What Would Falsify IDWT

Most discussions of a new theory focus on what it predicts. Equally important is what it forbids. A theory that cannot be killed by any experiment is not science — it is metaphysics. IDWT is falsifiable in very specific ways, and not all of them are the obvious kind.

There are two types. First, positive measurements: numbers that IDWT predicts precisely and that experiments will either confirm or contradict. Second — and this is the unusual part — null results: things that IDWT says cannot exist, each for a geometric reason, where a single positive detection anywhere in the world ends the theory. Several of the most intensely searched-for phenomena in modern physics fall into this second category.

These are numbers. IDWT derives them from \(n_s = 4\) and \(m_e\) alone. If experiments measure something outside these values, IDWT is wrong.

• Neutrino mass sum: \(\Sigma m_\nu = 60.4\) meV. The three neutrino masses follow from the \(d=5\) sector with no oscillation data used. The sum is within reach of CMB-S4. A measurement outside the 55–65 meV window falsifies IDWT.
• Normal mass ordering. The lightest neutrino is \(\nu_1\). An inverted ordering — \(\nu_3\) lightest — is a direct contradiction and would be established by a combination of oscillation experiments and cosmological bounds.
• CP-violating phase: \(\delta_{CP} = 197.1°\). This follows from spectral flow on the charged-lepton sector manifolds. DUNE and Hyper-Kamiokande will measure this with sufficient precision to confirm or rule out the prediction by 2028–2030. The Jarlskog invariant \(J = -0.00981\) is a direct consequence.

The following are not "unlikely" or "suppressed." They are geometrically impossible within IDWT. The reason in each case is the same structure that produces the particle masses — so these are not separate assumptions, they are consequences of the same geometry.

In IDWT, gravity is not a force mediated by a particle. It is the curvature of the full infinite-dimensional manifold \(M_\infty\), sourced by whatever mass is present. Fields have quanta; geometry does not. There is no gravitational boson — no spin-2 massless particle propagating through space, no quantum of the gravitational field — because there is no gravitational field in the quantum field theory sense.

This means any experiment that detects a graviton falsifies IDWT. Not as an anomaly to be explained — as a direct contradiction of what the theory says gravity is. The ultraviolet divergence problem of quantum gravity (which motivates much of string theory and loop quantum gravity) does not arise in IDWT for the same reason: you cannot have divergent graviton loop integrals when there is no graviton to loop.

Gravity couples to every particle through that particle's mass \(m(n,d) = S(n,d) \times m_{\text{scale},d}\) — the count of sector microstates. Heavier particles curve \(M_\infty\) more. But the coupling is geometric, not via an exchange particle, and it cannot be quantised.

Two of the most actively searched-for signatures at the LHC come from extra-dimension frameworks: the ADD (Arkani-Hamed–Dimopoulos–Dvali) large extra dimensions model, which predicts missing energy from gravitons escaping into compact extra dimensions; and the Randall-Sundrum warped geometry model, which predicts a tower of massive KK graviton resonances visible as bumps in the diphoton or dilepton spectrum at TeV energies.

Both predictions assume compact extra dimensions — spaces wound into circles or intervals of some radius R. When a dimension is compact and periodic, standing waves form. Those standing waves are the Kaluza-Klein modes: an infinite tower of particles with masses of order 1/R, 2/R, 3/R, and so on.

IDWT has no compact dimensions. The six sectors are infinite spaces — mathematically, manifolds that extend without boundary. Particles are not plane waves in these spaces; they are Gaussian-localised modes of the sector harmonic potential, like a harmonic-oscillator ground state. The sector mode amplitude decays as \(e^{-r^2/L_d^2}\) in the sector direction even though the space extends to infinity. No periodicity, no standing waves, no KK tower.

The absence of a KK tower is not an approximation or a limit. It is a structural feature of the geometry. Every published experimental bound on large extra dimensions — every Eöt-Wash torsion balance test, every LHC missing-energy search, every collider limit on KK graviton resonances — assumes a KK tower. Without one, those bounds do not apply to IDWT. But the prediction is clear in the other direction: any positive detection of a KK mode at any mass scale falsifies IDWT. A TeV graviton resonance at the HL-LHC would contradict IDWT's prediction of no KK graviton tower.

For decades, precision experiments have tested Newton's law at short distances, looking for the deviation that compact extra dimensions would produce. The Eöt-Wash experiment has pushed this to below 50 micrometres with no deviation found.

IDWT predicts there will never be one. The reason is the same as above: Gaussian localisation. For a sector with localisation length \(L_d = \lambda_d^{-1/4}\), the sector mode amplitude decays as \(e^{-r^2/L_d^2}\) in the sector direction. At any macroscopic distance \(r \gg L_d\), this is effectively zero — faster even than exponential suppression. The sector contributes nothing new to gravitational propagation at that scale. There is no correction to Newton's law at short range, not even a tiny one, because the sector modes that would produce such a correction are Gaussian-absent from the \(d=3\) domain.

