Cosmological Redshift Rule
Cosmological redshift is treated as a consequence of already-established EOTU execution rules. It is not assigned to internal photon change, metric stretching, Doppler motion, or an independent postulate.
Redshift emerges from invariant King-cycle timing, discrete photon transport through Dormant Corridors, and epoch-dependent recurrence scaling recorded by Constellus.
The relation compares the recurrence scale at observation, \(CS_k(\tau_o)\), to the recurrence scale at emission, \(CS_k(\tau_e)\).
One Photon, Two Epochs
Consider a single photon emitted at formation coordinate \(\tau_e\) and absorbed at formation coordinate \(\tau_o\), with \(\tau_o > \tau_e\). The photon is a discrete \(\Delta\mu\) courier.
- It occupies one dormant cell per King-cycle boundary.
- It advances one lattice step per cycle.
- It carries no phase.
- It undergoes no internal evolution during transport.
The photon’s internal oscillatory structure is defined in King Time, not in epoch-dependent macroscopic units.
Invariant Quantities
The transport rule depends on quantities that remain invariant across all formation-coordinate snapshots.
| Quantity | Expression | Role |
|---|---|---|
| King-cycle duration | \(t_k = \mathrm{constant}\) | Defines the intrinsic recurrence interval. |
| Photon step length | \(\lambda_k = \mathrm{constant}\) | Defines the fixed lattice step per cycle. |
| Intrinsic photon period | \(P_{\mathrm{intrinsic}} = N_{\mathrm{period}}t_k\) | Defines the packet period before epoch interpretation. |
What Constellus Adds
At the end of each King cycle, Constellus records boundary-state changes. It records transport entries and recurrence-scale context, but it does not change the photon packet.
- \(\Delta\)-location entries record whether the photon moved.
- \(\Delta\)-amplitude entries are recorded when an emission or absorption event occurs.
- The epoch-specific recurrence unit \(CS_k(\tau_k)\) is assigned to the snapshot.
Constellus therefore supplies the cross-epoch comparison context without acting as a force, transport medium, or photon modifier.
Emission Epoch Interpretation
At emission, the photon has an intrinsic period defined by King-cycle counting.
Observers at \(\tau_e\) construct clocks using local processes that count King cycles and apply the local recurrence unit.
This is the local mapping from intrinsic time to macroscopic time at the emission epoch.
Transport Between Epochs
During transport from \(\tau_e\) to \(\tau_o\), the photon advances one dormant-cell hop per King cycle. The number of elapsed King cycles is an integer transport count.
No photon property depends on intermediate values of \(\tau_k\). No cumulative distortion occurs during transport, and no memory of intermediate epochs is stored in the photon packet. Only Constellus snapshots record the evolving recurrence-scale values.
Observation Epoch Interpretation
At absorption, the photon still has the same intrinsic period.
Observers at \(\tau_o\) interpret that same intrinsic period using the local recurrence unit of the observation snapshot.
The observed-to-emitted period comparison is therefore:
This period ratio is the same endpoint recurrence-scale ratio used by the redshift relation.
Section Summary
Cosmological redshift follows from comparing one unchanged transported packet across two formation-coordinate mappings. The photon is emitted under one recurrence scale, transported without internal evolution, and absorbed under another recurrence scale.
The redshift value is therefore not carried as a changing property of the photon. It is evaluated from the Constellus recurrence-scale comparison between \(\tau_e\) and \(\tau_o\).