Redshift as Endpoint Comparison
In the EOTU framework, redshift is the recurrence-scale comparison between an emission epoch and an absorption epoch. A photon transports a fixed curvature-transfer packet through the Dormant Corridor network. Its packet identity is preserved during propagation.
Let a photon be emitted at King-cycle coordinate \(\tau_e\) and absorbed at \(\tau_o\). The observed redshift is determined by the endpoint recurrence scaling between those two Constellus snapshots.
Here, \(CS_k(\tau_e)\) represents the recurrence scale of the emission snapshot, and \(CS_k(\tau_o)\) represents the recurrence scale of the observation snapshot.
Ledger Interpretation
Redshift is the ratio between the absorption-epoch recurrence scale and the emission-epoch recurrence scale. The emitted \(\Delta\mu\) packet remains invariant. The measured redshift reflects the mapping between the local ledger context at emission and the local ledger context at absorption.
This means redshift is not produced by a modification of the transported packet. The comparison is produced by the difference between the recurrence contexts in which the packet is emitted and later interpreted.
Corridor Path Length and Hop Count
The number of hops a photon takes along Dormant Corridors is directly proportional to the delay between emission and absorption. Each hop corresponds to one update interval \(\tau_0\).
Hop count determines transport delay. Redshift is determined by endpoint recurrence scaling.
Distance and redshift correlate when greater corridor distance corresponds to an earlier emission snapshot. The redshift value itself is the endpoint recurrence-scale comparison.
Packet Identity and Wavelength Comparison
The photon packet preserves its emitted identity during propagation. Its axial packet length remains the operative wavelength identity.
The propagated packet does not change its axial identity while moving through Dormant Corridors. Observed wavelength comparison arises from recurrence-scale interpretation at the absorption epoch.
This relation expresses endpoint recurrence-scale comparison, not wavelength growth inside the transported packet.
Constancy of \(\Delta\mu\)
The transported \(\Delta\mu\) packet remains invariant during propagation. Its packet identity, axial length, and transition origin are preserved through Dormant-Corridor transport.
The observed redshift is therefore an endpoint mapping between the emission snapshot and the absorption snapshot.
Amplitude Context of Active Sites
Active sites are interpreted through the recurrence scale associated with their Constellus snapshot. A photon emitted at \(\tau_e\) and absorbed at \(\tau_o\) is compared across two recurrence contexts.
The redshift signature is the ratio between those endpoint recurrence scales.
Redshift Encoded in Constellus
Constellus records the emission event, the transport entries, and the absorption event as boundary-state ledger information. The redshift arises from the difference between the ledger context of emission and absorption.
- Emission is recorded as a \(\Delta\)-amplitude event.
- Transport is recorded through \(\Delta\)-location entries.
- Absorption is recorded as a later \(\Delta\)-amplitude event.
- The transported \(\Delta\mu\) packet is not modified by the redshift relation.
Mechanics Summary
Redshift in EOTU arises from \(\Delta\mu\) transport across Dormant Corridors, fixed hop timing, fixed hop length, endpoint recurrence scaling, and ledger-defined comparison through Constellus.
Redshift is the curvature-ledger evolution of the universe, not a dynamical stretching of radiation.