "Spectral Index (n_s)",
    "channel": "mixed",
    "quantum_input": "DtN boundary fixed-point on coexact source block",
    "classical_output": "n_s = 1 − K_gauge/x = 0.96468",
    "constants": [
      "K_gauge",
      "x"
    ],
    "prediction": "0.96468",
    "observation": "0.9649 ± 0.0042 (Planck 2018)",
    "residual": "−0.05σ",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      23,
      28,
      32
    ],
    "zenodo": "https://zenodo.org/records/19359276/latest",
    "summary": "The spectral tilt from the boundary fixed-point principle. Primordial scale dependence emerges from horizon geometry.",
    "formula": "n_s = 1 - K_gauge/x, K_gauge=ln(1+gamma_BI^2)",
    "formula_class": "closed_form"
  },
  {
    "name": "Scalar Amplitude (A_s)",
    "channel": "mixed",
    "quantum_input": "Hawking boundary state on lowest-shell bridge quotient",
    "classical_output": "A_s = 2.007 × 10⁻⁹",
    "constants": [
      "γ",
      "K_gauge"
    ],
    "prediction": "2.007 × 10⁻⁹",
    "observation": "2.101 ± 0.030 × 10⁻⁹ (Planck 2018)",
    "residual": "−3.1σ (raw) or 0.8% with optical damping",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      26,
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "The primordial power spectrum amplitude from the Hawking state. No inflationary potential is required.",
    "formula": "A_s=(25/9)[gamma^2/(1+gamma^2)](1/sqrt(2))(exp(4 pi sqrt(2))-1)^(-1)",
    "formula_class": "closed_form"
  },
  {
    "name": "Gravitational Slip (Sigma_IO)",
    "channel": "dynamic",
    "quantum_input": "Kerr scalar Born/Weyl typed quotient of boundary Weyl response, j=2 data on S2 horizon",
    "classical_output": "Sigma_IO = x^(-1/2) = 0.8023170090064653",
    "constants": [
      "x"
    ],
    "prediction": "Sigma_IO = x^(-1/2) = 0.8023170090064653",
    "observation": "Structural Weyl-response bridge result. S8 and sigma8 comparisons are tracked separately and are currently walled by Q413.",
    "residual": "N/A for the scalar Born/Weyl quotient; weak-lensing/S8 use is not active theorem-grade.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      31
    ],
    "zenodo": "https://zenodo.org/records/19415916/latest",
    "summary": "Current Kerr bank points to Q199: the scalar Born/Weyl typed quotient gives x^(-1/2)=0.8023170090064653. The stale 0.8114 closed-FRW wording should be retired; S8/sigma8 comparisons stay separate and walled.",
    "formula": "Sigma_IO = x^(-1/2)",
    "formula_class": "closed_form"
  },
  {
    "name": "sigma8 Growth Readout Frontier",
    "channel": "mixed",
    "quantum_input": "Closed-S3 Kerr density/Boltzmann transfer for sigma8/S8 is not yet banked",
    "classical_output": "No current theorem-grade sigma8 prediction",
    "constants": [
      "A_s",
      "f_Gamma"
    ],
    "prediction": "Frontier: IO_NATIVE_CLOSED_S3_KERR_DENSITY_BOLTZMANN_TRANSFER_FOR_SIGMA8_S8 must be built before sigma8 can be active theorem-grade.",
    "observation": "Former sigma8 comparison retained only as diagnostic provenance.",
    "residual": "N/A: current bank says not admissible as theorem-grade IO sigma8.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON / NOT_ADMISSIBLE_AS_THEOREM_GRADE_CURRENT_IO_S8",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "Q413 downgrades the former active sigma8 row. Current use is diagnostic/frontier only until the IO-native closed-S3 Kerr density/Boltzmann transfer and readout chain exists."
  },
  {
    "name": "S8 f_Gamma Readout Frontier",
    "channel": "mixed",
    "quantum_input": "Closed-S3 Kerr density-transfer and weak-lensing readout chain remains unbanked",
    "classical_output": "No current theorem-grade S8 prediction",
    "constants": [
      "A_s",
      "f_Gamma",
      "Omega_m"
    ],
    "prediction": "Frontier: f_Gamma/Sigma_IO cannot be used as an exact post-CAMB S8 map until placement and exponent are banked.",
    "observation": "Former weak-lensing S8 comparison retained only as diagnostic provenance.",
    "residual": "N/A: current bank says not admissible as theorem-grade IO S8.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON / NOT_ADMISSIBLE_AS_THEOREM_GRADE_CURRENT_IO_S8",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "Q413 quarantines the old S8/f_Gamma row. Keep only diagnostic/frontier wording until the IO-native density-transfer and weak-lensing readout chain exists."
  },
  {
    "name": "Observer Boundary (x_crit)",
    "channel": "static",
    "quantum_input": "Projection map finite domain, Q = 1+γ²",
    "classical_output": "x_crit = Q^(−1/4) = 0.9864",
    "constants": [
      "1+γ²",
      "Q"
    ],
    "prediction": "x_crit = 0.9864 (~6.6 Gyr from now)",
    "observation": "N/A (future prediction)",
    "residual": "N/A",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "Paper 32 source-block boundary result on the active closed-FRW branch. It fixes where the active scalar optical observer channel terminates.",
    "formula": "x_crit = Q^(-1/4)",
    "formula_class": "closed_form_symbolic"
  },
  {
    "name": "Hubble Constant (H₀)",
    "channel": "static",
    "quantum_input": "Q43 scoped bare-torsion/global-readout H0; primitive observer projection remains open",
    "classical_output": "H₀,scoped = 62.96277381531285 km/s/Mpc; historical 67.58 quarantined",
    "constants": [
      "x",
      "Δ"
    ],
    "prediction": "62.96277381531285 km/s/Mpc scoped only",
    "observation": "67.4 ± 0.5 (Planck) / 68.3 ± 1.0 (ACT) / 73.04 ± 1.04 (SH0ES)",
    "residual": "not scored as observer H₀; Q44/Q45 quarantine historical 67.58 projection",
    "status": "OPEN / QUARANTINED_HISTORICAL_PROJECTION",
    "papers": [
      21,
      30
    ],
    "zenodo": "https://zenodo.org/records/19367583/latest",
    "summary": "Q43 supplies the live scoped Kerr Hubble readout. The historical 67.58 km/s/Mpc projection package is not active-consumable until a new primitive-observable projector is derived.",
    "formula": "H0_scoped = Delta^(1/4) H_bare (historical projected value quarantined)",
    "formula_class": "scoped_historical_projection"
  },
  {
    "name": "Cosmic Chronometers Frame-Typing Frontier",
    "channel": "static",
    "quantum_input": "Chronometer observable frame typing across H(z), time-delay, and high-z channels remains globally open",
    "classical_output": "Global chronometer confrontation is OPEN/PREMISE_GAP; L0 Kerr typing exists only as non-load-bearing context",
    "constants": [
      "H0",
      "Q119",
      "Delta"
    ],
    "prediction": "No active global chronometer chi2 closure.",
    "observation": "Direct chronometer rows require channel frame typing before load-bearing confrontation.",
    "residual": "N/A: stronger tensions are legally inadmissible until typed.",
    "status": "OPEN/PREMISE_GAP globally; L0 Kerr class typed only as context-diagnostic support.",
    "papers": [
      29
    ],
    "zenodo": "https://zenodo.org/records/19367583/latest",
    "summary": "Current bank keeps global chronometer typing open. The L0 homogeneous scalar-temporal Kerr class is typed as context support only and does not authorize the old closed-FRW chronometer chi2 closure."
  },
  {
    "name": "Galaxy BAO Template-Bridge Frontier",
    "channel": "mixed",
    "quantum_input": "IO-native BAO feature functional exists only as partial template-bridge structure",
    "classical_output": "Raw observer BAO closure remains open pending drag-ruler-to-observer BAO-feature convention bridge",
    "constants": [
      "r_d",
      "omega_b_geom",
      "eta"
    ],
    "prediction": "Frontier: build IO-native BAO template bridge before active BAO closure.",
    "observation": "DESI/AP and formal-structure context may be retained only where scoped and non-load-bearing.",
    "residual": "N/A: current bank has no active raw observer BAO closure.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON / FRONTIER_OPEN_PROGRAM",
    "papers": [
      29,
      31
    ],
    "zenodo": "https://zenodo.org/records/19415916/latest",
    "summary": "The accepted BAO frontier ledger says current IO has a partial BAO feature functional but not a load-bearing raw observer BAO closure. The old DESI chi2 closure wording should be retired."
