# Part III. RMRM: Reverse Mathematician Research Matrix as a Research Router The goal of RMRM is not to imitate mathematician personalities, but to decompose exceptional mathematical research methods into composable, routable, and verifiable research operators. The current framework contains: $$ \boxed{ 11\text{ cognitive primitives} + 38\text{ operators} + 28\text{ dynamics} } $$ and 10 phase-aware mathematician fingerprints. The static fingerprint: $$ m\mapsto\mathfrak F_m $$ is upgraded to: $$ \boxed{ (m,t)\mapsto\mathfrak F_m(t). } $$ Current primary transformed-object policies: | Mode | Primary Processed Object | |---|---| | Tao | Obstruction | | Grothendieck | Relational Structure | | Ramanujan | Result Seed | | Erdős | Problem / Obligation | | Thurston | Manipulable Understanding | | Mirzakhani | Global Law / Research Hub | | Gowers | Diagnostic Research State | | Bourgain | Quantitative Interface | | Perelman | Closure-Bearing Structure | | Noether | Structural Carrier / Theorem Architecture | A true composite mathematician is not: $$ \text{Tao}+\text{Noether}+\text{Perelman}, $$ but rather a research-state-dependent dynamic routing: $$ \boxed{ \text{Problem State} \rightarrow \text{appropriate methodology} \rightarrow \text{new state} \rightarrow \text{re-route}. } $$ Formally: $$ \mathcal S_0 \xrightarrow{\text{Noether}} \mathcal S_1 \xrightarrow{\text{Tao}} \mathcal S_2 \xrightarrow{\text{Gowers}} \mathcal S_3 \xrightarrow{\text{Bourgain}} \mathcal S_4 \xrightarrow{\text{Perelman}} \mathcal S_5. $$ And we propose a research action value function: $$ \boxed{ J(a\mid\mathcal S_t) = \alpha G_{\mathrm{closure}} + \beta\Delta_{\mathrm{frontier}} + \gamma G_{\mathrm{transfer}} - \lambda\Delta V - \mu C_{\mathrm{correlation}}. } $$ where: $$ G_{\mathrm{closure}} = \text{gain from genuinely approaching global closure}, $$ $$ \Delta_{\mathrm{frontier}} = \text{reduction in valid escape space}, $$ $$ G_{\mathrm{transfer}} = \text{gain from reusable methods}, $$ $$ \Delta V = \text{newly added verification debt}, $$ $$ C_{\mathrm{correlation}} = \text{risk of shared hidden assumptions / self-consistency hallucinations}. $$ Selection rule: $$ \boxed{ a_t^\ast = \arg\max_a J(a\mid\mathcal S_t). } $$ ---