Newton's law is predicted to be exact at all tested and testable distance scales. Any future measurement finding a deviation — at a micrometre, a nanometre, or any other scale — falsifies IDWT.

The equivalence principle — that all objects fall at the same rate regardless of their composition — is not an assumption in IDWT. It is a theorem. For any mode (n,d) in any sector, the gravitational mass and inertial mass are both equal to \(S(n,d) \times m_{\text{scale},d}\). The ratio is 1 exactly, for every particle in every sector, with no corrections.

This means there is no fifth force. A fifth force would require a composition-dependent coupling — different particles coupling differently to some new field. In IDWT, every particle couples to gravity through its mass and to the other forces through its sector geometry. There is no room for an additional sector-dependent gravitational coupling that would produce a fifth force.

The MICROSCOPE satellite tested the equivalence principle to one part in \(10^{15}\) using titanium and platinum test masses. It found no violation. Future missions aim for \(10^{17}\). IDWT predicts they will find nothing, at any precision.

Neutrinoless double beta decay (0νββ) requires that the neutrino be its own antiparticle — a Majorana fermion. Majorana mass terms are constructed from the charge-conjugate of a spinor, and this construction is only possible for specific spinor types.

The sector of the neutrino is \(d=5\), whose geometry is \(S^5\). The Clifford algebra of a five-dimensional space has a precise mathematical property: when \(d \bmod 8 = 5\), no Majorana condition can be imposed on the spinor. This is not a statement about energy scales or coupling strengths. It is a statement about the neutrino's spinor type, determined by the geometry of \(S^5\). The Majorana condition cannot be written down for a spinor on \(S^5\).

The consequence is not "the 0νββ rate is very small." The Majorana mass term is absent at all orders — not as a fine-tuned cancellation, but because the charge conjugation matrix \(C\) required to write \(\psi^T C\psi\) does not exist on the \(S^5\) spinor bundle. This is a property of the bundle, not of coupling constants. Cross-sector coordinate couplings — the only inter-sector interactions in IDWT — can generate Dirac mass corrections but cannot produce Majorana-type operators at any loop order, because the operator itself cannot be formulated. KamLAND-Zen, nEXO, LEGEND, and every other 0νββ experiment is searching for a signal that IDWT says cannot exist. Any positive detection falsifies IDWT's \(d=5\) spinor structure.

The IDWT particle spectrum is closed. Part 1 of the technical notes establishes that the 15 observed particles — the quarks, leptons, bosons, and Higgs — are the complete and exhaustive set of stable states selected by the co-fixed-point condition. (See The Six Sectors for the geometric structure behind this.) Any new stable particle would require either a new sector (excluded by T3: the sector set {2,3,4,5,6,10} is uniquely determined by the Hopf fibration chain and two geometric termination conditions) or a new co-fixed-point mode index (computationally verified absent for n ≤ 200 in all six sectors). The co-fixed-point stability condition is a structural postulate; its derivation from the IDWT equations of motion is open but its consequences match the observed spectrum.

Supersymmetry doubles the particle content of the Standard Model: every boson gets a fermionic superpartner and vice versa. Neutralinos, charginos, squarks, sleptons, the gravitino — none of these states have sector geometry to live in. The IDWT spectrum closure is not a numerical coincidence; it is a structural consequence of the two geometric filters. A neutralino detection at the LHC or in a direct dark matter search would require sector geometry that the theory does not admit.

The same spectrum closure that excludes superpartners excludes WIMPs and all other hypothetical stable particles beyond the Standard Model. XENON, PandaX, LUX-ZEPLIN, and their successors are searching for a weakly-interacting massive particle that scatters off nuclei. If such a particle exists, it must be a stable particle beyond the SM. IDWT says no such particle can exist. Any positive WIMP detection falsifies IDWT.

This is a sharp prediction because dark matter is real — something produces the gravitational lensing and rotation curves that make its presence obvious. IDWT does not currently offer a dark matter candidate beyond the neutrino sector (\(\Sigma m_\nu = 60.4\) meV, too light to account for structure formation on its own). This is an open question in the framework, not a solved one. But the geometric closure of the spectrum is unambiguous: whatever dark matter is, it cannot be a new stable fundamental particle.

This list is unusual for a theory at this stage of development. Most frameworks that claim to go beyond the Standard Model have flexible parameters that can be tuned away from null results. In IDWT, \(n_s = 4\) and \(m_e\) fix everything — so there is nothing to tune. Every null prediction is sharp and permanent. The theory either survives or it does not.

Several of these searches are among the most expensive and technically demanding experiments in contemporary physics. Every year they run without finding a signal is consistent with IDWT. Every year they run without finding a signal also tightens the pressure on every other framework that predicts those signals exist.

That is what it looks like when a theory has something to lose.