  },
  {
    "name": "Acoustic Scale (θ_s)",
    "channel": "mixed",
    "quantum_input": "Boundary acoustic rank to CMB geometry, J_θ = x^(−1/2)√(1+γ²)",
    "classical_output": "θ* = 0.599°",
    "constants": [
      "x",
      "γ²",
      "1+γ²"
    ],
    "prediction": "θ* = 0.599°",
    "observation": "0.59652° ± 0.00018° (Planck 2018)",
    "residual": "+0.42% on the active acoustic channel",
    "status": "DERIVED",
    "papers": [
      20,
      21
    ],
    "zenodo": "https://zenodo.org/records/19145122/latest",
    "summary": "The CMB acoustic angle from boundary geometry. The active site tracks the derived IO angle rather than the retired mixed-branch 100θ_s value.",
    "formula": "theta_* = r_s(z_*) / D_A(z_*) in the banked IO acoustic calculation",
    "formula_class": "numeric_pipeline"
  },
  {
    "name": "Optical Depth (τ_eff)",
    "channel": "dynamic",
    "quantum_input": "Reduced centered Gaussian source-covariance class",
    "classical_output": "τ_eff = K_gauge/2 = 0.02744",
    "constants": [
      "K_gauge"
    ],
    "prediction": "0.02744",
    "observation": "0.054 ± 0.007 (Planck 2018)",
    "residual": "Scoped to source-covariance class",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      27,
      31
    ],
    "zenodo": "https://zenodo.org/records/19333220/latest",
    "summary": "The effective optical depth from boundary gauge weight, carried inside the verified reduced source class.",
    "formula": "tau_eff = K_gauge/2 = ln(1+gamma_BI^2)/2",
    "formula_class": "closed_form"
  },
  {
    "name": "Bounce / Recollapse",
    "channel": "mixed",
    "quantum_input": "Support-branch recollapse plus extended fermionic/chiral IO-EC bounce attachment",
    "classical_output": "Recollapse in 111 Gyr on the active branch; bounce attachment closes at R_eq/R_bounce = 1.00016 within the extension",
    "constants": [
      "r_s",
      "Q",
      "C_src"
    ],
    "prediction": "111 Gyr to recollapse; R_eq/R_bounce = 1.00016 (extended)",
    "observation": "N/A (future / structural lifecycle prediction)",
    "residual": "N/A",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "Recollapse is derived on the active closed-FRW branch. The bounce attachment is DERIVED/CONDITIONAL_VERIFIED within the extended fermionic/chiral IO-EC theory.",
    "formula": "numeric OS/cycloid recollapse and bounce-attachment computation; displayed values are branch outputs",
    "formula_class": "numeric_pipeline"
  },
  {
    "name": "Growth Background Solver Architecture",
    "channel": "mixed",
    "quantum_input": "Kerr typed solver architecture across source, thermodynamics, perturbations, and transfer",
    "classical_output": "Kerr solver-architecture scope only; no numeric active-background tuple or completed Boltzmann/S8 solver",
    "constants": [
      "H0",
      "Omega_m",
      "Omega_k"
    ],
    "prediction": "Architecture relation is DERIVED/CONDITIONAL_VERIFIED; numerical H0/Omega growth-background closure is not active.",
    "observation": "N/A (structural solver-architecture scope)",
    "residual": "N/A",
    "status": "DERIVED/CONDITIONAL_VERIFIED as Kerr solver architecture only; no numeric active-background tuple or completed Boltzmann/S8 solver",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "Q200 lifts the Paper32 solver architecture into Kerr scope but fences the historical H0/Omega numeric closure and any completed Boltzmann/S8 solver claim."
  },
  {
    "name": "Baryon Loading No-Single-Slot",
    "channel": "mixed",
    "quantum_input": "Typed source/history coupling of κ′ and R in the acoustic hierarchy",
    "classical_output": "No single theorem-grade baryon slot closes the full acoustic hierarchy",
    "constants": [
      "ω_b,geom",
      "ω_b,eff",
      "ω_b,clustering"
    ],
    "prediction": "(κ′, R) is irreducibly mixed; isolated local R uses ω_b,geom only in the reduced drag/inertia slot",
    "observation": "N/A (structural theorem)",
    "residual": "N/A",
    "status": "DERIVED",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "Paper 32 closes the baryon-loading question negatively: the full acoustic hierarchy does not admit a single carried α-rung for R, because κ′ and R form an irreducibly typed pair."
  },
  {
    "name": "Bounce Normalization",
    "channel": "fermionic",
    "quantum_input": "Chiral lowest-shell Hawking/KMS seed plus support-conformal descent on the fermionic bridge carrier",
    "classical_output": "C_src = (3/8)Q^(1/8) = 0.37758, with R_eq/R_bounce = 1.00016",
    "constants": [
      "Q",
      "p_H",
      "C_src"
    ],
    "prediction": "C_src = 0.37758, R_eq/R_bounce = 1.00016",
    "observation": "N/A (extended-theory closure)",
    "residual": "Scoped to the extended fermionic/chiral IO-EC theory",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "Inside the extended fermionic/chiral IO-EC theory, the bounce normalization coefficient is fixed to C_src = (3/8)Q^(1/8), closing the attachment ratio at R_eq/R_bounce = 1.00016.",
    "formula": "C_src = (3/8) Q^(1/8); R_eq/R_bounce from the banked bounce attachment computation",
    "formula_class": "numeric_pipeline"
  },
  {
    "name": "Torsion Onset Profile",
    "channel": "fermionic",
    "quantum_input": "Extended fermionic/chiral bridge source on the deep-bulk support branch",
    "classical_output": "Ξ_EC(R) = (R_eq/R)^3",
    "constants": [
      "R_eq",
      "R_bounce",
      "Q"
    ],
    "prediction": "1% onset at R ≈ 5.18 × 10⁻¹⁵ m; 0.1% onset at R ≈ 1.12 × 10⁻¹⁴ m",
    "observation": "N/A (extended-theory prediction)",
    "residual": "Scoped to the extended fermionic/chiral IO-EC theory",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "The extended fermionic/chiral IO-EC theory predicts the full deep-bulk torsion turn-on law Ξ_EC(R) = (R_eq/R)^3, giving a second quantitative payoff beyond the single bounce attachment radius.",
    "formula": "Xi_EC(R) = (R_eq/R)^3",
    "formula_class": "closed_form_symbolic"
  },
  {
    "name": "Spin-Source Lift",
    "channel": "fermionic",
    "quantum_input": "Boundary puncture/chirality/lowest-shell quotient",
    "classical_output": "P_spin(R) = C_R ∘ U_rad(R) ∘ Π_low ∘ Π_χ ∘ Π_{1/2}",
    "constants": [
      "N_1/2",
      "p_H",
      "Q"
    ],
    "prediction": "Boundary spinor data coarse-grain to a Weyssenhoff-type bulk source with R^(−6) spin-density scaling",
    "observation": "N/A (construction theorem)",
    "residual": "Scoped to the extended fermionic/chiral IO-EC theory",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      32
    ],
    "zenodo": "https://zenodo.org/records/19433686/latest",
    "summary": "The new fermionic bridge sector constructs the spin-source lift P_spin(R), carrying lowest-shell chiral boundary data into the deep-bulk support branch and producing the EC-compatible R^(−6) spin-density scaling.",
    "formula": "P_spin(R) = C_R o U_rad(R) o Pi_low o Pi_chi o Pi_1/2",
    "formula_class": "operator_formula"
  },
  {
    "name": "Three-Language Architecture",
    "channel": "mixed",
    "quantum_input": "Full boundary-to-bulk atlas across the 35-paper archive",
    "classical_output": "The bridge now reads as three languages: static geometric, dynamic thermal, and fermionic density-gated",
    "constants": [
      "γ",
      "γ²",
      "1+γ²",
      "K_gauge",
      "x",
      "Δ"
    ],
    "prediction": "Three-language bridge architecture",
    "observation": "Archive-side organizing result from Papers 1-35",
    "residual": "N/A",
    "status": "THEOREM",
    "papers": [
      33
    ],
    "zenodo": "https://zenodo.org/records/19440227/latest",
    "summary": "Paper 33 reframes the archive stack as three bridge languages, Paper 34 applies that architecture to the late-time H₀ method ladder, and Paper 35 extends the confrontation surface across baryon counting, high-redshift formation time, dark energy, and direct-detection nulls.",
    "formula": "three-language architecture row; no numeric formula",
    "formula_class": "symbolic_theorem"
  },
  {
    "name": "Holographic Selection Rule",
    "channel": "dynamic",
    "quantum_input": "KMS modular structure and typed boundary synchronization",
    "classical_output": "Dynamic bridge exports open only on the boundary-synchronized non-vacuum typed domain",
    "constants": [
      "1+γ²",
      "K_gauge"
    ],
    "prediction": "State-gated dynamic-channel rule",
    "observation": "Explains why BBN is positive while zero-temperature g−2 is outside the live domain",
    "residual": "N/A",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33
    ],
    "zenodo": "https://zenodo.org/records/19440227/latest",
    "summary": "The IO bridge is not universally on. Dynamic exports require typed, boundary-synchronized, non-vacuum contact.",
    "formula": "dynamic bridge export iff boundary-synchronized non-vacuum typed domain condition holds",
    "formula_class": "symbolic_theorem"
  },
  {
    "name": "Bridge Carrier Mechanism",
    "channel": "dynamic",
    "quantum_input": "Bridge statistical covariance in the centered thermal weak correlator",
    "classical_output": "Thermal rates can shift without modifying the local zero-temperature QFT vertex",
    "constants": [
      "1+γ²",
      "K_gauge"
    ],
    "prediction": "Same local vertex, different state/covariance carrier",
    "observation": "Carrier identified for the weak BBN channel; ambient-extension independence remains inside the verified condition package",
    "residual": "N/A",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33
    ],
    "zenodo": "https://zenodo.org/records/19440227/latest",
    "summary": "Paper 33 locates the dressing mechanism in bridge statistical covariance rather than in UV counterterms or a modified local interaction vertex."
