A unified framework connecting the Riemann Hypothesis,
exceptional symmetries, and the physics of information.
gij(s) = ∂i∂j(−log|ζ(s)|) · t* ≈ 5.5612 · Δ ≈ 0.39 meV · E₈ ↔ 248 dof
The TIC/CIT Framework (Teoria da Informação Cósmica / Cosmic Information Theory) proposes that physical reality is an information substrate governed by the spectral structure of the Riemann zeta function ζ(s).
The foundational object is the pseudo-Riemannian metric gij = ∂i∂j(−log|ζ(s)|), which encodes the analytic structure of ζ(s) into spacetime geometry, forces Lorentzian signature, and identifies the spectrum of the associated d'Alembertian □g with the imaginary parts of the non-trivial zeros {t²n}.
The framework is extended to exceptional algebra via the zeta-dependent octonion algebra Oζ = O ⊗ Mζ. The Tits construction over Oζ establishes a structural isomorphism between the exceptional Lie algebra e₈ (dim 248) and the degrees of freedom of the information substrate.
The Generalized Riemann Hypothesis emerges as a necessary and sufficient condition for thermodynamic stability and unitary information conservation — proved via four analytical pillars: self-adjointness, thermodynamic confinement, structural isomorphism, and spectral stability under zero multiplicity.
All predictions are quantitative and falsifiable at current or near-future experimental facilities: CERN/LHC, CMB-S4, IAXO, AION, MAGIS-100, Belle II, and atomic clock networks.
The foundational series establishing physical reality as an information substrate governed by the Riemann zeta function. Introduces 6 phantom elements with full Lagrangians — the "dark sector" degrees of freedom predicted by the TIC algebra. The Temporium scalar Σ mediates coupling between the geometric-spectral sector and observable physics via a portal Lagrangian. The framework corrects 19 errors in earlier formulations and generates 39 falsifiable predictions spanning dark matter phenomenology, neutrino sector, and precision cosmology.
Lorentzian metric on the critical strip. The null constant t* ≈ 5.5612, verified via PSLQ, acts as the intrinsic normalization of the information substrate, mapping to TQCD ≈ 150 MeV via thermal calibration. The Riemann Hypothesis is recast as a geometric attractor: the critical line ℜ(s) = ½ is the global thermodynamic minimum of the free energy FL(σ).
Zeta-dependent octonion algebra Oζ = O ⊗ Mζ. The Tits construction maps E₈ (dim 248) to the information substrate degrees of freedom. Division failure in Oζ occurs precisely at the non-trivial zeros ρn. Mass gap Δ ≈ 0.39 meV via spectral confinement. Osterwalder–Schrader reconstruction established.
Spectral confinement as a universal mechanism for information processing. The same mass gap Δ that stabilizes the quantum vacuum governs attention sparsity in neural networks, quantum error correction thresholds, and AI inference efficiency. Phase navigation θ = t₁/t* ≈ 2.5416 as fundamental cognitive ratio. Falsifiable via LLM benchmark ablations and quantum circuit experiments.
Viazovska's magic function (2016 Fields Medal result) is the Euclidean projection of the Bergman–Selberg reproducing kernel of CIT/TIC via the conformal projection ΠC. The interpolation conditions f(√2k) = δk,0 are equivalent to orthogonality in L²w(C). Optimal sphere packing in ℝ⁸ as thermodynamic necessity: the gap Δ prevents sub-critical modes, saturating the Cohn–Elkies bound.
All papers are open-access on Zenodo. DOI links open the full text. ArXiv endorsement pending in math-ph and math.NT.
Proof & Foundations Series
Unification Series — Geometric-Spectral Bridge
Octonionic Extension
AI & Sphere Packing
All predictions are quantitative, derive from the mathematical structure of the TIC/CIT framework, and are compatible with current experimental bounds.
