Jérôme Beau

The Cosmochrony Research Programme: A Structural Roadmap and Paper Inventory

The Cosmochrony programme develops a pre-geometric framework in which physical structure — spacetime, quantum mechanics, gauge symmetry, and Standard Model observables — arises from a single primitive: the local structure of admissible non-injective transitions between observable...

Gauge Structure from Admissible Non-Injective Projection

Starting from the axiomatic foundation of admissible non-injective transitions, we derive the structure of gauge theory without introducing it as a postulate. Gauge charges are identified as invariants of equivalence classes in the projection fibre: two configurations are gauge-e...

Admissible Non-Injective Transitions as the Primitive of Physical Description

Quantum mechanics is the effective theory of physically real unresolved admissible structures and their resolution. This paper establishes the minimal axiomatic foundation from which this claim follows: physical structure is derived from a single primitive, the local structure of...

Quaternionic Rigidity of Admissible Morphisms: Every Admissible Φq,ρ Necessarily Factors through su(2)

Let $\Phi_{q,\rho} \colon V_q \to V_\rho$ be a morphism from the Weil representation space of $\mathrm{Heis}_3(\mathbb{Z}/q\mathbb{Z})$ to a representation space of $2I \subset \mathrm{SU}(2)$, subject to three structural constraints imposed by the admissible projection $\Pi$: in...

Canonical Fourier Filtration and the Obstruction to a Spatial Continuum Limit

The companion Foundation paper establishes that the admissible fibre carries the Weil representation of ${\mathrm{Heis}_3}({\mathbb{Z}}/q{\mathbb{Z}})$ at a fixed non-trivial central character, and defines the canonical filtration of the fibre as the orbit spans $\Omega_n = \math...

Asymptotic Calibration of the BFS Window and Effective Dimension of the Admissible Trajectory

The O25 programme identified the ratio $n_1(q)/q$ as the central open asymptotic variable controlling the finite-size drift of $\bar{\delta}_{\mathrm{pair}}(q)$, and O26–O27 identified the effective dimension $r_{\mathrm{eff}} = d_\rho^2$ of the per-pair covariance operator in $\...

Carrier Identification via the Veronese Collapse: Effective Dimension of the Admissible Covariance in End(Heff)

Paper O28 established that the per-pair covariance ${\mathcal{C}_c}$ in ${\operatorname{End}}({H_{\mathrm{eff}}})$ has rank ${r_{\mathrm{eff}}} = 3$ with invariant eigenvalue structure $[1: \tfrac{1}{2}: \tfrac{1}{2}]$. The present paper gives the structural explanation of this r...

Three Admissible Directions and Three Spatial Dimensions: A Structural Bridge Candidate between Heff ≃ C³ and the Horizontal Geometry of Heis3(R)

Two independent sub-programmes of the Cosmochrony framework independently produce the integer three as a structural output. Paper Q5b derives a four-dimensional effective Lorentzian geometry from the homogeneous dimension ${D_{\mathrm{hom}}} = 4$ of ${\mathrm{Heis}_3}(\mathbb{Z}/...

Projective Temporal Ordering and Cumulative Projected Capacity: Numerical Evidence from the Spectral Admissibility Cascade

We identify a monotone proxy for temporal ordering within the Cosmochrony spectral admissibility programme. The natural observable along the BFS cascade is not the residual capacity $\sigma_{\mathrm{pair}}(n)$, which decays by construction, but the cumulative projected capacity $...

A Finite Obstruction to Heisenberg Carrier Selection from Admissibility Constraints

We test whether the admissibility axioms of the Cosmochrony framework, together with Born–Infeld parity, select a finite Heisenberg group and its irreducible carrier. The load-bearing algebraic implication is that a finite faithful irreducible unitary carrier, equipped with a min...

Quadratic Completion of Admissible Spectral Pairs via Binary-Icosahedral Representation

We investigate the structural nature of the pair observable $\sigma_{\mathrm{pair}}(n) = \sigma_c(n)\,\sigma_{q-c}(n)$ arising in the Weil-block analysis of the Heisenberg Cayley graphs $\mathrm{Heis}_3(\mathbb{Z}/q\mathbb{Z})$. Building on the canonical construction of conjugate...

The Born–Infeld Saturation Margin of the Chiral Modulus: Antisymmetric Structure, Lorentzian Genus, and Electric Determination of the Generation Split

This note is the companion of the Projective Residue Schur reduction and takes up the first of its open deliverables: the definition of the Lorentzian saturation functional ${\mathcal{B}}(s)$ along the ${J_{\Pi}}$-odd modulus that controls the three-generation split coefficient $...

An Exact Laplacian-Eigenvalue Degeneracy Between the Spin-½ and Spin-3/2 Representations of 2I

On the binary icosahedral group $2I$ with the canonical generating set $S = 10a \cup 10b$ ($|S|=24$), the spin-$\tfrac{1}{2}$ and spin-$\tfrac{3}{2}$ irreducible representations share the same Cayley-graph Laplacian eigenvalue, $\lambda_{1/2} = \lambda_{3/2} = 18$. The spin-$\tfr...

Fourier-Support Rigidity in Conjugate Weil Sectors: A No-Go Result for Rank-Based Quantum Signatures

We prove an exact, unconditional identity in the finite Weil (oscillator) representation of the Heisenberg group $\mathrm{Heis}_3(\mathbb{Z}/q\mathbb{Z})$, $q$ an odd prime: for every complete (inversion-symmetric) BFS shell of the Cayley graph $\mathrm{Cay}(\mathrm{Heis}_3(\math...