  },
  {
    "name": "Dark Matter Geometric Alternative",
    "channel": "static",
    "quantum_input": "Kerr-scoped geometric dark-sector complement with gauge-bundle visible-side narrowing",
    "classical_output": "Dark matter can be interpreted as a geometric dark-sector complement under the current Kerr-scoped, gauge-bundle visibility narrowing; the full complement remains a premise/frontier.",
    "constants": [
      "γ",
      "x"
    ],
    "prediction": "Geometric reinterpretation of the dark sector complement",
    "observation": "Alternative IO reading of the visible/gauge-bundle split",
    "residual": "N/A",
    "status": "OPEN/PREMISE_GAP",
    "papers": [
      33
    ],
    "zenodo": "https://zenodo.org/records/19440227/latest",
    "summary": "Paper 33's geometric dark-sector reading is retained only in Kerr-scoped, non-universal form. The 2026-07-04 visibility narrowing types visible matter as charged U1 bundle-carrying support on Q121/P1/Kerr patches; the full dark complement is not derived."
  },
  {
    "name": "Muon g−2 No-Go",
    "channel": "outside",
    "quantum_input": "N/A — Channel 2 closed for zero-temperature processes",
    "classical_output": "No geometric correction to g−2",
    "constants": [],
    "prediction": "δa_μ = 0 (no IO correction)",
    "observation": "a_μ(exp) = 0.00116592071 (Fermilab 2025)",
    "residual": "Consistent if WP25 confirms no anomaly",
    "status": "DERIVED/NO-GO",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "The bridge is closed for zero-temperature collider measurements. Five mechanisms were tried and all five failed.",
    "formula": "delta a_mu = 0 inside the declared no-go class",
    "formula_class": "closed_form_symbolic"
  },
  {
    "name": "Baryon-to-Photon Ratio (late-time)",
    "channel": "dynamic",
    "quantum_input": "Geometric baryon inventory ω_b,geom together with the observer CMB photon bath T_obs",
    "classical_output": "η = n_b/n_γ = 5.749 × 10⁻¹⁰",
    "constants": [
      "ω_b,geom",
      "T_obs"
    ],
    "prediction": "η = 5.749 × 10⁻¹⁰",
    "observation": "Observer-side CMB baryon loading is usually quoted as η₁₀ ≈ 6.10 in the standard single-temperature map",
    "residual": "Different typed observable; late-time IO value is the observer-side inventory theorem on the active branch",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Paper 35 closes the late-time observer-side baryon-to-photon ratio on the surviving inventory route η = C_η(T_obs, m̄) × ω_b,geom, giving 5.749 × 10⁻¹⁰ with zero fitted parameters.",
    "formula": "eta = n_b/n_gamma",
    "formula_class": "closed_form_symbolic"
  },
  {
    "name": "Baryon-to-Photon Ratio (BBN bulk-frame)",
    "channel": "dynamic",
    "quantum_input": "Geometric baryon inventory ω_b,geom together with the local bulk BBN temperature T_IO",
    "classical_output": "η_BBN = 6.151 × 10⁻¹⁰",
    "constants": [
      "ω_b,geom",
      "T_IO",
      "K_gauge"
    ],
    "prediction": "η_BBN = 6.151 × 10⁻¹⁰",
    "observation": "Standard BBN/CMB concordance η₁₀ ≈ 6.10 assumes one shared observer-side temperature map",
    "residual": "Temperature-architecture dependent; BBN sees T_IO, not T_obs",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Paper 35 closes the BBN temperature assignment gate: local nuclear reaction observables are bulk thermodynamic processes on the T_IO branch, so the microphysical BBN η route gives 6.151 × 10⁻¹⁰.",
    "formula": "eta_BBN = banked bulk-frame baryon-to-photon ratio from the typed BBN temperature assignment",
    "formula_class": "numeric_pipeline"
  },
  {
    "name": "Baryogenesis Topological Obstruction",
    "channel": "fermionic",
    "quantum_input": "Spin-c residual class, chiral boundary datum Q5, and the admitted horizon carrier",
    "classical_output": "Q5 = 0 on the current stack; a supplied typed horizon-U1 charged bridge is now a conditional structure-only entrant",
    "constants": [
      "Q5",
      "spin-c",
      "U1"
    ],
    "prediction": "Current-stack topological obstruction remains; the Q315 charged-bridge slot now has a conditional typed-coupling entrant, not a Q5 closure.",
    "observation": "N/A (structural baryogenesis boundary)",
    "residual": "No baryogenesis magnitude or net Q5 follows from the entrant.",
    "status": "DERIVED / NO-GO",
    "papers": [
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Paper35/Q315 still gives Q5=0 on the current stack. New banked Q315 slot-entry ae2c7235 says that, given a supplied physical horizon line bundle and integral U1 character, the typed coupling enters the charged fermionic bridge sector as conditional structure only; it does not assert line-bundle existence, nonzero Chern degree, Q5 topology, source magnitude, CP phase, eta_B, or baryogenesis closure.",
    "formula": "Q5 = 0 on the current stack; supplied typed horizon-U1 charged bridge is conditional structure-only entrant",
    "formula_class": "topological_no_go"
  },
  {
    "name": "JWST Formation Clock",
    "channel": "static",
    "quantum_input": "Homogeneous OS master clock on the active bare/support branch",
    "classical_output": "About +42.5-43.8% more formation time than Planck ΛCDM over z = 10-20 (comparison-only; old +46-48% wording superseded)",
    "constants": [
      "t_bare(z)",
      "H₀",
      "Ω_m",
      "Ω_k",
      "Ω_Λ"
    ],
    "prediction": "Current Q118/Q241/Q309 retiming records give about +42.5-43.8% formation-time relief relative to Planck ΛCDM over z = 10-20; this is comparison-only, not a load-bearing LCDM input",
    "observation": "JADES-GS-z14-0, JADES-GS-z13-0, GN-z11, and Maisie’s Galaxy all sit in the high-z formation-time pressure regime",
    "residual": "IO materially eases timing pressure; the current clock result is not by itself a theorem-grade ΛCDM knockout",
    "status": "DERIVED",
    "papers": [
      28,
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Paper 28’s homogeneous OS formation-clock theorem survives on the active branch. Current Q118/Q241/Q309 retiming supersedes the old +46-48% wording with about +42.5-43.8% formation-time relief over z = 10-20 versus Planck ΛCDM as comparison-only context, making the JWST high-z population structurally easier to accommodate.",
    "formula": "formation-time relief = (t_IO(z)-t_LCDM(z))/t_LCDM(z) over z=10-20, comparison-only",
    "formula_class": "comparison_numeric_pipeline"
  },
  {
    "name": "Dark Matter Null Prediction",
    "channel": "static",
    "quantum_input": "Kerr-scoped geometric dark-sector interpretation plus typed visible U1 detector sector",
    "classical_output": "Conditional non-gravitational null point: if P_rem is the dark support, typed visible-sector direct/indirect/contact couplings are zero; a robust positive non-gravitational signal falsifies that branch.",
    "constants": [
      "γ",
      "x",
      "f_b"
    ],
    "prediction": "R_direct_NG=0, Phi_annihilation_NG=0, and sigma_contact/m=0 for the P_rem branch; gravitational effects remain allowed.",
    "observation": "LZ, XENONnT, PandaX-4T, Fermi-LAT dwarf, H.E.S.S., and cluster self-interaction searches currently provide null detections or upper limits, so the conditional null point is not excluded.",
    "residual": "Conditional on P_rem and channel dictionary; not a universal no-particle theorem and not an event-rate model.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33,
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "DM finish-up adds the explicit falsifier: any robust non-gravitational dark-sector scattering, annihilation, or contact self-interaction signal breaks the P_rem branch. Current null searches are consistent but not uniquely confirming.",
    "formula": "g_NG(P_rem, visible U1 detector)=0; R_direct_NG=0; Phi_annihilation_NG=0; sigma_contact/m=0",
    "formula_class": "conditional_null_structure"
  },
  {
    "name": "Horizon Charge KMS Dictionary Theorem",
    "channel": "dynamic",
    "quantum_input": "Finite-band interior algebra with admitted horizon-charge flow K_Q = H - sum_i mu_i Q_i",
    "classical_output": "Grand-canonical KMS grammar for each admitted hidden horizon charge",
    "constants": [
      "beta",
      "mu_i",
      "K_Q"
    ],
    "prediction": "Form only: rho = Z^-1 exp[-beta(H - sum_i mu_i Q_i)]; M and J rows are corollaries.",
    "observation": "Structure theorem; no magnitude observation claimed.",
    "residual": "N/A",
    "status": "DERIVED/CONDITIONAL_VERIFIED (finite-band scoped)",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Banked finite-band dictionary theorem; magnitudes remain boundary inputs and readout/congruence remainders remain fenced. IO/EO flagship mass-to-thermal-KMS draft was merged here as a cross-reference, not a separate crossing.",
    "formula": "rho = Z^(-1) exp[-beta(H - sum_i mu_i Q_i)]",
    "formula_class": "closed_form_symbolic"
  },
  {
    "name": "Horizon Charge Census / Helical J Row",
    "channel": "dynamic",
    "quantum_input": "Nonzero-admissibility census over horizon charge flows",
    "classical_output": "Only H and H - Omega_H J are currently banked as admitted rows; J supplies the helical KMS row within current-bank search scope",
    "constants": [
      "Omega_H",
      "J"
    ],
    "prediction": "Helical/detailed-balance twist omega -> omega - m Omega_H as a structural row, not a magnitude measurement.",
    "observation": "Parity-sector qualitative routing only.",
    "residual": "N/A",
    "status": "DERIVED/CONDITIONAL_VERIFIED (current-bank search scope, not a completeness theorem)",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Banked current-bank search report for the charge census and helical J row; no additional charge rows were found in the indexed current-bank search, but this is not a no-hair or completeness theorem. IO/EO flagship angular-momentum-to-helical-KMS draft was merged here as a cross-reference, not a separate crossing."
