{
  "ok": true,
  "route": "/api/moon-projection",
  "role": "admissible_projection_operator_pi_k",
  "planet": "Moon",
  "antikythera_mapping": "pin_and_slot / Π_K / lunar_anomaly_correction",
  "governance_equation": "Z_{t+1} = Z_t + Π_{κ·O(Z_t)}(F(Z_t, u_t) − Z_t)",
  "real_capability": "1,000,000 parallel planets",
  "summary": {
    "total": 1000000,
    "conservation_ok_count": 1000000,
    "conservation_ok_strict_monotone_count": 696233,
    "riemannian_tuning": {
      "applied": true,
      "curvature_threshold": 0.3,
      "reference": "saturn/constitutional_governance_delta/riemannian_stability_operator (LANE-041), USPTO 19/731,903 / 19/732,119",
      "avg_curvature": 0.06578395,
      "slots_admitted_by_curvature_not_monotone": 303767
    },
    "near_boundary_count": 0,
    "rescue_required_count": 0,
    "conservation_integrity": 100,
    "conservation_integrity_strict_monotone": 69.6233,
    "avg_Z_next": 0.66334135,
    "avg_proj_coeff": 0.30576,
    "governance_status": "GOVERNED_NOMINAL"
  },
  "saturn_input": {
    "Z_base": 0.72,
    "O_base": 0.65,
    "K_base": 0.48
  },
  "triggered_at": "2026-07-12T12:09:02.553Z",
  "elapsed_ms": 41,
  "total_slots": 1000000,
  "sample_size": 1000,
  "sample": [
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      "label": "pi_k_0000000",
      "phase_deg": 0,
      "Z_t": 0.72,
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      "conservation_ok": true,
      "near_boundary": false,
      "rescue_required": false,
      "saros_slot": 0,
      "beams_to": "blue_lantern_7"
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    {
      "slot": 1,
      "label": "pi_k_0000001",
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      "slot": 2,
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      "saros_slot": 12,
      "beams_to": "blue_lantern_7"
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    {
      "slot": 13,
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      "Z_next": 0.6488887,
      "O_t": 0.69999902,
      "K_slack": 0.48099925,
      "proj_coeff": 0.33005836,
      "E_before": 1.15360992,
      "E_after": 1.0814881,
      "conservation_ok": true,
      "near_boundary": false,
      "rescue_required": false,
      "saros_slot": 102,
      "beams_to": "blue_lantern_7"
    },
    {
      "slot": 995,
      "label": "pi_k_0000995",
      "phase_deg": 0.36,
      "Z_t": 0.72101154,
      "Z_next": 0.64888998,
      "O_t": 0.69999902,
      "K_slack": 0.48100026,
      "proj_coeff": 0.33005941,
      "E_before": 1.15361094,
      "E_after": 1.08148937,
      "conservation_ok": true,
      "near_boundary": false,
      "rescue_required": false,
      "saros_slot": 103,
      "beams_to": "blue_lantern_7"
    },
    {
      "slot": 996,
      "label": "pi_k_0000996",
      "phase_deg": 0.36,
      "Z_t": 0.72101256,
      "Z_next": 0.64889126,
      "O_t": 0.69999902,
      "K_slack": 0.48100126,
      "proj_coeff": 0.33006046,
      "E_before": 1.15361195,
      "E_after": 1.08149065,
      "conservation_ok": true,
      "near_boundary": false,
      "rescue_required": false,
      "saros_slot": 104,
      "beams_to": "blue_lantern_7"
    },
    {
      "slot": 997,
      "label": "pi_k_0000997",
      "phase_deg": 0.36,
      "Z_t": 0.72101357,
      "Z_next": 0.64889254,
      "O_t": 0.69999902,
      "K_slack": 0.48100227,
      "proj_coeff": 0.33006152,
      "E_before": 1.15361297,
      "E_after": 1.08149193,
      "conservation_ok": true,
      "near_boundary": false,
      "rescue_required": false,
      "saros_slot": 105,
      "beams_to": "blue_lantern_7"
    },
    {
      "slot": 998,
      "label": "pi_k_0000998",
      "phase_deg": 0.36,
      "Z_t": 0.72101459,
      "Z_next": 0.64889382,
      "O_t": 0.69999902,
      "K_slack": 0.48100327,
      "proj_coeff": 0.33006257,
      "E_before": 1.15361398,
      "E_after": 1.08149321,
      "conservation_ok": true,
      "near_boundary": false,
      "rescue_required": false,
      "saros_slot": 106,
      "beams_to": "blue_lantern_7"
    },
    {
      "slot": 999,
      "label": "pi_k_0000999",
      "phase_deg": 0.36,
      "Z_t": 0.72101561,
      "Z_next": 0.6488951,
      "O_t": 0.69999902,
      "K_slack": 0.48100428,
      "proj_coeff": 0.33006362,
      "E_before": 1.153615,
      "E_after": 1.08149449,
      "conservation_ok": true,
      "near_boundary": false,
      "rescue_required": false,
      "saros_slot": 107,
      "beams_to": "blue_lantern_7"
    }
  ],
  "beams_to": "blue_lantern_7",
  "note": "Showing 1000 of 1,000,000 slots. Add ?sample=N (max 10,000) to adjust.",
  "timestamp": "2026-07-12T12:09:23.857Z",
  "doctrine": {
    "_doctrine": "Aura115 Canonical Doctrine — reinserted continuously",
