Shadow Theory / Five complete reading editions
Gravity and holography
Transport reveals a connection. A vacuum gives rise to a local state and a thermal description. Boundary balls can miss a gravitational perturbation at first order and detect it at second order. Each result tells us what a particular readout can establish.
Same balls. Different orders.
What a readout reveals depends on both where you look and which order of response you measure. On one fixed boundary slice, first-order ball data leave a non-gauge kernel. For an explicit transverse AdS perturbation in that kernel, the same balls give positive bulk canonical energy at second order.
The gravitational calculation stands on its own hypotheses. Interpreting it as a boundary relative-entropy Hessian also requires the holographic dictionary and a corresponding admissible state family.
Follow the complete arguments
Read the transport reconstruction first, then follow the modular and local horizon results into the boundary-ball pair. The five papers share the source–readout question. Each derives its result from its own preparation, readout and physical assumptions.
Transport and Projective Reduction in a Source–Readout Derivation of Einstein Gravity
Reconstruct the affine connection from smooth transport, remove the projective ambiguity with a volume-restored observable, and follow the complete off-shell spin-two bootstrap to Einstein–matter dynamics within the admitted realization.
Read the full edition →Modular Transport and Spherical Holographic Entanglement Entropy in a Source–Readout Architecture
One vacuum preparation supplies a restricted diamond state and a thermal state on the hyperbolic cylinder. Modular transport fixes the temperature; the regulated entropy calculation adds the holographic dictionary.
Read the full edition →Local Horizon Thermodynamics and Einstein Gravity in a Source–Readout Architecture
Heat, temperature and area readouts of a shrinking null pencil recover the Einstein equation under the stated thermodynamic and conservation assumptions. A finite generator segment and finite transverse width pose different questions.
Read the full edition →Boundary Ball Readouts and Linearized Einstein Gravity in a Source–Readout Architecture
First-order ball data on a fixed boundary slice recover a projected Einstein constraint. The fixed-frame kernel shows why recovering the full field equation needs more frame data and boundary assumptions, and why that recovery is distinct from reconstructing the metric.
Read the full edition →Second-Order Detection by Boundary Balls in a Source–Readout Architecture
An explicit transverse AdS perturbation has zero first-order area and energy variations on the fixed-slice balls. The same balls register positive bulk canonical energy at second order. A boundary relative-entropy interpretation adds a holographic dictionary and an admissible state family.
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