>[!warning] >This content has not been peer reviewed. # Implementation status and problems Summary of what is **implemented**, **tested**, **verified**, and **documented**, and where there are **problems or limitations**. --- ## Implemented and verified (with script + run) | Application | Subfolder | Script | Verification | |:---|:---|:---|:---| | **Information theory and entropy** (foundational) | foundation/Information and Entropy | rst_information_signal_noise.py | Runs; plot of mu, nu, I/W vs eta (budget split). | | **Navier-Stokes smoothness** | further applications/Navier-Stokes Smoothness | rst_navier_stokes_regulator.py | Runs; plot of regulated vs classical vortex. | | **BSD conjecture** | further applications/BSD Conjecture | rst_bsd_solver.py | Runs; plot of fidelity vs L-noise proxy. | | **Homeostasis (identity loop)** | further applications/Homeostasis | rst_homeostasis_identity_loop.py | Round-trip Omega -> I -> Omega'; max rel err ~3.6e-10; PASS. | | **Micro-Graph Generator (Pure Axiom)** | further applications/Micro-Graph Generator | rst_axiom_pure.py | Pure Axiom Substrate derives n, d_B; canonical. Ledger/genesis (`rst_genesis.py`) alternative for bare vs dressed. See [[Genesis - Bare vs dressed]]. | These scripts **plug into** `rst_engine/` and have been run successfully. Documentation: application note, Code note, Results note (or equivalent). --- ## Implemented (application note + illustrative script) | Application | Subfolder | Script | Note | |:---|:---|:---|:---| | **Hodge conjecture** | further applications/Hodge Conjecture | rst_hodge_fractions.py | Algebraic vs transcendent fractions ($\mu$, $\nu$); plot only, no test of conjecture. | | **P vs NP** | further applications/P vs NP | rst_pvsnp_verify_solve.py | Verify (poly) vs solve (exp) toy; efficiency $\mu$ vs input size. | | **Riemann hypothesis** | further applications/Riemann Hypothesis | rst_riemann_zeros_illustration.py | Mock zeros along critical line; noise proxy and fidelity. | | **Yang-Mills existence and mass gap** | further applications/Yang-Mills | rst_yangmills_fractions.py | Force fractions ($\mu$, $\nu$, $1-\mu$); mass gap = low-$\eta$. | | **Foundation notes 2–10** (Thermodynamics and Landauer, Measure, Scaling, Spectral, Continuum/PDEs, Gauge, Cosmology and GR, Complexity, Algebraic and geometric) | foundation/ | Each has `rst_*.py` | Run **`foundation/run_all_foundation_scripts.py`** to aggregate. See **[[foundation/Foundation index]]**. | These applications have an RST reframe plus an **illustrative** script (plot); they do **not** constitute proofs of the corresponding Millennium or open problems. --- ## Implemented (application note only; no script) *(None — all further applications with notes now have at least an illustrative script.)* --- ## Conceptual (documented only; no script) | Concept | Status | Note | |:---|:---|:---| | **Graph Size Hierarchy** | Conceptual (documented) | No script; links gauge groups to $K_2$, $K_3$; used by Standard Model, Periodic Table, Cosmology. See [[Graph Size Hierarchy (RST)]]. | --- ## Not yet implemented (roadmap Todo) - Levinthal paradox - The Nature of the Chemical Bond - Origin of Life (prebiotic chemistry) - Kleiber's Law (3/4 power law) - Consciousness (recursive self-maintenance) - Black Hole Information Paradox - Quantum measurement problem - Hubble Tension - High-temperature superconductivity - Dark energy / cosmological constant - Hierarchy problem --- ## Known problems and limitations 1. **Conceptual applications:** Hodge, P vs NP, Riemann, Yang-Mills have **illustrative** scripts (plots); the RST angle is documented. Turning any of them into a proof (or counterexample) is out of scope. 2. **Engine path:** Scripts under `foundation/` and `further applications/` use three levels up to reach workspace root. If the repo is moved or restructured, `sys.path.insert` in each script may need adjustment (see [[How we do applications]]). 3. **SPARC / evaluation layer:** The evaluation code under **`expanded theory/sparc evaluation/`** (rawt, SPARC notebooks) **now uses the same `rst_engine`** for the interpolation function μ(η,n) and for the generic acceleration solver. `rawt/interpolation.py` imports `mu_rst` and `solve_omega` from `rst_engine` (workspace root); cosmology (a₀(z), n(z)) and rotation-curve helpers remain in rawt. So there is **one** implementation of the core RST maths; evaluation and application scripts share it. 4. **Millennium and other applications:** They are **conceptual reframes** (and in Navier-Stokes/BSD, **illustrative** scripts). --- ## How to re-verify All paths below assume the current layout: foundational apps under **foundation/** and Millennium/other apps under **further applications/** (see **[[further applications/Further applications index]]**). From workspace root: - `python "expanded theory applied/foundation/Information and Entropy/rst_information_signal_noise.py"` - `python "expanded theory applied/further applications/Navier-Stokes Smoothness/rst_navier_stokes_regulator.py"` - `python "expanded theory applied/further applications/BSD Conjecture/rst_bsd_solver.py"` - `python "expanded theory applied/further applications/Homeostasis/rst_homeostasis_identity_loop.py"` - `python "expanded theory applied/further applications/Micro-Graph Generator/rst_axiom_pure.py"` - `python "expanded theory applied/further applications/Riemann Hypothesis/rst_riemann_zeros_illustration.py"` - `python "expanded theory applied/further applications/P vs NP/rst_pvsnp_verify_solve.py"` - `python "expanded theory applied/further applications/Hodge Conjecture/rst_hodge_fractions.py"` - `python "expanded theory applied/further applications/Yang-Mills/rst_yangmills_fractions.py"` Or run all further-application scripts at once: **`python "expanded theory applied/further applications/run_all_further_scripts.py"`** Super-relational mapping and lensing scripts live under `expanded theory/python calculations/` and use the engine via their own path setup; see [[How we do applications]] and rst_engine README. --- ## Links - **Roadmap:** [[Applications Roadmap]] - **How we do applications:** [[How we do applications]] - **Engine:** rst_engine/ at workspace root