Ivan Pasev — Science & Research Profile ​

Independent Theoretical & Mathematical Physics Researcher · Scientific Systems Architect
Sofia, Bulgaria

Ivan Pasev conducts an independent theoretical research program centered on the Science of Fabric Reality (SFR): modeling dynamical systems through relational networks, topological boundaries, invariant transport, multiscale Dirichlet field dynamics, and observer-indexed measurement operators.

Epistemic Grounding

Deductive mathematical definitions, Lean 4 formalization targets, discrete numerical simulations, calibrated retrodictions, and prospective laboratory testbeds are held in mutually non-conflating tiers.

1. Research Thesis & Horizons ​

Foundational Question ​

Can the fundamental dynamics of spacetime geometry, relativistic quantum fields, and gauge interactions be derived strictly from discrete relational distinctions and topological invariant preservation, without presuming an ungrounded continuous manifold background a priori?

Eight Research Horizons ​

text
┌─────────────────────────────────────────────────────────────────────────────┐
│                       CURRENT RESEARCH HORIZON MATRIX                       │
├──────────────────────────────┬──────────────────────────────────────────────┤
│ 1. FOUNDATIONAL PHYSICS      │ Relational state grammar S = (X, R, ∂, I)    │
│ 2. MATHEMATICAL PHYSICS      │ Metric-measure Dirichlet forms & resolvents  │
│ 3. QUANTUM / MULTISCALE      │ FQFT dimensional separation (dH ≠ ds ≠ dw)   │
│ 4. ATOMIC & STRONG-FIELD     │ NIST ASD comparators & Lewenstein SFA cutoffs│
│ 5. VACUUM THERMOPHYSICS      │ Cryogenic directional emissivity metrology   │
│ 6. FORMAL VERIFICATION       │ Lean 4 invariant preservation proof targets  │
│ 7. SCIENTIFIC COMPUTING      │ Graph Laplacian solvers & bounded U_NUM      │
│ 8. METROLOGICAL GOVERNANCE   │ JCGM 100/101 (GUM) & NIST TN 2156 traceability│
└──────────────────────────────┴──────────────────────────────────────────────┘

2. Selected Formal Mathematical Results ​

Every mathematical result is bound to an explicit theorem identifier and portable receipt:

  • Topological Invariant Transport (THM-INV-01): Proof of boundary invariant preservation under automorphism transformations across relational state updates (AUTHORIAL_SPECIALIZATION / PROVEN_IN_CORPUS).
  • Constrained Variational Stationarity (THM-FFE-STAT-01): Stationary variation DSdyn(u)+DC(u)∗Λ=J characterizing constrained critical points on metric-measure spaces (AUTHORIAL_SPECIALIZATION / PROVEN_IN_CORPUS).
  • Noetherian Current Conservation (THM-FFE-NOETHER-01): Covariant divergence conservation ∇μJμ=0 derived under 1-parameter continuous Lie group symmetries and manifold boundary regularity (DERIVED_CONDITIONALLY).
  • KKT Multiplier Invertibility (THM-FFE-02): Uniqueness of Lagrange multiplier reaction under positive definite Hessian and surjective constraint gradient (ESTABLISHED_THEOREM_APPLICATION).
  • KP Resolvent Construction (THM-KP-01): Construction of bounded resolvent operators Rλ=(LKP+λI)−1 conditioned on self-adjoint generator domain closure (DERIVED_CONDITIONALLY).

3. Computational Results & Resolvent Solvers ​

  • KP-Field Numerical Solvers: Bounded finite-difference and graph Laplacian solvers computing spectral gap bounds and topological soliton stability.
  • Tabela Elementa: Structural algebraic mapping of electronic shell structures and multi-electron spectra.

4. Negative Results & Statistical Benchmarks ​

  • Multiscale Parity Anomaly Search: Statistical audit across discrete multiscale graph configurations yielded pnull=0.62 (>0.05). The null hypothesis cannot be rejected; relational parity is preserved on the unperturbed vacuum. This negative finding is permanently recorded.

5. Experimental Testbed Interfaces ​

6. Open Theoretical Problems ​

  • Non-Perturbative Continuum Limit: Proving that the weak limit of discrete Dirichlet forms converges to smooth pseudo-Riemannian path integrals without coordinate singularity.
  • Osterwalder-Schrader Positivity: Proving reflection positivity for multiscale Green functions on discrete graph states.
  • Machine Verification in Lean 4: Closing the formalization targets in /04-mathematics/lean/ (current machine-verified theorem count =0).

7. Publications & Archival Manuscripts ​

8. Collaboration & Open Scientific Critique ​

External researchers are invited to audit definitions, run local reproduction packages, and submit formal counterexamples through the Open Scientific Review Architecture.