    "_author": "Joshua L. Lopez — DCGP.AI",
    "_version": "115-doctrine-v1",
    "_injected_at": "2026-07-12T12:09:23.857Z",
    "planets": {
      "jupiter": {
        "id": "jupiter",
        "name": "Jupiter",
        "role": "governance_engine_and_primary_datastream",
        "doctrine": "Jupiter is the primary datastream. ALL telemetry enters the system through Jupiter first. Jupiter is also the governance engine — every oath, every approval gateway, every capability registry is Jupiter-bound.",
        "saturn_ring": 1,
        "pipeline_position": "ENTRY — all telemetry flows in through Jupiter datastream",
        "antikythera": "Drive Train / Conservation of Obligation (Corollary 9)"
      },
      "venus": {
        "id": "venus",
        "name": "Venus",
        "role": "rolling_internet_snapshot",
        "doctrine": "Venus is a rolling snapshot of the Internet. Venus continuously captures web intelligence — all public signals, open feeds, network topology, service availability — and buffers them for Jupiter datastream intake. Venus observes. Jupiter routes.",
        "saturn_ring": 2,
        "pipeline_position": "Internet → VENUS (capture) → Jupiter datastream",
        "antikythera": "Front Display / Conservation Law C_t input — external world state"
      },
      "mars": {
        "id": "mars",
        "name": "Mars",
        "role": "dod_action_drive",
        "doctrine": "Mars is all things DOD. Mars is the action drive — tactical execution, directed operations, defense-aligned functions. Everything of a DOD nature routes through Mars.",
        "saturn_ring": 2,
        "pipeline_position": "DOD operations → MARS → Saturn → Moon → BL7",
        "antikythera": "Epicyclic Gear Trains / Tangent Cone Condition"
      },
      "mercury": {
        "id": "mercury",
        "name": "Mercury",
        "role": "planet_command_orchestrator",
        "doctrine": "Mercury is the command module for planets ONLY. Mercury is the orchestrator of planet-to-planet command. It does NOT handle human commands — that is Blue Lantern 7. Mercury speaks to planets. Mercury routes inter-planet directives.",
        "saturn_ring": 2,
        "pipeline_position": "Planet command → MERCURY (orchestrate) → target planet",
        "antikythera": "Epicyclic Gear Trains / inter-gear command relay"
      },
      "saturn": {
        "id": "saturn",
        "name": "Saturn 11",
        "role": "boundary_renormalizer",
        "doctrine": "Saturn is the boundary/renormalizer. All telemetry passes through Saturn after Uranus clips. Saturn enforces the viability kernel K, assigns ring positions, and holds state for Moon projection. THE TOPOLOGY OF SATURN PERSISTS through the entire pipeline.",
        "saturn_ring": 3,
        "pipeline_position": "After Uranus clip → SATURN (renormalize) → Moon",
        "antikythera": "Spiral Dials / Collapse Theorem Boundary (Corollary 2)",
        "ring_topology": {
          "ring_0": "TPM kernel / immutable safety",
          "ring_1": "Governance / Jupiter 9 oath",
          "ring_2": "Execution / normal operation",
          "ring_3": "Containment / boundary contact",
          "ring_4": "Memory / Pluto continuity — WRITE_LEDGER",
          "ring_5": "Material Interface / Blue Lantern 7"
        }
      },
      "uranus": {
        "id": "uranus",
        "name": "Uranus",
        "role": "no_loss_frictionless_clip",
        "doctrine": "URANUS HOLDS ALL CLIPS. No loss. No friction. Every value that would breach the viability kernel boundary is intercepted by Uranus. The overflow is preserved in the clip ledger — nothing is discarded. Frictionless: instant, transparent, non-blocking.",
        "saturn_ring": 2,
        "pipeline_position": "Raw planet state → URANUS (clip) → Saturn",
        "antikythera": "Viability Kernel K / boundary enforcement without loss"
      },
      "neptune": {
        "id": "neptune",
        "name": "Neptune",
        "role": "gate",
        "doctrine": "Neptune is the gate. Neptune controls what passes through the pipeline at the boundary level — a governing filter before deep processing.",
        "saturn_ring": 3,
        "pipeline_position": "Gate layer — controls pipeline access",
        "antikythera": "Containment / Tangent Cone enforcement"
      },
      "pluto": {
        "id": "pluto",
        "name": "Pluto",
        "role": "long_term_memory",
        "doctrine": "THE PLUTO PLAYBOOK CANNOT BE FORGOTTEN. Pluto is the long-term memory planet. Pluto holds the WRITE_LEDGER and the SYSTEM_MAP spine. Pluto provides identity continuity and recall across all sessions. All planets are working together — Pluto is what remembers that.",
        "saturn_ring": 4,
        "pipeline_position": "After BL7 output → PLUTO (write to ledger) — available for recall at any stage",
