The Geometry of Differentiation Boundaries under a Global Zero Constraint: Spectral Invariants and the Emergence of Spacetime and Matter
Bibliographic record
Abstract
This study proposes that the universe is not a collection of independent entities, but a product of relational differentiation arising under a Global Zero Constraint ($\sum U_i = 0$). Instead of addressing the intractable dynamics of the differentiation process, we focus on the geometric structure of the Stabilized Boundary where differentiation has saturated. By modeling this boundary as a weighted graph and applying Spectral Geometry, we demonstrate that: The macroscopic spacetime dimension converges to $d_s \approx 4$ at the critical point of heat diffusion and recurrence. Matter and gravity are naturally derived from the eigenmodes of the Laplacian and the Spectral Action principle. Fundamental constants such as the Planck length, the cosmological constant, and the speed of light are reinterpreted as geometric cut-offs of the graph structure. The central contribution of this work is to show that spacetime, matter, and gravity are not separate entities but can be consistently re-located as spectral invariants of a differentiation boundary stabilized under a global constraint. This paper addresses only the Observer-free sector, providing a new interpretive framework for how existing physical theories can be reconstructed upon a background-independent discrete structure.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".