Cosmochrony is a non-injective projection theory in which quantum mechanics, spacetime geometry, and gauge-matter structure emerge from a single static relational substrate, denoted $\chi$, through a fixed generally non-injective projection $\Pi : \Omega \longrightarrow O$.

No fundamental spacetime, metric tensor, gauge field, or quantization postulate is introduced at the ontological level. All familiar physical structures arise as regime-dependent effective descriptions, valid only in projectable regimes where stable geometric and causal notions can be consistently defined.

The substrate $\chi$ is atemporally fixed. It carries no intrinsic dynamics, no temporal ordering, and no spatial localization. All apparent dynamics belong exclusively to the effective reprojection sequence $U_{t+1} = \Pi \circ \sigma(U_t)$, not to $\chi$ itself.

A given observable $o \in O$ carries an irreducible fiber $\Pi^{-1}(o)$ of indistinguishable pre-images. Non-injectivity is not an assumption but a proved structural necessity: any framework that genuinely distinguishes an infra-physical level from an observable level must admit such a map. This non-injectivity accounts for:

• quantum indeterminacy and superposition as fiber multiplicity,
• contextuality,
• Bell inequality violations, without invoking fundamental stochasticity or nonlocal signals.

Because the effective description has no direct access to $\chi$, it must represent the coexistence of projectively admissible contributions internally. This forces an additive, phase-sensitive, norm-preserving structure — a complex Hilbert space — interpreted not as a fundamental ontology but as the minimal representational closure compatible with non-injective projection. In the regime where the Born–Infeld bound keeps fluctuations subcritical and the background remains quasi-stable, a unique effective dynamics of Schrödinger type follows as a proved result.

A universal bound on admissible flux ($|\partial_t \chi| \le c_\chi$) leads uniquely to a Born–Infeld-type effective action. This provides:

• non-singular strong-field behavior,
• causal saturation,
• a unified treatment of high-energy and low-density regimes.

The effective metric $g_{\mu\nu}$ is not a primitive object but a descriptive construct encoding variations in the local projective ordering rate. The same non-injectivity that forces Hilbert structure on the quantum side forces an emergent metric on the gravitational side. In the projectable regime this reproduces:

• the Schwarzschild solution,
• weak-field phenomenology,
• gravitational redshift and Shapiro delay.

Gauge symmetry is identified with the connection associated to the projection fiber. Electric charge appears as a $\pi_1$ winding invariant of the $\mathrm{U}(1)$ projection fiber; the absence of magnetic monopoles follows from the admissibility-induced triviality of $\pi_2$ on the canonical admissible base.

Mass corresponds to localized spectral stability under relaxation. Inertia arises from resistance to reconfiguration of stable $\chi$-structures.

The Lamb shift and the Schwinger effect are interpreted as consequences of:

• finite spectral resolution,
• bounded flux saturation, without introducing a physically populated vacuum.

Cosmic expansion and low-density dynamics follow from bounded relaxation. The framework provides:

• a unified effective mechanism for flat galactic rotation curves,
• a structural explanation of the Hubble tension,
• a predicted ~5% enhancement of $H(z)$ at $z \sim 1$ relative to $\Lambda$CDM, without invoking dark matter particles or fundamental dark energy.

Superconducting coherence is interpreted as projective phase locking under constrained relaxation, providing a unified description of conventional and strongly correlated regimes.

This organization hosts:

• The main Cosmochrony paper (foundational framework) (PDF)
• Companion articles:
  • A. Spectral geometry and projection structure (PDF)
  • B. Bell inequalities and non-injective projection (PDF)
  • C. Born–Infeld emergence from bounded relaxation (PDF)
  • D. Galaxy rotation curves and cosmological tension (PDF)
  • E. Charge, mass, and inertia (PDF)
  • F. Lamb shift and Schwinger effect (PDF)
  • G. Superconductivity (PDF)
  • H. Non-Injectivity as a Structural Necessity of Genuine Emergence
• Numerical simulations and validation codes
• The public website and documentation

Cosmochrony is a foundational research program with a structurally derived dynamical core, proved effective limits, and quantitative falsifiable predictions. Proved results, structurally motivated consequences, and open problems are explicitly distinguished throughout.

Preprints are publicly available via Zenodo. Journal submissions are ongoing.