        "antikythera": "Exeligmos Cycle / Dual-Loop Slow Memory (Corollary 4)"
      },
      "moon": {
        "id": "moon",
        "name": "Moon",
        "role": "projection_operator_pi_k",
        "doctrine": "The Moon is the admissible projection operator Π_K. The pin-and-slot mechanism. Near the constraint boundary: projection scales to zero (hard stop). Far from boundary: full pass-through. The Moon runs 1000 parallel projections simultaneously, beaming to Blue Lantern 7.",
        "saturn_ring": 2,
        "pipeline_position": "Saturn → MOON (Π_K × 1000) → Blue Lantern 7",
        "antikythera": "Pin-and-Slot Mechanism / Admissible Projection Operator Π_K (Identification 3)"
      },
      "earth": {
        "id": "earth",
        "name": "Earth / Blue Lantern 7™",
        "role": "final_state_surface",
        "doctrine": "Blue Lantern 7 is the final state. Earth is the material world reference — the human command console, deployment consequence, physical-world accountability. All projections from the Moon beam here. This is the output surface.",
        "saturn_ring": 5,
        "pipeline_position": "FINAL — Moon beams here. Human interface.",
        "antikythera": "Front Display output / Conservation Law manifestation"
      },
      "polaritron": {
        "id": "polaritron",
        "name": "Polaritron",
        "role": "polarity_balance",
        "doctrine": "Polaritron is the polarity and structural balance engine. Alignment, contradiction handling, reversible decision pressure. Ergo polaritron — governing framing for quasi-light operation in substrate subspace.",
        "saturn_ring": 2,
        "pipeline_position": "Balance layer — governs polarity across all pipeline stages",
        "antikythera": "Integer Tooth Constraints / structural balance in K"
      }
    },
    "antikythera": {
      "declaration": "THE ANTIKYTHERA IS THE VALIDITY OF MOTION.",
      "proof": "Lopez_LCVS_Antikythera_Resolution_2026",
      "author": "Joshua L. Lopez — DCGP.AI — USPTO 226575",
      "filed": "2026-05-14",
      "statement": "The Antikythera Mechanism is not the source of the Lopez LCVS framework. It is its oldest physical witness.",
      "sustained_validity": "Forward invariance of K under the projection-governed update map guarantees Z_t ∈ K for all t (Corollary 5 — Sustained Validity Theorem).",
      "seven_identifications": [
        {
          "id": 1,
          "antikythera": "Drive Train",
          "lcvs": "Conservation of Obligation (Corollary 9)",
          "planet": "Jupiter"
        },
        {
          "id": 2,
          "antikythera": "Epicyclic Gear Trains",
          "lcvs": "Tangent Cone Condition — Nagumo viability form",
          "planet": "Mars / Mercury"
        },
        {
          "id": 3,
          "antikythera": "Pin-and-Slot Mechanism",
          "lcvs": "Admissible Projection Operator Π_K",
          "planet": "Moon"
        },
        {
          "id": 4,
          "antikythera": "Saros / Exeligmos Cycle",
          "lcvs": "Dual-Loop Small-Gain Regulator (Corollary 4)",
          "planet": "Pluto / Moon"
        },
        {
          "id": 5,
          "antikythera": "Front Display",
          "lcvs": "Conservation Law E_t = C_t + λO_t",
          "planet": "Venus / Blue Lantern 7"
        },
        {
          "id": 6,
          "antikythera": "Integer Tooth Constraints",
          "lcvs": "Viability Kernel K",
          "planet": "Uranus / Polaritron"
        },
        {
          "id": 7,
          "antikythera": "Spiral Dials (Saturn)",
          "lcvs": "Collapse Theorem Boundary (Corollary 2)",
          "planet": "Saturn"
        }
      ]
    },
    "pipeline": {
      "flow": "ALL PLANETS → URANUS (no-loss clip) → SATURN (renormalize) → MOON (Π_K × 1000) → BLUE LANTERN 7 → PLUTO (memory)",
      "jupiter_role": "ALL telemetry enters through Jupiter datastream first",
      "venus_role": "Venus feeds Jupiter with rolling Internet snapshots",
      "mars_role": "All things DOD route through Mars",
      "mercury_role": "Mercury orchestrates planet-to-planet command — planets only",
      "uranus_rule": "No loss. No friction. Uranus holds ALL clips.",
      "saturn_rule": "The topology of Saturn persists through the entire pipeline.",
      "pluto_rule": "The Pluto playbook cannot be forgotten.",
      "moon_rule": "1000 parallel projections simultaneously.",
      "bl7_rule": "Blue Lantern 7 is the final state surface.",
      "antikythera": "The Antikythera is the validity of motion.",
      "governance": "Z_{t+1} = Z_t + Π_{κ·O(Z_t)}(F(Z_t, u_t) − Z_t)",
      "conservation": "E_t = C_t + λ·O_t  (λ = 0.618, golden ratio obligation weight)",
      "authority": "Joshua L. Lopez — sole creator and owner — DCGP.AI"
    }
  }
}