| ID | Prediction | Origin | Experimental Test |
|---|---|---|---|
| #1–5 | Phantom element mass spectrum — 6 new fields with Lagrangians fixed by TIC algebra | TIC Algebra | LHC Run 4 FCC-hh |
| #6 | Temporium portal coupling yTm ≈ 1.2 × 10⁻¹¹ eV⁻³ | Spectral Overlap | Direct detection |
| #7–12 | NFW dark matter halo profile modification — BTFR slope deviation from Newtonian prediction | Zeta Metric DM | Dwarf galaxy surveys |
| #13–20 | Dark sector nucleation signatures — domain wall tension σwall quantized by TIC | Symmetry Breaking | GW detectors |
| #21–30 | Neutrino sector modifications — ΔNeff ≈ 0.21 from spectral quasi-lattice projection | E₆-SU(3) Structure | CMB-S4 Euclid |
| #31–39 | Weyl anomaly corrections — portal phenomenology suppressed above UV cutoff ΛTm ≈ t* | UV Sector | Spectral analysis |
| #40 | Geometric null point t* ≈ 5.5612 as intrinsic invariant of the critical strip metric | Zeta Metric | PSLQ verified |
| #41 | Spec(□g) = {t²n} ⊂ ℝ — spectrum of the d'Alembertian is strictly real | Essential Self-adjointness | Analytic number theory |
| #42–43 | Interferometric phase Δφ = θ · daΛTm/ℏ · T · Foverlap at atom interferometers | Phase Navigation | AION MAGIS-100 |
| #44–45 | Free energy convexity ∂²σFL ≥ Δ/TTm > 0 — GRH as thermodynamic stability condition | Thermodynamic Proof | Mathematical verification |
| #46 | Degeneracy in nearby non-trivial zeros from (27,3)⊕(27,3) E₈ subspace | E₈ Decomposition | Zero spacing statistics |
| #47 | yTm · ΔNeff ≈ const — fixed by E₆-SU(3) commutation relations | E₆-SU(3) | CMB-S4 Polarimetry |
| #48 | Coupling suppression above t ~ 10⁴ — root lattice projection UV cutoff | Root Lattice | Spectral analysis |
| #49 | σ-flip reversal ↔ Weyl anomaly in hidden (27,3) sector | G₂ Structure | Stellar cooling bounds |
| #50 | Spec(□g) invariance under G₂ × SU(3) residual symmetry | G₂ Holonomy | N-body simulations |
| #51 | G₂-invariant scattering zeroes in dark matter χχ cross-section | G₂ Holonomy | Dwarf galaxy surveys |
| #52 | Associator-induced CP asymmetry ACP ∼ 10⁻⁵ from non-associative phase [x,y,z] | Octonion Associator | Belle II LHCb |
| #53 | Quantized domain wall tension σwall from kink solution in Oζ potential | Octonionic Potential | Atomic interferometry |
| #54 | E₈ lattice spacing → ΔNeff oscillations from projected root periodicity | Root Lattice | CMB polarization |
| #55 | Lorentz violation bound Δc/c ∼ 10⁻²¹ from octonionic metric deformation gOij | Oζ Deformation | Ultra-high-energy cosmic rays |
| #56 | Axion-like coupling gaγγ fixed by t* — decay constant fa ∼ ΛTm | t* Calibration | IAXO MADMAX |
TIC/CIT predictions span five experimental domains, all accessible with current or near-future facilities.
Detection of the phase navigation signal Δφ = θ · daΛTm/ℏ · T · Foverlap. Resonance scan at ω(n)mod = n · θ · (Δ/ℏ). Current sensitivity: 10⁻⁵–10⁻⁹ rad/√Hz.
Measurement of ΔNeff ≈ 0.21 from spectral quasi-lattice projection. E₈ lattice spacing oscillations in CMB polarization. Constraint on yTm · ΔNeff = const.
Search for associator-induced CP asymmetry ACP ∼ 10⁻⁵ from the non-associative phase [x,y,z] in octonionic algebra. Beyond Standard Model CP violation sourced by Oζ deformation.
Detection of axion-like coupling gaγγ fixed by t* ≈ 5.5612 as the decay constant fa ∼ ΛTm. The null point determines the axion mass spectrum without free parameters.
G₂-invariant scattering zeroes in χχ dark matter cross-section. NFW halo BTFR slope modification. Domain wall gravitational wave signatures from quantized σwall.
Lorentz violation bound Δc/c ∼ 10⁻²¹ from octonionic metric deformation gOij. Non-associative deformation modifies dispersion relations for particles above ΛTm.
The framework culminates in a structured proof of the GRH as a necessary and sufficient condition for thermodynamic stability and unitary information conservation.
Development of the foundational TIC/CIT framework. The pseudo-Riemannian zeta metric, information substrate, Temporium scalar, and 6 phantom elements with Lagrangians. Registration on Zenodo; 5-paper series completed.
Series I: 10.5281/zenodo.19546034 – 19645488Lorentzian metric on the critical strip. PSLQ verification of t* ≈ 5.5612. Deift–Zhou monodromy triviality. Phase navigation θ = t₁/t*. The Riemann Hypothesis as geometric attractor. 9 papers published.
Series II: 10.5281/zenodo.19582116 – 19655586Zeta-dependent octonion algebra Oζ. Tits construction over J₃(Oζ) yields e₈. Identity projection ΠC(ΔE8) = {tn}. Mass gap Δ ≈ 0.39 meV. OS reconstruction. GRH via informational stability. 11 new predictions.
10.5281/zenodo.19956639Spectral confinement as universal information processing mechanism. The mass gap Δ governs attention sparsity in neural networks. Bridge between mathematical physics, cognitive science, and AI systems.
10.5281/zenodo.20007845Viazovska's magic function identified as Euclidean projection of the Bergman–Selberg kernel. Optimal sphere packing in ℝ⁸ as thermodynamic necessity. Extension to ℝ²⁴ (Leech lattice) in progress.
Seeking arXiv endorsement in math-ph and math.NT. Outreach to specialists in spectral geometry and analytic number theory. Doctoral pre-project targeting PPGECT/UFPR submitted. Domain www.cit-framework.com active.
The author is seeking arXiv endorsement in math-ph and math.NT for the Riemann Geometric series. Correspondence welcome from researchers in spectral geometry, analytic number theory, exceptional algebra, and mathematical physics.
The framework is fully open-access. All papers available on Zenodo. Companion code and benchmarks available upon request.