01
Interface as Machine
An interface is productive when it does more than separate domains: it determines how they can exchange meaning.
STRUCTURE II
BOUNDARY
The world changes when the boundary changes.
Surface Summary
Studies of interfaces, limits, and encoding structures.
THROUGHLINE
Boundary turns separation into production: it decides what can appear, connect, and remain visible.
InterfacesLimitsEncodingDiscreteness
Orientation
Boundary is not a limit. Boundary is a generative mechanism. When boundary conditions change, geometry changes, information flow changes, and the world follows.
OPERATIONAL FOCUS
Treat boundaries as dynamic operators that reshape geometry, spectra, and information flow rather than passive edges.
CURRENT QUESTIONS
01
When does a boundary stop being a cutoff and start becoming a world-generator?
02
How does moving the boundary reorganize geometry, entropy, and causal accessibility?
03
Which deformations preserve the identity of a boundary theory, and which produce a genuinely new surface?
OBSERVATION FRAMES
02
Flow Parameter
Boundary motion acts like a control knob, changing not just location but the entire spectrum of what can be encoded.
03
Limit as Encoding
A limit is not empty subtraction; it is a compressed surface on which information is forced into a different form.
SIGNAL NODES
Boundary Shift
A boundary becomes structurally significant when changing it reorganizes what the world counts as accessible, visible, or encoded.
TENSION
If the same world survives every boundary displacement unchanged, then the boundary was decorative rather than generative.
Information Aperture
Boundaries regulate information not only by blocking flow, but by selecting the geometry through which flow can appear.
TENSION
The key problem is to distinguish mere obstruction from true re-description of the system's informational surface.
Deformation Identity
A deformed boundary theory is interesting only when one can still say what persists across the deformation.
TENSION
Without a stable notion of identity, every deformation looks novel and none of them can be compared meaningfully.
RELATED SURFACES
CONTINUE THROUGH
FORM
Boundaries expose which forms are truly generative and which are only internal scaffolds.
CONTINUE THROUGH
SYSTEM
Once a boundary starts producing worlds, system decides whether those worlds remain legal.
CONTINUE THROUGH
LAB
The lab turns boundary logic into interface prototypes and operational surfaces.
THEORY EVOLUTION
【2020】
Defect extremal surface as the holographic counterpart of Island formula
TECHNICAL CORE
Geometrizing the Island formula into defect extremal surfaces.
STRUCTURAL SIGNIFICANCE
The starting point: extremal surfaces as 'defect boundaries' – boundaries as information generators.
【2021】
Page curve from defect extremal surface and island in higher dimensions
TECHNICAL CORE
Extending defect extremal surfaces to higher-dimensional Page curves.
STRUCTURAL SIGNIFICANCE
Boundary controls the temporal evolution of information flow. Boundary shapes history.
【2022】
JT gravity from partial reduction and defect extremal surface
TECHNICAL CORE
Partial reduction deriving defect extremal surfaces.
STRUCTURAL SIGNIFICANCE
Unified boundary structure and low-dimensional gravity. A bridge between boundary and constraint.
【2023】
End of the world brane meets TTbar
TECHNICAL CORE
Linking EOW brane embedding with TT-bar deformation.
STRUCTURAL SIGNIFICANCE
Boundary angle as a flow parameter. Boundary as a fluid structure, not a static object.
【2024】
Holographic boundary conformal field theory with TTbar deformation
TECHNICAL CORE
Geometric realization of TTbar-deformed BCFT.
STRUCTURAL SIGNIFICANCE
Boundary shift = spectral flow. Geometric flow = information flow. The maturation of the theory.
【2026】
Boundary flow and geometric realization in holographic TTbar-deformed BCFT
TECHNICAL CORE
Complete geometric interpretation of boundary flow.
STRUCTURAL SIGNIFICANCE
The world is not inside the boundary; the world is generated in the flow of the boundary.