Jérôme Beau

Toward Three Spatial Directions from a Supplied Spinor Carrier: Requirements for an Equivariant Bridge

Two sub-programmes of the Cosmochrony framework produce the integer three as a structural output, and this paper states what an equivariant bridge between them would require. On the geometric side, paper Q5b derives an effective Lorentzian co-metric on $\mathbb{R}_\tau \times {\m...

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 (PRS) and takes up its open deliverable on the Lorentzian saturation functional: the definition of ${\mathcal{B}}(s)$ along the ${J_{\Pi}}$-odd modulus that controls the three-generation split coefficient $u$. W...

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 $\...

Veronese Collapse in the Measured Trajectory Span: What the O28 Covariance Does and Does Not Identify

Paper O28 reported effective covariance rank ${r_{\mathrm{eff}}}=3$ in the supplied three-coordinate space ${H_{\mathrm{eff}}}$. This paper audits what that finite-data result identifies. In an extended recomputation, rank three remains modal but is not invariant: it occurs in $3...

BFS Shell Stratification and the Emergence of Four-Dimensional Lorentzian Geometry

Earlier versions of the companion paper Q5a claimed, conditionally, that the admissibility forms ${\mathcal{E}_q}$ on the Heisenberg carrier of ${\mathrm{Heis}_3(\mathbb{Z}/q\mathbb{Z})}$ converge in the Mosco sense to a second-order operator ${L_\Pi} = -A\partial_x^2$ on $L^2(\m...

Canonical Fourier Filtration and the Obstruction to a Spatial Continuum Limit

On a supplied Heisenberg carrier, the admissible fibre carries the Heisenberg–Schrödinger representation of ${\mathrm{Heis}_3}({\mathbb{Z}}/q{\mathbb{Z}})$ at a fixed non-trivial central character — not the associated Weil action of the symplectic automorphism group, which is a f...

Admissible Morphisms on the Weil Pair Sector: The su(2) Action on End(Vρ) and the Open Vector Lift

Let $\Phi_{q,\rho}$ be a morphism out of the Weil pair space $V_q$ of $\mathrm{Heis}_3(\mathbb{Z}/q\mathbb{Z})$, subject to three constraints imposed by the admissible projection $\Pi_{\mathrm{adm}}$: involution equivariance, quadratic compatibility with $\sigma_{\mathrm{pair}}$,...

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...

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 $...

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...

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...

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...