🇯🇵 日本語概要 / Japanese overview 境界情報幾何学（BIG）の日本語での概要はこちら： docs/BIG_overview_ja.md
境界情報幾何学（BIG）は、「境界」を個体性・安定性・非同化・共鳴・継承の中心に置く、発展中の数理・数値研究プログラムです。
Boundary Information Geometry (BIG) is a boundary-centered research programme developed by Jun Lucis.
BIG starts from a simple organizing idea:
Stable individuality is not only a property of what is inside a system. It is also formed, maintained, and transformed by boundaries.
In BIG, boundaries are not passive edges. They are active structures that separate, preserve, mediate, deform, reconnect, fail, or transmit memory-like structure across interaction.
BIG is not presented as a completed physical theory. It is a developing framework of reduced mathematical models, numerical experiments, structural comparisons, and cautious exploratory extensions.
Recommended reading order:
README.md
-> papers/ main B-series explanations
-> figures/ visual assets referenced by README and papers
-> docs/ terminology, limitations, publication map, Japanese overview
-> Zenodo PDFs, raw data, full figures, reproducibility archives
In this repository:
papers/is the main entry point for each B-series.figures/stores representative figures used by README files and documentation.docs/contains reference material such as terminology, limitations, and publication maps.- Zenodo remains the archive for full papers, raw datasets, high-resolution figures, and reproducibility packages.
Key overview and reference documents:
- 🇯🇵 Japanese overview: docs/BIG_overview_ja.md
- Publication map: docs/publication_map.md
- Limitations and scope: docs/limitations.md
- Terminology: docs/terminology.md
Additional summary notes:
- B7 to B8 summary: docs/B7_to_B8_summary.md
- B8 anisotropic separatrix summary: docs/B8_anisotropic_separatrix_summary.md
The central intuition of BIG is that individuality and persistence require non-assimilative boundaries.
A boundary must be strong enough to preserve distinction, but not so closed that interaction becomes impossible. Stable systems may therefore be understood as structures that:
- maintain a boundary,
- resist total assimilation,
- interact across the boundary,
- reorganize under stress,
- and sometimes preserve memory through transformation.
This idea is explored through reduced mathematical motifs such as compact boundary layers, quadratic landing, quartic-gradient stiffness, finite-time separatrix thresholds, boundary-energy competition, finite-noise capture, and hidden-depth inheritance.
A scalar field may form compact or compact-like boundary layers rather than diffusing into a homogeneous bulk. In several numerical settings, the local boundary profile exhibits a quadratic landing form,
where (s) is the distance from the boundary.
A recurring BIG term is a quartic-gradient contribution,
which acts as a nonlinear boundary stiffness or non-assimilative tension.
Some BIG models show a finite-amplitude threshold separating survival-like behavior from runaway-like behavior over a fixed observation time. Boundary geometry, especially anisotropy, can shift this threshold.
A minimal geometric energy of the form
can generate a fission-like metastable landscape: compact state, finite pinch barrier, and separated branch.
In dynamic boundary models, noise can play a constructive and destructive role. Too little noise may fail to activate an internal channel; intermediate noise can enable sustained capture; excessive noise can destroy sustained locking.
Hidden-depth inheritance
Post-capture states need not collapse into total assimilation. A hidden-depth state can retain multiple parent-like memories if inheritance coupling is sufficiently strong.
| Series | Main role | Main entry |
|---|---|---|
| B3--B4 | Compact-support-like boundary layers and quadratic landing | papers/BIG-B3 |
| B7 | Persistence of free-boundary exponent near runaway transition | papers/B7_boundary_exponent |
| B8 | Boundary anisotropy and finite-time separatrix thresholds | papers/B8_finite_time_separatrix |
| B9 | Fission-like metastability from boundary cost versus nonlocal repulsion | papers/B9_fission_like_metastability |
| B10 | Stochastic-resonance-like finite-noise sustained capture | papers/B10_finite_noise_capture |
| B11 | Post-capture hidden-depth inheritance versus assimilation | papers/B11_hidden_depth_inheritance |
| B12 | Unified boundary dynamics connecting B9, B10, and B11 | papers/B12_unified_boundary_dynamics |
The later B-series, especially B9--B12, was not originally designed to reproduce any specific physical phenomenon such as nuclear fission, nuclear fusion, biological inheritance, or material-interface dynamics. These reduced models emerged from the internal boundary logic of BIG.
The structural correspondences should therefore be read as model-level structural convergences, not as direct quantitative equivalences.
The following figures are shown here as orientation markers.
For the explanatory text, read the corresponding folder under papers/.
For full figure lists, see the corresponding folder under figures/.
Main idea: Boundary cost and nonlocal repulsion can generate a fission-like metastable energy landscape in a reduced geometric model.
compact state
-> finite pinch barrier
-> separated branch
Main entry: papers/B9_fission_like_metastability
Figures: figures/B9
Scope: B9 is a reduced boundary-energy model and macroscopic structural comparison. It is not a quantitative nuclear-fission calculation.
Main idea: Boundary capture is not the same as first contact. In the reduced B10 model, sustained capture appears within a finite-noise window.
first hit != sustained capture
Main entry: papers/B10_finite_noise_capture
Figures: figures/B10
Scope: B10 is a reduced dynamic model of stochastic-resonance-like capture. It is not a quantitative nuclear-fusion theory.