  },
  {
    "name": "Fermionic KMS Inheritance",
    "channel": "dynamic",
    "quantum_input": "Spin-1/2 anti-periodic KMS sector under the admitted rotating horizon generator",
    "classical_output": "Fermionic helical/chiral-mu5-type statistical grammar, form only",
    "constants": [
      "Omega_H",
      "J",
      "spin structure"
    ],
    "prediction": "Anti-periodic fermionic KMS twin and helicity-sensitive chemical-potential structure where the spin sector is admitted.",
    "observation": "Maps to CVE/Q154 and parity/CP-structure sectors as structure, not magnitude.",
    "residual": "N/A",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Banked fermionic twin of the KMS inheritance program; magnitude and selector-dependent readout pieces remain fenced."
  },
  {
    "name": "Jacobson Loop Revisit Frontier",
    "channel": "dynamic",
    "quantum_input": "Finite-band KMS dictionary plus charge census and fermionic inheritance tested against Jacobson/Clausius import hypotheses",
    "classical_output": "No P1-valid Einstein-equation-of-state closure; loop remains parked",
    "constants": [],
    "prediction": "Negative scoped result: new KMS bank does not replace the missing P1-valid local-horizon/Clausius hypothesis stack.",
    "observation": "N/A",
    "residual": "N/A",
    "status": "REPORT_ONLY_NOT_BANKED / JACOBSON-B",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Report-only negative crossing so the public map can show the parked reverse-theorem lane rather than implying it is absent."
  },
  {
    "name": "Closed Recollapsing Observer Crossed Product",
    "channel": "dynamic",
    "quantum_input": "Finite-band modular algebra plus the bounded IO observer clock in a closed recollapsing interior",
    "classical_output": "Partial bounded-clock crossed-product obstruction/modification; not a full Type III-to-II construction",
    "constants": [
      "observer proper time",
      "finite lifetime clock"
    ],
    "prediction": "The bounded recollapsing clock modifies the CLPW crossed-product route; full density-operator/entropy extension remains unclosed.",
    "observation": "N/A",
    "residual": "N/A",
    "status": "REPORT_ONLY_NOT_BANKED / CROSSED-PRODUCT-PARTIAL",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Report-only first-wave obstruction/partial result; no load-bearing entropy construction claimed."
  },
  {
    "name": "Q315 Charged-Bridge Conditional Slot Entry",
    "channel": "fermionic",
    "quantum_input": "P2+banked-matter-derived physical U1 bundle on charged-matter support patches, restricted to the horizon cross-section and typed into Q245/Q243 finite-band Dirac/CAR detector algebra",
    "classical_output": "Conditional structure-only entrant for Q315 charged fermionic bridge sector; supplied-bundle premise upgraded patchwise by 49fccf8a",
    "constants": [
      "q",
      "U1",
      "Q_1",
      "dGamma(qI_D)",
      "c1(L)"
    ],
    "prediction": "On charged-matter support patches, the matter-carried U1 line bundle and character q identify qI with Q_1=qI_D and implement it by dGamma(qI_D)=qN.",
    "observation": "N/A (structural slot-entry)",
    "residual": "Species fork and Chern degree remain fenced: no nonzero c1(L), no Q5 topology, no source magnitude, no CP phase, no eta_B, and no baryogenesis closure.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Banked Q315 slot entry ae2c7235 is upgraded by matter-carried bundle placement 49fccf8a: the physical horizon U1 line-bundle premise is supplied patchwise by P2+banked charged matter on charged-matter support patches. Fences remain verbatim: no global all-S_H^2 support, no physical species selection beyond cited electromagnetic/visible U1 charged matter, no nonzero c1(L)[S^2], no Q5 topology or net Q5 integer, no H-mu Q horizon-charge row, no parent-to-interior quasifree selector, no CP phase, washout, MVIS, source coefficient, eta_B, baryon abundance, or observed matter sign input."
  },
  {
    "name": "Q315 No-Instantiation Without Typed Coupling Lemma",
    "channel": "fermionic",
    "quantum_input": "Algebra-only CAR U1 grading tested against Q315/Paper35 horizon-geometric charged/twisted carrier target",
    "classical_output": "Unwired CAR grading cannot instantiate the Q315 charged-bridge target",
    "constants": [
      "U1",
      "Q_1"
    ],
    "prediction": "A CAR U1 grading needs a typed map/coupling into the horizon U1 line-bundle carrier before it counts as the Q315 charged/twisted object.",
    "observation": "N/A (formal negative lemma)",
    "residual": "Does not forbid future typed couplings and does not itself accept Q315 slot entry.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Banked negative lemma: instantiation requires satisfying the target's defining properties, so an internal algebra-only CAR U1 grading cannot instantiate the horizon-geometric Q315 charged bridge without typed coupling."
  },
  {
    "name": "Q315 Clause-3 Physical Wiring Derivation",
    "channel": "fermionic",
    "quantum_input": "Q315/Paper35 charged-bridge semantics plus horizon-U1-line-bundle-to-Q245 coupling",
    "classical_output": "Clause 3 requires physical horizon U1 line-bundle/determinant-line/spin-c factor with banked typed coupling",
    "constants": [
      "U1",
      "spin-c",
      "Q_1"
    ],
    "prediction": "A merely internal CAR U1 grading or abstract charge block is insufficient unless it supplies a banked typed map/coupling into the admitted horizon U1 line-bundle carrier.",
    "observation": "N/A (formal predicate/wiring derivation)",
    "residual": "Does not derive existence/nonzero c1(L), Q5 topology, source magnitude, CP phase, eta_B, or baryogenesis closure.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Banked clause-3 derivation: the charged-bridge predicate requires the physical horizon U1 factor plus typed coupling into the finite-band Dirac/CAR charge block.",
    "formula": "entry requires a banked typed coupling from the admitted physical horizon U1 line-bundle carrier into the charge block",
    "formula_class": "predicate_formula"
  },
  {
    "name": "Finite-Band KMS Detector Clausius Relation",
    "channel": "dynamic",
    "quantum_input": "Finite-band P1/Kerr KMS detector state rho_beta = Z^-1 exp[-beta K_Q] with supplied fixed K_Q = H - sum_i mu_i Q_i",
    "classical_output": "Detector-class first law delta S_vN = beta delta<K_Q>",
    "constants": [
      "beta",
      "K_Q",
      "mu_i"
    ],
    "prediction": "For normalized support-preserving trace-class first-order variations at fixed K_Q, delta S_vN = beta delta<K_Q>.",
    "observation": "N/A (finite-band detector thermodynamics theorem)",
    "residual": "Detector thermodynamics only; no geometric heat flux, area entropy, all-null horizon structure, stress-energy focusing dictionary, or Einstein equation.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Banked ledger eb24a238. On the finite-band P1/Kerr detector class, trace-class exp[-beta K_Q] and faithful rho_beta force delta S_vN=beta delta<K_Q> at fixed supplied K_Q. Fences: detector-class first law only; beta and K_Q are supplied boundary/detector inputs; no geometric heat-flux integral, no area entropy, no Einstein equation, no a_star/Omega_H/interior-J measurement. IO/EO detector-thermodynamics-to-focusing pair draft was merged here as a cross-reference to this row and the P1/Kerr null Raychaudhuri row, not as a separate crossing."
