🇯🇵 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, hidden-depth inheritance, observation-like state selection, boundary history, moving-boundary readout, boundary-core channels, and finite-time response geometry.
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 |
| B13 | Boundary folding and observation-like state selection | papers/B13_boundary_folding_observation |
| B13.1 | Rotated-basis observation and empirical selection kernel | papers/B13_1_rotated_basis_observation |
| B14 | Boundary history and lineage-level trace persistence | papers/B14_boundary_history |
| B15 | Operator representation of observation traces and history | papers/B15_operator_representation |
| B16 | Memory-bearing moving free boundaries | papers/B16_memory_bearing_free_boundaries |
| B17 | Stored history versus locally readable history | papers/B17_readable_history |
| B18 | Boundary-dependent readout and interface-core path exposure | papers/B18_boundary_readout_operators |
| B19 | Direction-dependent boundary-core channel diagnostics | papers/B19_boundary_core_channels |
| B20 | Operator-generated finite-window response boundaries | papers/B20_response_boundaries |
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 later B-series shifts from state selection and history to moving-boundary readout and finite-window response geometry. The figures below are representative diagnostics; the Zenodo records remain the canonical source for complete results and reproducibility material.
Main idea: Boundary-mediated coupling can bias hidden-depth basin selection in the reduced B13 model. Born-like curves are used only as empirical references; B13 does not derive quantum measurement or the Born rule.
Main entry: papers/B13_boundary_folding_observation
Main idea: History becomes an explicit state variable that can be written, relaxed, partitioned, propagated, and represented through reduced state-update operators.
Main idea: Retaining a history field is not sufficient for later response. B17 separates stored from locally readable history, and B18 extends this to boundary-dependent, path-integrated interface/core exposure.
stored history
-> locally readable history
-> path / interface-core exposure
-> later response
Main idea: B19 finds direction-dependent boundary-core channel organization in finite synthetic divergence-free vorticity families. B20 then defines a finite-window response function
$ F_T(P)=Z[U_T(P)]-Z[P] $
and studies its zero set
B20.6 prospectively scanned frozen parameter-space trajectories. In the archived scan, one trajectory (d03) produced a sign-changing bracket over
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
-> observation-like boundary folding
-> boundary history and operator representation
-> memory-bearing moving boundaries
-> boundary-dependent readout
-> boundary-core channel families
-> operator-generated finite-time response boundaries
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.
- BIG-B13--B15 do not derive quantum mechanics, the Born rule, consciousness, or biological heredity.
- BIG-B16--B18 are reduced history/readout models, not calibrated models of biological, neural, chemical, or material memory.
- BIG-B19--B20 use finite synthetic vorticity families and finite observation windows; they do not prove Navier--Stokes blow-up or regularity.
- 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 entries include:
| Series | Theme | DOI / record |
|---|---|---|
| B7 | Free-boundary exponent across 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 | Finite-noise sustained capture | https://doi.org/10.5281/zenodo.20819427 |
| B11 | Post-capture hidden-depth inheritance | https://doi.org/10.5281/zenodo.20828439 |
| B12 | Unified boundary dynamics | https://doi.org/10.5281/zenodo.20872005 |
| B13 | Boundary folding as observation / self-measurement | https://doi.org/10.5281/zenodo.21072783 |
| B13.1 | Rotated-basis observation and empirical selection kernel | https://doi.org/10.5281/zenodo.21108338 |
| B14 | Boundary history and lineage-level persistence | https://doi.org/10.5281/zenodo.21144373 |
| B15 | Observation traces and boundary history | https://doi.org/10.5281/zenodo.21173333 |
| Layered framework | Layered mathematical consolidation through B15 | https://zenodo.org/records/22161614 |
| B16 | Memory-bearing free boundaries | https://zenodo.org/records/22660005 |
| B17 | Stored versus readable history | https://zenodo.org/records/22677581 |
| B18 | Boundary readout operators | https://zenodo.org/records/22690970 |
| B19 | Boundary-core channel diagnostics | https://zenodo.org/records/22726848 |
| B19 follow-up | Finite-time response-boundary diagnostics | https://zenodo.org/records/22769513 |
| B20 | Operator-generated finite-window response boundaries | https://zenodo.org/records/22846729 |
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/
│ ├── B13_boundary_folding_observation/
│ ├── B13_1_rotated_basis_observation/
│ ├── B14_boundary_history/
│ ├── B15_operator_representation/
│ ├── B16_memory_bearing_free_boundaries/
│ ├── B17_readable_history/
│ ├── B18_boundary_readout_operators/
│ ├── B19_boundary_core_channels/
│ └── B20_response_boundaries/
├── figures/
│ ├── B9/
│ ├── B10/
│ ├── B11/
│ ├── B12/
│ ├── B13/
│ ├── B14/
│ ├── B15/
│ ├── B16/
│ ├── B17/
│ ├── B18/
│ └── B19/
├── 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