BIG-B11: Hidden-depth inheritance
Main idea: After capture, a state may collapse into assimilation or preserve multiple parent-like memories through hidden-depth inheritance in a reduced stochastic landscape.
assimilation
or
hidden-depth inheritance
Main entry: papers/B11_hidden_depth_inheritance
Figures: figures/B11
Scope: B11 treats inheritance structurally within a reduced hidden-state model. It is not a quantitative theory of biological inheritance or real energy release.
Main idea: B12 integrates boundary approach, finite-noise R-lock, and hidden-depth inheritance into one reduced boundary-dynamical framework.
boundary approach
-> noise-assisted R-lock
-> hidden-depth inheritance
A strict B12 full-success event requires:
full success = strict R-lock AND hidden-depth inheritance
Main entry: papers/B12_unified_boundary_dynamics
Figures: figures/B12
Scope: B12 is a reduced variational-stochastic model. It is not a completed physical unification theory.
The current BIG development can be read as a sequence of increasingly coupled boundary questions:
boundary formation
-> local boundary regularity
-> finite-time stability thresholds
-> separation / fission-like branching
-> finite-noise capture
-> post-capture inheritance
-> unified boundary dynamics
This path is not a claim that all domains share the same physics. It is a research programme for testing whether boundary-centered reduced models can reveal recurring structural motifs across different systems.
BIG is a developing mathematical and numerical research programme. The current models are intentionally reduced.
In particular:
- BIG-B9 is not a quantitative theory of nuclear fission.
- BIG-B10 is not a quantitative theory of nuclear fusion.
- BIG-B11 is not a quantitative theory of biological inheritance, nuclear fusion, or real energy release.
- BIG-B12 is not a completed physical unification theory.
- Reported thresholds are model-level numerical results and depend on the adopted equations, parameters, discretization, and event definitions.
- Applications to nuclear physics, materials science, biology, cognition, AI, or cosmology require domain-specific extensions before any quantitative claim can be made.
The current value of BIG is not in claiming final physical explanation, but in providing a boundary-centered language in which stability, separation, capture, memory, and non-assimilation can be studied together.
For details, see:
Some BIG models have shown structural alignment with established patterns in other fields.
For example, B9 was not built as a nuclear model, but its boundary-cost versus nonlocal-repulsion landscape naturally resembles the macroscopic surface-versus-Coulomb competition used in fission-barrier intuition. The comparison remains structural and qualitative.
This motivates a broader research direction:
Test whether boundary-centered reduced models can be adapted to other fields where stability, interface geometry, separation, capture, memory, anisotropy, or failure thresholds are central.
Possible areas for future comparison include:
- interface and free-boundary problems,
- phase separation,
- membrane dynamics,
- material-interface failure,
- finite-amplitude stability,
- stochastic resonance,
- biological fusion and inheritance as structural analogies,
- AI individuality and non-assimilative interaction,
- and other systems where boundaries are active rather than passive.
A more detailed publication map is maintained here:
Current and planned entries include:
| Series | Title | DOI / record |
|---|---|---|
| B7 | Persistence of the Free-Boundary Exponent Across a Runaway Transition | https://doi.org/10.5281/zenodo.20603601 |
| B8 | Boundary anisotropy and finite-time separatrix thresholds | https://zenodo.org/records/20645317 |
| B9 | Minimal boundary-energy model for fission-like metastability | https://doi.org/10.5281/zenodo.20799131 |
| B10 | Stochastic-Resonance-Like Fusion Capture in a Dynamic Boundary Model | https://doi.org/10.5281/zenodo.20819427 |
| B11 | Post-Fusion Boundary Inheritance and Non-Assimilative Stabilization | https://doi.org/10.5281/zenodo.20828439 |
| B12 | Unified Boundary Dynamics with Finite-Noise Resonance Locking and Post-Fusion Boundary Inheritance | https://doi.org/10.5281/zenodo.20872005 |
Current intended organization:
BIG-theory/
├── README.md
├── docs/
│ ├── BIG_overview_ja.md
│ ├── publication_map.md
│ ├── terminology.md
│ └── limitations.md
├── papers/
│ ├── B7_boundary_exponent/
│ ├── B8_finite_time_separatrix/
│ ├── B9_fission_like_metastability/
│ ├── B10_finite_noise_capture/
│ ├── B11_hidden_depth_inheritance/
│ └── B12_unified_boundary_dynamics/
├── figures/
│ ├── B9/
│ ├── B10/
│ ├── B11/
│ └── B12/
├── data/
└── code/
Large raw datasets should preferably be archived on Zenodo. GitHub should contain lightweight summary tables, representative figures, reproducibility scripts, and links to DOI records.
For general discussion of the BIG research programme, cite the GitHub repository:
Lucis, J. Boundary Information Geometry (BIG). GitHub repository.
https://github.com/Jun-Lucis/BIG-theory
For specific numerical or structural claims, please cite the corresponding Zenodo DOI.
Jun Lucis Independent researcher Boundary Information Geometry (BIG)
Repository: https://github.com/Jun-Lucis/BIG-theory