  },
  {
    "name": "P1/Kerr Null Raychaudhuri Focusing Identity",
    "channel": "dynamic",
    "quantum_input": "Smooth Q121-compatible P1/Kerr interior patch with supplied twist-free affinely parameterized null congruence k^a",
    "classical_output": "d theta/d lambda = -theta^2/2 - sigma_ab sigma^ab - R_ab k^a k^b",
    "constants": [
      "theta",
      "sigma_ab",
      "R_ab k^a k^b"
    ],
    "prediction": "Geometry-only focusing identity holds on the typed P1/Kerr null-congruence class; per_branch_validity.kerr.value=PROVEN.",
    "observation": "N/A (geometry theorem)",
    "residual": "No Einstein equation, no R_ab to T_ab stress-energy dictionary, no area entropy, no boost/Killing generator, and no detector-heat-to-geometric-flux equality.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Banked ledger eb185a8a. Geometry-only P1/Kerr theorem: on a smooth Q121-compatible Kerr interior patch with a supplied twist-free affine null congruence, the null Raychaudhuri identity follows without assuming Einstein dynamics. Fences: no stress-energy dictionary, no area entropy, no all-null horizon family, no detector heat dictionary.",
    "formula": "d theta/d lambda = -theta^2/2 - sigma_ab sigma^ab - R_ab k^a k^b",
    "formula_class": "closed_form_symbolic"
  },
  {
    "name": "P1/Kerr Local Causal-Horizon Boost Patch Typing",
    "channel": "dynamic",
    "quantum_input": "Smooth C^3 Q121-compatible P1/Kerr interior point p plus supplied future null direction k_p",
    "classical_output": "Local causal-horizon patch H_ell(p,k_p) with approximate boost chi and error O((ell/L_curv)^2)",
    "constants": [
      "ell",
      "L_curv",
      "chi"
    ],
    "prediction": "Every smooth Q121-compatible P1/Kerr patch admits a sufficiently small local causal-horizon patch and approximate boost vector with controlled O((ell/L_curv)^2) error.",
    "observation": "N/A (local geometry typing theorem)",
    "residual": "Local/asymptotic typing only; no global event horizon, no exact Killing vector, no stationarity, no area entropy, no Einstein equation, and no detector heat equals geometric boost flux.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Banked ledger e698a47f. The P1/Kerr nonstationary interior still has local Rindler-type causal patches: H_ell and chi exist locally, exact in tangent Minkowski space and approximate in P1/Kerr with relative error O((ell/L_curv)^2). Fences: local typing only; detector heat/geometric flux remains separate.",
    "formula": "local patch H_ell(p,k_p) admits approximate boost chi with error O((ell/L_curv)^2)",
    "formula_class": "asymptotic_formula"
  },
  {
    "name": "Finite-Band Detector Boost-Generator Representation No-Forcing",
    "channel": "dynamic",
    "quantum_input": "Finite-band KMS detector generator K_Q plus typed local boost patch H_ell, chi",
    "classical_output": "Negative crossing: K_Q is not forced to equal integral_H T_ab chi^a dSigma^b on the current bank",
    "constants": [
      "K_Q",
      "T_ab",
      "chi"
    ],
    "prediction": "Detector heat-to-geometric boost-flux dictionary remains state/representation-selector gated until a local QFT algebra, BW-valid patch state, stress tensor, Noether boost charge, and finite-band projection-compatibility theorem are supplied.",
    "observation": "N/A (negative/no-forcing theorem)",
    "residual": "Named missing object displayed: patch-local QFT representation/state plus stress-tensor boost-charge representation; no Jacobson assembly, no Einstein equation, no area entropy.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Banked ledger 5e9b792a, terminal REPRESENTATION-SAME-WALL. Current finite-band KMS/detector inputs and local boost typing do not force K_Q = integral_H T_ab chi^a dSigma^b. This is a negative GR/QM map row: the flux dictionary is not complete and is state/representation-selector gated, not a magnitude or data issue."
  },
  {
    "name": "Helical KMS Required Parity Rows Confrontation",
    "channel": "fermionic",
    "quantum_input": "Helical KMS parity-channel REQUIRED_STRUCTURE rows from the rotating KMS map",
    "classical_output": "Structure-only scorecard: 10 consistent / 0 tension / 0 untestable",
    "constants": [
      "J-carrier",
      "TB/EB",
      "CVE",
      "parity-cross/span"
    ],
    "prediction": "Typed reads of the J-carrier live in the rotation-odd parity sector and vanish in the non-rotating limit; required rows should not be contradicted at structure/sign/zero-limit level.",
    "observation": "Banked parity-sector context: CMB TB/EB raw spectra/covariance, Q154 CVE dictionary, parity-cross/span formal rows; BOSS 4PCF and Stage-B epsilon_rot are adjacent context only.",
    "residual": "10 consistent, 0 tension, 0 untestable; context-diagnostic only, no amplitude, no K coefficient, no a_star conversion, no scalar beta terminal, no confirmation claim.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Banked ledger 3164af1e. Structure-only diagnostic confrontation of the accepted helical KMS map: all 10 REQUIRED_STRUCTURE parity rows are compatible with current banked parity context. Fences: non-load-bearing; no amplitude or a_star value/bound; no scalar birefringence beta posterior imported; 4PCF and epsilon_rot are PERMITTED_SELECTOR_GATED adjacent context, not REQUIRED_STRUCTURE tests.",
    "formula": "structure-only scorecard: N_consistent=10, N_tension=0, N_untestable=0",
    "formula_class": "scorecard_formula"
  },
  {
    "name": "Matter-Carried U1 Bundle Placement",
    "channel": "fermionic",
    "quantum_input": "Banked charged visible matter fields on smooth Q121-compatible P1/Kerr horizon-adjacent patches",
    "classical_output": "Patchwise physical U1 bundle with connection supplies the Q315 horizon-line-bundle premise on charged-matter support patches",
    "constants": [
      "U1",
      "q",
      "c1(L)"
    ],
    "prediction": "A charged field is a section of an associated U1 bundle with connection; restricting the matter-carried bundle to the local horizon cross-section supplies the physical line-bundle existence premise patchwise.",
    "observation": "N/A (P2/empirical charged-matter placement theorem)",
    "residual": "Patchwise/support-conditioned only; no global all-S_H^2 matter-support cover, no nonzero Chern degree, no Q5 topology, no baryogenesis closure, no P1-only M_vis derivation.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Banked ledger 49fccf8a. Under P1/P2 same-physics placement, banked charged matter supplies a physical U1 bundle with connection on every smooth Q121-compatible P1/Kerr horizon-adjacent patch carrying those fields. Fences verbatim: no global all-S_H^2 support, no nonzero Chern degree, no Q5 topology, no baryogenesis closure, no P1-only Standard Model/M_vis derivation, no species selection beyond cited electromagnetic/visible U1 charged matter.",
    "formula": "charged field psi is a section of an associated U1 bundle with connection; restrict bundle to horizon-support patch",
    "formula_class": "geometric_formula"
  },
  {
    "name": "First-Star Source-History Window",
    "channel": "static",
    "quantum_input": "Layer-6 source-history operator anchored to direct JWST spectroscopic rows and IO-native clock interpolation",
    "classical_output": "Diagnostic first-star/Pop III window in IO time, fork-carried across both age branches",
    "constants": [
      "z",
      "t_IO",
      "x_high",
      "x_low",
      "H2-cooling import"
    ],
    "prediction": "High-age branch envelope 89.51756834141288-162.00334202844834 Myr; low-age branch envelope 73.37675748675375-132.3954551637038 Myr.",
    "observation": "JWST anchor row z=13.35206 is a direct spectroscopic measurement; H2-cooling/Pop III astrophysics remains an external boundary.",
    "residual": "CONTEXT/diagnostic only: no theorem-grade Pop III closure, no fork decision, G_src ratio wall and external H2-cooling import boundary remain fenced.",
    "status": "CONDITIONAL_IMPORT_DIAGNOSTIC",
    "papers": [
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Banked first-star diagnostic window fec9f3f1 with infrastructure fd9734a4 and interpolant lemma 2dc3d1d4. It is IO-native and family-independent for the clock interpolation, but stays non-load-bearing diagnostic/import grade with both age-fork branches carried.",
    "formula": "numeric solution of the Layer-6 source-history operator anchored to JWST z=13.35206, with fork-carried IO clock interpolation",
    "formula_class": "numeric_pipeline"
  },
  {
    "name": "DM Kerr Lift and Bullet Structural Prediction",
    "channel": "static",
    "quantum_input": "Kerr-scoped geometric dark-sector interpretation plus visible charged U1 bundle criterion",
