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...

Three Neutral Directions from a Spinor Carrier: Conditional Status of the Threefold Admissibility Threshold

O21 defined the observable shell $n_{3}$ by the threshold $\Sigma_{c}(n_{3}) = 3$ and used it as structural input. This paper determines the exact status of the value three. The positive result is conditional: if the admissible neutral sector is carried by an irreducible two-dime...

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...

Fourier Structure of the Pre-Saturation Admissible Pipeline: What the Three-Coordinate Projection Does and Does Not Measure

The numerical pipeline of the spectral admissibility programme stores, for each conjugate Weil pair $(c, q-c)$, two distinct objects: a full Gram–Schmidt basis of ${\mathbb{C}}^q$ reaching rank $q$ at saturation, and a three-coordinate array of projections onto the first three se...

Projective Persistence and the Physical Sub-Spectrum: A Dynamical Selection Criterion for the Capacity Exponent

The O12–O19 sequence establishes that the physically relevant observable on $\mathrm{Heis}_3(\mathbb{Z}/q\mathbb{Z})$ is the canonical pair-level quantity $\sigma_{\mathrm{pair}}^{\mathrm{can}}(n)$, with capacity exponent $\delta_{\mathrm{pair}} \approx 7.44$ consistent with the...

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...

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 $...

Native Span Growth from Capacity Decay and the Failure of the Heisenberg Capacity-to-Rate Transfer

The spectral admissibility programme measures a projective block capacity $\sigma_c(n)$ along the breadth-first cascade of the Heisenberg Cayley graph and converts capacity exponents into growth exponents through the relation $\beta = 1/(\delta + \tfrac{1}{2})$, derived on Ramanu...

The Spectral Admissibility Sub-Programme

The spectral admissibility sub-programme of the Cosmochrony corpus addresses a single central question: which spectral sectors of the Weil representation of ${\mathrm{Heis}}_3(\mathbb{Z}/q\mathbb{Z})$ survive the Born–Infeld bounded-flux constraint? The answer organises the entir...

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...

SU(3) from Colour Triplet Co-admissibility: Towards the Complete Standard Model Gauge Group

Papers O27–O30 complete the analytical account of the ${\mathrm{SU}}(2)$ sector of the admissibility programme, closing the chain $\text{emergence} \Rightarrow \mathfrak{su}(2) \Rightarrow d_\rho = 2 \Rightarrow \lambda_1/\lambda_2 = 2$. The remaining gauge-sector problem address...

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 $\...

Systematic Pair-Level Campaign for δpair: Convergence, Inter-Pair Concentration, and Normalization Structure

The O-series defines a canonical pair-level capacity observable and establishes that vertical non-injectivity does not change its observable rank. The further prescription ${\beta^{*}}=1/({\delta_{\mathrm{pair}}}+\tfrac12)$, however, imports the changing-degree LPS growth equatio...

Cosmochrony: A Non-Injective Projection Theory of Emergent Physics

Cosmochrony is a pre-geometric relational framework that does not replace quantum mechanics or general relativity, but operates at a deeper structural level from which both emerge as effective descriptions in appropriate regimes. Its aim is to expose the common infra-physical fou...

The Fermionic Matter Sub-Programme

The fermionic matter sub-programme of the Cosmochrony corpus addresses a single central question: where do fermions, chirality, hypercharge, and three generations come from? The answer is that they are not postulated as external fields: they arise as the spinorial face of the adm...

Asymptotic su(2)-Isotropy of the Effective Quadratic Form and the Identification AH = 2

Papers Q7 Q9 of the Cosmochrony spectral geometry programme establish that the effective operator $L_{\mathrm{eff}}$ on $\mathbb{R}_\tau \times {\operatorname{Heis}}_3(\mathbb{R})$ has a principal symbol $\sigma_2(L_{\mathrm{eff}})|_{H_{\mathrm{eff}}} = A_H(k_X^2+k_Y^2) + A_Z k_Z...

Three Neutral Directions from a Spinor Carrier: Conditional Status of the Threefold Admissibility Threshold

O21 defined the observable shell $n_{3}$ via the threshold condition $\Sigma_{c}(n_{3}) = 3$ and used it as structural input for the fibre-level transfer ${\delta_{\mathrm{pair}}} \to {\beta^{*}}$. The present paper determines the exact status of the value three in that threshold...

Equivariant Born–Infeld Parity and the Fibre-Identification Problem of the Non-Injective Projection

The identification of conjugate Weil blocks $\{c,\, q-c\}$ as the fibres of the non-injective projection ${\Pi}:{\chi}\to{\mathcal{O}}$ was stated as a structurally motivated hypothesis in O16 and used in O17 to derive the pair-level observable and the exponent doubling ${\delta_...

The Emergent Geometry Sub-Programme

The emergent geometry sub-programme of the Cosmochrony corpus addresses a single central question: how does the admissible Weil–Heisenberg fibre give rise to an effective four-dimensional Lorentzian geometry? Starting from the admissibility filter $\Pi_q$ acting on the Weil repre...

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}/...