{
  "artifact_id": "qft.artifact.holography-quantum-gravity.wormholes-gravitational-path-integrals-and-ensembles.double-trace-traversability-window",
  "owner_page_id": "qft.topic.holography-quantum-gravity.traversable-wormholes-couplings-and-energy-conditions",
  "title": "Double-trace traversability protocol and control window",
  "kind": "causal-and-control-window-map",
  "schematic": true,
  "not_to_scale": true,
  "reader_question": "How does an explicit double-trace interaction create a temporary causal route, and which sign, ordering, and backreaction failures close the derived window?",
  "takeaway": "Traversability requires an explicit causal interaction, negative complete horizon-averaged null energy, and a net opening larger than the message width; entanglement alone is insufficient.",
  "scope": {
    "protocol": "transient Gao-Jafferis-Wall and Maldacena-Stanford-Yang type two-boundary traversability protocol",
    "state": "thermofield-double state of two identical large-N theories before the pulse",
    "geometry": "controlled semiclassical two-sided AdS black-hole regime",
    "suppressed_directions": "all angular or transverse directions",
    "quantitative_status": "qualitative causal incidence and exact control logic; no line length, area, shift magnitude, or capacity is plotted quantitatively"
  },
  "conventions": {
    "metric_signature": "+---",
    "boundary_times": "t_L and t_R both increase toward the physical future",
    "coupling_time": "t_L = t_R = t_0 in future-directed physical clocks",
    "source_killing_time_translation": "GJW O_R(t) O_L(-t) is the same equal-physical-time coupling because the stationary Killing coordinate reverses orientation in the left exterior",
    "horizon": "V = 0 with U affine on the undeformed generator",
    "horizon_average": "E_U = integral dU <T_UU>_ren",
    "opening": "alpha_open is a positive opening magnitude rather than the sign of a coordinate displacement",
    "common_normalization": "alpha_open, alpha_sig, sigma_V, and alpha_net use one fixed Kruskal normalization",
    "net_shift": "alpha_net = alpha_open - alpha_sig is same-normalization effective bookkeeping for nonlinear or eikonal message backreaction, not a subtraction of two T_UU horizon integrals"
  },
  "causal_panel": {
    "boundaries": [
      "timelike left boundary partial M_L",
      "timelike right boundary partial M_R"
    ],
    "time_directions": "both physical boundary-time arrows point toward the future",
    "interaction": "two boundary events at t_0 are joined outside the bulk diagram by a dashed bidirectional link labeled explicit L-R interaction U_g; the link is not a bulk path",
    "input": "psi_in is inserted on the left at t_in < t_0",
    "negative_energy_support": "a directly labeled patterned segment on V = 0 represents E_U < 0",
    "uncoupled_control": "the dotted future-directed trajectory ends at the future singularity",
    "transmitted_route": "the solid shifted trajectory reaches the right boundary at t_out > t_0",
    "direction_symmetry": "the displayed left-to-right protocol has a right-to-left counterpart after exchanging the two identical sides"
  },
  "required_chain": [
    {
      "order": 1,
      "stage": "early insertion",
      "condition": "t_in < t_0"
    },
    {
      "order": 2,
      "stage": "brief supported coupling",
      "condition": "correct coupling sign, boundary clocks, and retarded support"
    },
    {
      "order": 3,
      "stage": "negative complete horizon average",
      "condition": "E_U < 0 in the declared model"
    },
    {
      "order": 4,
      "stage": "positive opening magnitude",
      "condition": "alpha_open > 0"
    },
    {
      "order": 5,
      "stage": "same-normalization packet test",
      "condition": "alpha_net > sigma_V"
    },
    {
      "order": 6,
      "stage": "opposite-boundary output",
      "condition": "t_out > t_0"
    }
  ],
  "failed_controls": [
    {
      "id": "reversed-sign",
      "intervention": "replace g by -g at leading order",
      "effect": "the time advance reverses to a delay",
      "outcome": "no derived opening"
    },
    {
      "id": "wrong-ordering",
      "intervention": "move the message or pulse outside the required retarded ordering",
      "effect": "the message does not sample the exponentially enhanced scattering configuration",
      "outcome": "the message misses the derived window"
    },
    {
      "id": "excessive-backreaction",
      "intervention": "increase the positive-energy message shock",
      "effect": "alpha_sig becomes comparable to alpha_open or perturbation theory fails",
      "outcome": "the derived window closes or the retained approximation becomes inconclusive"
    }
  ],
  "claim_ceiling": {
    "causality": "the explicit boundary interaction is a causal communication resource; the figure does not depict signaling by entanglement alone",
    "energy": "the patterned segment represents a complete renormalized horizon average in the stated model, not a universal local negative-energy criterion",
    "backreaction": "loss of perturbative control is not proof that the exact physical wormhole closes",
    "geometry": "the artifact does not establish an autonomous, permanent, macroscopic, or asymptotically flat wormhole",
    "capacity": "the artifact is not a universal quantitative capacity curve"
  },
  "visual_encoding": {
    "solid_arrowed_curve": "shifted transmitted bulk route",
    "dotted_arrowed_curve": "uncoupled route ending at the future singularity",
    "dashed_bidirectional_external_link": "explicit interboundary coupling, not a bulk path",
    "thick_patterned_horizon_segment": "negative complete horizon-averaged null energy",
    "solid_flow_arrows": "required protocol chain",
    "dashed_stop-bar_lines": "independent failed controls",
    "pale_regions": "directly labeled causal regions; fill carries no independent meaning"
  },
  "caption": "Schematic pulsed double-trace protocol in one declared Kruskal normalization. A brief explicit left-right interaction makes the complete renormalized horizon average negative and produces an opening shift. An early probe reaches the opposite boundary only when the causal ordering is correct and its positive-energy backreaction leaves a net shift larger than the packet width. Reversing the sign or missing the retarded support closes the derived window; excessive backreaction either closes it or invalidates the perturbative calculation. The coupling is itself a communication resource; this is neither an autonomous wormhole nor a quantitative macroscopic geometry. Not to scale.",
  "alt_text": "A two-sided black-hole causal diagram shows an early probe entering from the left, simultaneous boundary coupling events joined by a separately labeled left-right interaction, a patterned negative-energy horizon segment, and a shifted solid trajectory reaching the right boundary while the dotted uncoupled trajectory ends at the singularity. A companion flow shows correct sign, timing, and small backreaction leading to output, with failure branches for reversed sign, missed timing, and excessive message energy."
}