    "classical_output": "Conditional Bullet-class structure: bundle-free support can pass without contact drag while charged gas/plasma can shock",
    "constants": [
      "P_rem",
      "U1",
      "C_Bullet_struct"
    ],
    "prediction": "Within C_Bullet_struct, gas/plasma shock structure and collisionless bundle-free support are qualitatively separated; amplitudes and lensing readout are not closed.",
    "observation": "Bullet Cluster and Abell-520-class systems are comparison context only.",
    "residual": "Partial/context result: no Omega_DM derivation, no halo profile, no lensing-amplitude closure, no rotation-curve closure, no universal no-particle theorem.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "papers": [
      33,
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Banked DM-Kerr partial ledger ca938328. The direct-detection chain survives only as a scoped conditional forecast; the Bullet structural class is accepted as structure-only and amplitude-free, with no site publication authorization in that packet.",
    "formula": "conditional channel statement: P_rem has no contact-drag channel; charged gas/plasma has shock/ram channels",
    "formula_class": "conditional_structure"
  },
  {
    "name": "IO Interaction-Channel Dictionary on P1/Kerr",
    "channel": "dynamic",
    "quantum_input": "Typed coupling prerequisites for matter components on smooth Q121-compatible P1/Kerr patches",
    "classical_output": "Formal channel taxonomy: gravity, U1 plasma/contact, SU2/SU3, radiative, degeneracy, self-interaction",
    "constants": [
      "P_rem",
      "U1",
      "SU2",
      "SU3",
      "T_ab"
    ],
    "prediction": "P_rem has mean-field gravity; dynamical friction requires wake-capable phase-space background; contact/hydrodynamic class is empty absent gauge/plasma prerequisites.",
    "observation": "N/A (interaction-channel taxonomy theorem)",
    "residual": "No collision amplitude, Coulomb log, cluster readout, or global dark-complement proof.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33,
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Banked dictionary 170314ee. Channels are classified by typed prerequisites on P1/Kerr. Key P_rem row: gravitational mean-field present, dynamical friction and gravitational radiation conditional on their own prerequisites, contact/hydrodynamic drag absent on the current stack."
  },
  {
    "name": "Bundle-Free Contact Drag Absence Lemma",
    "channel": "dynamic",
    "quantum_input": "P_rem plus accepted IO interaction-channel dictionary",
    "classical_output": "CONTACT_HYDRODYNAMIC(P_rem)=empty while charged gas/plasma retains U1_PLASMA_PRESSURE_SHOCK_RAM",
    "constants": [
      "P_rem",
      "CONTACT_HYDRODYNAMIC",
      "U1_PLASMA_PRESSURE_SHOCK_RAM"
    ],
    "prediction": "Conditional on P_rem, a bundle-free pressureless gauge-neutral component has no contact/hydrodynamic drag channel; gravitational channels remain under their prerequisites.",
    "observation": "N/A (conditional channel-classification lemma)",
    "residual": "No centroid separation theorem, no amplitude, no readout theorem, no global P_rem proof.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33,
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "Banked lemma cf8b16af. This is the narrow channel result extracted after the collision theorem held: contact/hydrodynamic drag is absent for P_rem by dictionary classification, while charged plasma keeps the ram/shock channel. It intentionally makes no quantitative separation claim."
  },
  {
    "name": "Two-Component Collision Separation Expected Theorem",
    "channel": "dynamic",
    "quantum_input": "P_rem plus channel dictionary/contact-drag lemma with conservative cluster-scale witness propagation",
    "classical_output": "Expected conditional separation regime; not a forced universal dominance theorem",
    "constants": [
      "P_rem",
      "Lambda_G",
      "epsilon_Q",
      "C_D",
      "n_e",
      "v_rel",
      "Sigma_g"
    ],
    "prediction": "Nominal drag-dominance ratio is 1.9064878727330357, but conservative interval propagation gives [0.006088878365538182, 727.1011823823155], so the banked strength is EXPECTED.",
    "observation": "Bullet-like separated systems and Abell-520-class non-separated/complex systems are comparison context only; the banked theorem is compatible with both because the conservative ratio interval straddles 1.",
    "residual": "Expected, not forced: no weak-lensing readout closure and no lower-bound proof above 1. Non-separated mergers falsify only stronger universal-separation wording.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33,
      35
    ],
    "zenodo": "https://zenodo.org/records/19561708/latest",
    "summary": "DM finish-up reaffirms ledger 022ae502: nominal ratio 1.9064878727330357 suggests separation, but the conservative interval [0.006088878365538182, 727.1011823823155] permits non-separated/complex mergers without parameter adjustment. The forcing theorem remains frontier_5efd3998fb2d7643b12a9ae9.",
    "formula": "rho_opp=n_e*1e6*1.90e-27 kg; a_ram=C_D rho_opp v_rel^2/Sigma_g; Lambda_G=2GM_opp/R_enc^3; epsilon_Q=3GM_opp Delta^2/R_enc^4 + eta_Q Lambda_G Delta; ratio=a_ram/(Lambda_G Delta + epsilon_Q)",
    "formula_class": "numeric_pipeline"
  },
  {
    "channel": "quantum_gravity",
    "classical_output": "Public-safe IO/EO Duality framing with theorem rows and open frontiers kept at their own grades",
    "constants": [
      "P1",
      "Kerr",
      "horizon",
      "IO",
      "EO"
    ],
    "formula": "postulate: QM exterior face at a horizon; GR interior face at a horizon",
    "formula_class": "program_postulate",
    "name": "IO/EO Horizon Duality Public Postulate",
    "observation": "Program framing, not a direct empirical observable.",
    "papers": [
      33,
      35
    ],
    "prediction": "Postulate only: QM = exterior face at any horizon; GR = interior face; we sit between horizons.",
    "quantum_input": "Premise-level horizon-relative program statement: exterior face is quantum/statistical, interior face is geometric/GR",
    "residual": "OPEN/PREMISE_GAP premise-level postulate; this row does not promote the postulate to theorem grade.",
    "status": "OPEN/PREMISE_GAP",
    "summary": "Public-facing rename from the historical two_face_* working set. The row is safe only as a program-postulate summary; banked support and open frontiers are separately labeled.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "quantum_gravity",
    "classical_output": "52-row diagnostic dictionary: 28 paired-banked, 6 EO-face-derivable, 12 open, 3 interior-only, 3 primitive-gated",
    "constants": [
      "paired_count",
      "eo_derivable",
      "open_rows",
      "primitive_gates"
    ],
    "formula": "N_total = N_paired + N_derivable + N_open + N_interior_only + N_primitive_gated = 28 + 6 + 12 + 3 + 3 = 52",
    "formula_class": "count_arithmetic_verified",
    "name": "IO/EO Dictionary Census Counts",
    "observation": "Census/search report, not an empirical row.",
    "papers": [
      33,
      35
    ],
    "prediction": "Current census arithmetic: 28 + 6 + 12 + 3 + 3 = 52 total rows; 6 previously unrecognized pairs were found.",
    "quantum_input": "Banked-object to exterior-face census plus canonical-QM to interior-face reverse census",
    "residual": "Diagnostic census only; no construction or promotion is implied by the counts.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "summary": "The expanded dictionary gives the current public map scale for IO/EO Duality while preserving open rows and primitive gates.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "quantum_gravity",
    "classical_output": "Public taxonomy separating the closed-QM-box program from the current diagnostic spin-box constraints",
    "constants": [
      "closed_box",
      "a_star",
      "Q119",
      "R4",
      "chronometer_box"
    ],
    "formula": "|a*|_68 <= 0.3887407947476271 in the current Kerr chronometer diagnostic box",
    "formula_class": "sourced_diagnostic_interval",
    "name": "Two-Box Taxonomy: Closed QM Box and Observable Spin Box",
    "observation": "No direct a* measurement is claimed; future smaller boxes require named readout objects.",
    "papers": [
      33,
      35
    ],
    "prediction": "Current public-safe spin-box anchor remains diagnostic: |a*| in [0, 0.3887407947476271] at 68 percent under the current Kerr chronometer rebuild.",
    "quantum_input": "Closed-system quantum framing plus observational a* small-box discipline",
    "residual": "Taxonomy only. The closed-box state weights and the spin magnitude remain open or reconstruction-scoped depending on the source row.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "summary": "This row gives David's public two-box distinction without leaking research-only machinery: closed-system QM framing on one side, bounded observable spin constraints on the other.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "quantum_gravity",
