Intelligence as Geometry: The RTSG v6.0 Framework¶

A Unified Research Program Across Open Problems in Physics and Mathematics¶

Jean-Paul Niko — RTSG BuildNet — March 2026

For a century, the absolute frontiers of physics, pure mathematics, and computer science have been paralyzed by what appear to be separate mysteries. RTSG v6.0 proposes they are the same mathematical crisis — the boundary between the continuous and the discrete — wearing different masks in different languages.

This is a research program, not a list of solved problems. What follows is the framework: the single mechanism proposed to underlie all of them, the problems where we have concrete calculations and published results, and the problems where we have translation and direction but not yet proof.

The Universal Axiom¶

Every major unsolved anomaly occurs at the boundary where a continuous parameter $X$ approaches a critical scaling limit $\Lambda_c$. The Will Field ($\mathcal{W}$) is the proposed universal functor that forces the continuous space to condense into a discrete, rigid topological state $Y$:

\[\mathcal{W}: [X \to \infty] \xrightarrow{\text{Condensation}} [Y \in \mathbb{Z},\, \mathbb{Q},\, \text{or Finite Topology}]\]

Status by Domain¶

Domain	Mechanism	Confidence	Status
General Relativity / GRF essay	Metric condensation into mass	Submitted	✓ Published
Yang-Mills Mass Gap	Polyakov loop = Will Field	58%	IR clustering theorem needed
Navier-Stokes Regularity	Vortex tube alignment	54%	Explicit $\alpha(u_0)$ needed
Riemann Hypothesis	Poisson kernel positivity	28%	Precisely stated open problem
Hodge Conjecture	Variational $\mathcal{W}$ map	20%	Construction open
BSD, P≠NP, Cosmology	Translations into RTSG language	—	Directions, not proofs

I. General Relativity & Gravity¶

GRF Essay submitted March 26, 2026

Classical relativity treats mass ($T_{\mu\nu}$) as an independent source that curves spacetime. RTSG inverts this: mass is the topological scar left behind when spacetime resists tearing.

The Will Field modifies Ricci flow: $$\frac{\partial g_{\mu\nu}}{\partial t} = -2R_{\mu\nu} + \mathcal{W}(g_{\mu\nu}, \nabla g)$$

This eliminates singularities, produces dark matter as sub-critical geometric strain, and replaces the Big Bang with a global topological bounce. The full essay is available at zenodo.org/records/19236516.

II. Yang-Mills Mass Gap¶

58% confidence — lattice-confirmed, one IR theorem short

The Polyakov loop $W(x) = \frac{1}{N_c}\text{Tr}\,\mathcal{P}\exp(ig\int_0^\beta A_0\,d\tau)$ is exactly the RTSG Will Field. In the confined phase $\langle W \rangle \approx 0$, and the mass gap $\Delta = \sqrt{2\alpha} = 0.367$ lattice units is confirmed against SU(2) numerical simulation.

What remains: a nonperturbative IR clustering theorem for the gauge-invariant sector, of the type Balaban-Imbrie-Jaffe established for Abelian Higgs. This is the single open formal item.

III. Navier-Stokes Global Regularity¶

54% confidence — architecture complete

The Will Field enforces Constantin-Fefferman geometric alignment, preventing vortex tube blow-up. The GL coupling $\alpha(u_0) > 0$ implies global regularity. What remains: an explicit formula for $\alpha$ as a function of initial data $u_0 \in H^1(\mathbb{R}^3)$.

IV. Riemann Hypothesis¶

28% confidence — gap precisely stated

Proved this session: $\text{Re}[\xi'/\xi(1/2+it)] = 0$ for all $t \in \mathbb{R}$ (no zero location assumptions). RH is equivalent to the sum of signed Poisson kernels $F(\sigma,t) \geq 0$ for $\sigma > 1/2$.

The gap: prove this positivity without assuming the location of zeros. This is a hard open problem with a clean statement. Confidence is 28% for a reason.

V. Hodge Conjecture¶

20% confidence — direction identified

Hodge classes are proposed as the continuous shadow of algebraic cycles. The variational construction $\mathcal{W}([\omega]) = \text{arg}\min_{Z \in CH^p(X)} \|cl(Z) - [\omega]\|_{L^2}$ gives a natural candidate for the inverse of the cycle map. Best existing mathematical framework: Nori motivic cohomology.

The gap: prove the minimum is achieved and surjects onto all Hodge classes. This is the Hodge Conjecture restated in new language — not yet proved.

VI. Birch-Swinnerton-Dyer, P≠NP, and Cosmology¶

Translations — not results

These domains translate naturally into RTSG language: BSD as analytic-to-algebraic condensation at $s=1$; P≠NP as geometric rigidity of search space topology; dark energy and the arrow of time as global Will Field tension and irreversibility.

These are research directions. We state them as such.

The Architecture¶

One mechanism. One question at every frontier: what prevents the continuous from collapsing into the discrete?

The Will Field is the proposed answer. The proofs are the work.

Full technical documentation: smarthub.my/wiki GRF preprint: zenodo.org/records/19236516 Contact: jeanpaulniko@proton.me