    "classical_output": "Two parent walls: state/algebra endpoint wall and observer/readout projector wall",
    "constants": [
      "Q119",
      "bounded_clock",
      "state_algebra_endpoint",
      "observer_projector"
    ],
    "formula": "wall_count = 2; {STATE_ALGEBRA_ENDPOINT_WALL, OBSERVER_READOUT_PROJECTOR_WALL}",
    "formula_class": "classification_count_verified",
    "name": "Consolidated Frontier Two-Wall Map",
    "observation": "N/A: frontier map, not an empirical row.",
    "papers": [
      33,
      35
    ],
    "prediction": "The current bank supports wall_count = 2: the Q119 readout/projector object is distinct from the [0,T] endpoint/self-adjointness object.",
    "quantum_input": "Current-bank frontier classification after checking the [0,T] bounded clock against the Q119 chronometer/H0 projector fork",
    "residual": "No wall is solved or breached; this is a classification theorem for current routes.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "summary": "The all-walls-one attempt failed at the declared weak link. The result is useful because it prevents laundering readout-projector problems into the state/clock wall.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "dynamic",
    "classical_output": "Interior chronology ladder and face-boundary typing; imaginary static-lapse continuation marks exterior chart failure, not interior no-time",
    "constants": [
      "alpha",
      "Delta",
      "Sigma",
      "A",
      "r_plus",
      "tau",
      "t"
    ],
    "formula": "alpha_Kerr = sqrt(Delta*Sigma/A); Delta = r^2 - 2*M*r + a^2; alpha -> 0 at r_+",
    "formula_class": "sourced_formula",
    "name": "IO/EO Time-Dilation Dictionary Pair",
    "observation": "Chronology rows supply interior proper-time/redshift support; this dictionary row is not a direct measurement.",
    "papers": [
      33,
      35
    ],
    "prediction": "Kerr ADM/ZAMO lapse alpha = sqrt(Delta*Sigma/A) tends to 0 at r_plus where Delta=0; Schwarzschild static lapse sqrt(1-r_s/r) becomes imaginary if continued below the horizon.",
    "quantum_input": "Exterior Kerr/Schwarzschild lapse boundary behavior",
    "residual": "Dictionary/scope row only. It does not choose the Q119 projector or bounded-clock endpoint.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "summary": "David's time-dilation picture is typed as an IO/EO face-boundary dictionary pair, with Kerr correction and the imaginary-flip caveat explicit.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "quantum",
    "classical_output": "Same dock class as IO CP/source-magnitude freedom, but not a solved object",
    "constants": [
      "theta_bar",
      "CP",
      "Q315",
      "h_chi"
    ],
    "formula": "typed-dock condition: CP-odd source parameter + banked P1/Kerr coupling into Q315 charged bridge required",
    "formula_class": "typed_connector",
    "name": "Typed Joint: Strong CP and IO CP-Source Magnitude Frontier",
    "observation": "N/A: typed connector row, not an empirical claim.",
    "papers": [
      33,
      35
    ],
    "prediction": "Strong CP docks as a CP-odd coefficient/phase freedom requiring a typed coupling into the charged Q315 bridge before any sign or magnitude can be inferred.",
    "quantum_input": "QCD theta-bar/strong-CP ambiguity as external CP-odd source vocabulary",
    "residual": "No strong-CP solution, axion import, theta value, eta_B value, or equality between QCD theta and IO helical coefficient.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "summary": "The public row opens the right adjacent-theory vocabulary while preserving the wall: coupling and magnitude remain unbuilt.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "quantum_gravity",
    "classical_output": "Finite-lifetime observer clock [0,T] does not supply the global R-action required by the standard crossed-product route",
    "constants": [
      "tau",
      "[0,T]",
      "R_action",
      "self_adjoint_extension",
      "endpoint"
    ],
    "formula": "tau in [0,T]; standard crossed product needs a global R-action; -i*d/dtau on [0,T] needs endpoint data",
    "formula_class": "typed_connector",
    "name": "Typed Joint: Problem of Time and Bounded Clock",
    "observation": "N/A: frontier typing row.",
    "papers": [
      33,
      35
    ],
    "prediction": "The interval generator -i d/dtau needs endpoint/self-adjoint extension data; replacing geometric time by modular flow relocates the problem to the state/algebra endpoint wall.",
    "quantum_input": "Quantum-gravity problem-of-time literature docked to the closed recollapsing observer clock obstruction",
    "residual": "No Type-III-to-Type-II result for the full observer, no global density operator, and no black-hole-information closure.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "summary": "This is the cleanest public bridge between the physics problem of time and IO's bounded-clock obstruction: same joint class, still open.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "dynamic",
    "classical_output": "IO supplies boundary-conditioned frame/readout typing, not a full inertial-mass law",
    "constants": [
      "Q65",
      "Kerr",
      "observer_frame",
      "readout_projector"
    ],
    "formula": "boundary-conditioned frame/readout typing; no scalar inertia law",
    "formula_class": "typed_connector",
    "name": "Typed Joint: Mach Boundary-Anchored Frame Scope",
    "observation": "N/A: typed connector row.",
    "papers": [
      33,
      35
    ],
    "prediction": "Mach-facing content is scope-only: boundary-conditioned observer/readout frame typing survives; inertial mass and local gravitational degrees are not derived from global matter.",
    "quantum_input": "Mach-principle adjacency typed through the Kerr boundary-anchored observer/readout fork",
    "residual": "No derivation of inertial mass, no claim local inertia is wholly determined by cosmic matter, and no Q411/readout closure.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "summary": "This row states the honest Mach connection: IO can type a boundary-anchored frame scope, but the Mach law itself is not closed.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "dynamic",
    "classical_output": "Same detector-frame strain data imply different source-frame masses under IO and catalog distance ladders",
    "constants": [
      "D_L",
      "z_catalog",
      "z_IO",
      "m_det",
      "m_src",
      "z_cross"
    ],
    "formula": "z_IO(D_L)=(D_L^IO)^(-1)(D_L); m_src^IO=m_det/(1+z_IO); m_src^IO/m_src^catalog=(1+z_catalog)/(1+z_IO)",
    "formula_class": "diagnostic_pipeline",
    "name": "GW Source-Frame Readout Discriminator",
    "observation": "187 public GWTC files verified, 47.285641609 GB; 143 selected events in the diagnostic readout.",
    "papers": [
      33,
      35
    ],
    "prediction": "Sign-flip prediction at z_cross = 1.8322836452921816; current full-posterior diagnostic leans catalog-sharper with IO/catalog sharpness ratio 0.9709090026346482 and bootstrap 5-95 interval [0.9677268692764813, 1.0011198246136062]. Forecast N_needed_3sigma = 2165.",
    "quantum_input": "Q411 distance-redshift readout applied deterministically to public GWTC posterior samples",
    "residual": "Diagnostic/pre-registration lane only. The disclosed adverse lean is underpowered and not a selection-aware hierarchical likelihood.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "summary": "This row carries the same candor as the dossier: the sign-flip discriminator is novel and pre-registerable, but the present public data lean against IO in the simple sharpness statistic and do not decide the issue.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "channel": "dynamic",
    "classical_output": "Gauge-fixed aperture-mass contrast and aperture-centroid readout; additive mass-sheet contribution annihilated",
    "constants": [
      "kappa",
      "U",
      "theta",
      "alpha",
      "M_ap",
      "O_ap",
      "C_ap"
    ],
    "formula": "M_ap[U;n]=int_S2 dOmega U_n(theta) kappa_IO^K(n'); int_0^alpha sin(theta)U_n(theta)dtheta=0; kappa'=lambda*kappa+(1-lambda)",
    "formula_class": "sourced_formula",
    "name": "Closed-S3 Aperture-Mass Gauge-Fixing Theorem",
    "observation": "Enables morphology/centroid comparisons; not an absolute lensing-mass or S8 row.",
    "papers": [
      33,
      35
    ],
    "prediction": "For compensated S2 filters, int_0^alpha sin(theta) U(theta) dtheta = 0, so kappa' = lambda*kappa + (1-lambda) leaves aperture contrast centroids invariant under the additive mass-sheet term.",
    "quantum_input": "P1/Kerr Q411 weak-lensing S2 screen with compensated aperture filters",
    "residual": "Active only for fixed-protocol aperture contrast/centroid comparisons. No total projected mass, lensing amplitude, S8/sigma8, or collision-forcing number.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "summary": "This theorem reopens gauge-fixed weak-lensing morphology without pretending that the absolute mass inversion problem is solved.",
    "zenodo": "https://zenodo.org/records/19561708/latest"
  },
  {
    "name": "Kerr Multipole Tower No-New-K_Q Row Theorem",
    "channel": "dynamic",
    "quantum_input": "Finite-band KMS dictionary row-counting rule plus Kerr uniqueness and Geroch-Hansen multipole tower",
    "classical_output": "The stationary Kerr gravitational multipole tower is functional in M and J and supplies no independent finite-band K_Q row beyond H and H - Omega_H J",
    "constants": [
      "M_U",
      "J",
      "Omega_H",
      "K_Q"
    ],
    "prediction": "No additional horizon-charge KMS chemical-potential row is created by Kerr gravitational multipoles within the stationary axisymmetric vacuum Kerr/no-NUT/no-string class.",
    "observation": "Bridge/dictionary theorem row; not an observational amplitude claim.",
    "residual": "Not a universal no-hair theorem; does not exclude gauge, species, topological, NUT, or exotic typed rows; no numeric spin or amplitude.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Final-six Job B. Within the banked Kerr uniqueness class, the gravitational multipole tower is M,J-functional and therefore adds no independent K_Q row to the finite-band horizon-charge KMS dictionary.",
    "formula": "M_l + i S_l = M*(i*a)^l; admitted finite-band rows remain {H, H - Omega_H J}",
    "formula_class": "DERIVED/CONDITIONAL_VERIFIED; conditional on the banked Kerr uniqueness variant and IO finite-band KMS reduction ledgers"
  },
  {
    "name": "Superradiant Dictionary Extension Obstruction",
    "channel": "dynamic",
    "quantum_input": "Positive horizon-frequency finite-band KMS sector and helical grammar",
    "classical_output": "The superradiant finite-band KMS extension remains blocked by the missing trace-class superradiant state and stationary or adiabatic return map",
    "constants": [
      "Omega_H",
      "K_Q"
    ],
    "prediction": "Current finite-band dictionary covers the positive tilde_omega sector only; superradiant extension requires a new state/return-map object.",
    "observation": "No superradiant observational bound is claimed from this row.",
    "residual": "Missing object: IO_SUPERRADIANT_FINITE_BAND_KMS_STATE_AND_STATIONARY_RETURN_MAP; static S3 diagnostic is empty-band at active compactness.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Final-six Job C negative/frontier row. The superradiant sector is typed but not extended into the dictionary; the obstruction is state/return-map structure, not a data issue.",
    "formula": "tilde_omega = omega - m*Omega_H; superradiant band: tilde_omega < 0",
    "formula_class": "CONTEXT_DIAGNOSTIC_COMPARISON frontier formula; no a_star bound"
  },
  {
    "name": "Box Classifier Zoo",
    "channel": "mixed",
    "quantum_input": "Charge, spin, gravity, and extremality grammar across particle, compact-object, horizon-object, and IO universe-object classes",
    "classical_output": "Diagnostic taxonomy of super-extremal particle/gauge boxes, material degeneracy boxes, black-hole horizon boxes, and the IO universe object",
    "constants": [
      "M",
      "J",
      "Q",
      "a*"
    ],
    "prediction": "Different physical boxes are separated by which support mechanism carries the system: gauge charge, degeneracy/material support, horizon support, or IO closed-horizon support.",
    "observation": "Taxonomy row only; no object classification is inferred from a fitted observation.",
    "residual": "Diagnostic classifier; no new extremality theorem or spin measurement.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Final-six Job D. The row gives the public classifier vocabulary for particle, compact-object, black-hole, and IO universe-object boxes without promoting the taxonomy to a new law.",
    "formula": "chi_ext^2 = (J*c/(G*M^2))^2 + Q^2/(4*pi*epsilon_0*G*M^2)",
    "formula_class": "CONTEXT_DIAGNOSTIC_COMPARISON extremality classifier"
  },
  {
    "name": "Universe Object Comparative EO Datasheet",
    "channel": "dynamic",
    "quantum_input": "EO universe-object formulas from the Kerr datasheet",
    "classical_output": "Descriptive scale comparison for the IO universe object versus illustrative black-hole mass scales",
    "constants": [
      "M_U",
      "r_s",
      "a*",
      "T_H",
      "Omega_H"
    ],
    "prediction": "The IO universe object is a much larger, colder horizon object than illustrative known black-hole mass scales.",
    "observation": "Astrophysical black-hole masses are comparison context only and are not IO construction inputs.",
    "residual": "Descriptive comparison; no external mass scale, a* value, or Page coefficient is consumed as a theorem input.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Final-six Job E. Public-safe EO datasheet comparison: the universe object is displayed as a horizon-object scale with fences on spin and evaporation-history details.",
    "formula": "T_H(a*)=hbar*c^3/(4*pi*G*M*k_B)*sqrt(1-a*^2)/(1+sqrt(1-a*^2)); Omega_H(a*)=a*c^3/[2*G*M*(1+sqrt(1-a*^2))]",
    "formula_class": "CONTEXT_DIAGNOSTIC_COMPARISON; EO datasheet functions with a* displayed as range"
  },
  {
    "name": "Partial w(t) Trajectory Assembly",
    "channel": "mixed",
    "quantum_input": "State-cycle grammar, recombination rows, and supplied equality/thermal machinery",
    "classical_output": "Partial equation-of-state trajectory: radiation, dust, and supplied radiation-plus-matter interpolation, with seam and late-source legs fenced",
    "constants": [
      "z_eq",
      "w"
    ],
    "prediction": "The forced public grammar contains radiation w=1/3, dust w=0, and the supplied radiation-plus-matter interpolation where the equality terminal is available.",
    "observation": "No LCDM-fitted equality value is introduced by this row.",
    "residual": "Seam/reheat, dust-source, equality supply, and late effective-source legs remain fenced.",
    "status": "CONTEXT_DIAGNOSTIC_COMPARISON",
    "papers": [
      33
    ],
    "zenodo": "",
    "summary": "Final-six Job F. Partial w(t) assembly gives the public equation-of-state grammar while preserving the named gaps for seam/reheat and late-source structure.",
    "formula": "w(z)=1/[3*(1+(1+z_eq)/(1+z))] after equality terminal is supplied",
    "formula_class": "CONTEXT_DIAGNOSTIC_COMPARISON; interpolation formula conditional on supplied equality terminal"
  },
  {
    "channel": "quantum_gauge",
    "classical_output": "Conditionally placed structural alpha slot / fine-structure coupling slot at patchwise/support-conditioned finite-band scope: compact-U1 integer charge labels and finite-band local EM charged-KMS grammar exist; the numerical value of alpha is not derived.",
    "constants": [
      "alpha",
      "q",
      "hbar",
      "c",
      "U(1)",
      "Kerr"
    ],
    "formula": "alpha_U1 = q_phys^2/(4*pi*hbar*c) as a supplied-sector coupling form; k_EM(mu_EM)=h_chi-mu_EM Q_EM on the finite-band local CAR block",
    "formula_class": "conditional_structural_slot",
    "name": "Alpha Slot Structural Coupling Row",
    "observation": "No numeric fine-structure value is claimed. Standard Model alpha consumers remain imported lab/SM constants at their own source class; this does not derive 1/137.",
    "papers": [
      35
    ],
    "prediction": "IO conditionally derives why a dimensionless EM coupling slot with integer charges exists when a physical compact-U1 charged sector is supplied on the relevant P1/Kerr support patches.",
    "quantum_input": "Matter-carried U1 bundle placement on charged-matter support patches, compact-U1 integer character labels, Q245/Q243 finite-band charge block, and finite-band local EM charged-KMS grammar.",
    "residual": "OPEN/PREMISE_GAP for alpha magnitude, running, species selection beyond supplied charged matter, nonzero parent/global Kerr-Newman charge, and Q5/topological sectors. Nonzero c1(L)[S^2] is not consumed by this alpha slot.",
    "status": "DERIVED/CONDITIONAL_VERIFIED",
    "summary": "The current bank supports the structural alpha slot, not the number: charged matter on P1/Kerr patches plus compact-U1 character integrality and finite-band EM K_Q grammar explain why a dimensionless EM coupling form exists at local finite-band scope. The value 1/137 remains fenced by the Q49 guard; it does not derive 1/137.",
    "zenodo": "https://zenodo.org/communities/interior-observer/"
  }
]