Redshift and Blueshift as Calibrated Frequency-Ratio Observables in USP Field Theory: Kinematic, Gravitational, Cosmological, and Interaction Baselines with Bounded Residual Tests

This document is a foundation-level reconstruction of msf:48230. Redshift and blueshift are defined as calibrated comparisons between the frequency assigned locally at emission and the frequency measured locally at observation: 1 + z = f_e / f_o. In covariant form: 1 + z = [(u_mu k^mu)_e] / [(u_mu k^mu)_o], where k^mu is the photon wave-vector and u^mu represents the emitter or observer four-velocity. The central foundation statement is: Redshift is a comparison between local rates at two events. It is not, by itself, evidence that a photon continuously loses or gains energy along every metre of empty space. Version 2.0 preserves the established quantitative baselines for: special-relativistic Doppler shift, gravitational redshift and clock-rate differences, Friedmann–Lemaître cosmological redshift, source and line-formation physics, material and plasma interactions, wavelength calibration, instrument response, and detector inference. For pure radial relative motion, the kinematic factor is: 1 + z_kin = square root of [(1 + beta) / (1 - beta)], with: beta = v_r / c. Positive radial velocity represents recession and produces redshift. Negative radial velocity represents approach and produces blueshift. For stationary emitter and observer in a static spacetime: 1 + z_grav = square root of [B(o) / B(e)]. In the weak-field limit: z_grav approximately equals [Phi(o) - Phi(e)] / c squared. Near Earth’s surface: Delta f / f approximately equals gh / c squared. This gravitational term is an endpoint potential difference. In a static conservative field, it is reversible, changes sign when emitter and observer are exchanged, and gives zero around a closed path: closed integral of grad Phi dot d ell = 0. It is therefore not interpreted as cumulative photon decay. For comoving emitter and observer in a Friedmann–Lemaître–Robertson–Walker geometry: 1 + z_cos = a(t_o) / a(t_e). The standard cosmological factor remains the required baseline. A valid cosmological interpretation must preserve its linked observables: wavelength scaling, transient time dilation, luminosity and angular-diameter distance duality, surface-brightness behavior, CMB blackbody preservation, CMB temperature scaling, and redshift drift. The required relations include: Delta t_o = (1 + z) Delta t_e, D_L = (1 + z) squared D_A, T_gamma(z) = T_0(1 + z), and: z dot = (1 + z)H_0 - H(z). A mechanism that shifts wavelengths but fails the linked timing, distance, brightness, or thermal tests is not an adequate cosmological explanation. Version 2.0 explicitly removes the earlier intrinsic vacuum-propagation law: f_o = f_e exp[-k(omega)d]. The canonical foundation value is now: k_vacuum(omega) = 0. This means the document does not propose that photons become red simply because they travel farther through otherwise empty vacuum. Absorption, scattering, dispersion, and frequency conversion remain possible in named physical environments. These include: plasma propagation, Compton and inverse-Compton scattering, Raman and Brillouin scattering, fluorescence and phosphorescence, collisions and recoil, pressure, Stark, and Zeeman shifts, moving media, moving lenses, and time-dependent gravitational potentials. These effects require their own conservation laws, cross-sections, temperatures, velocities, transfer equations, and instrument models. Attenuation is not automatically a frequency shift. A Beer–Lambert intensity law such as: I_nu(L) = I_nu(0) exp[-mu_ext(nu)L] describes transfer through a specified medium. It is not a cosmological redshift law and does not imply that every surviving photon changes frequency. The document also corrects the combination of multiple redshift factors. Independent factors combine multiplicatively: 1 + z_obs = (1 + z_kin) (1 + z_grav) (1 + z_cos) (1 + z_int) (1 + z_inst) (1 + delta z_USP). To obtain an additive bookkeeping form, version 2.0 defines: zeta = ln(1 + z). Then: zeta_obs = zeta_kin zeta_grav zeta_cos zeta_int zeta_inst delta zeta_USP. At very small redshift, zeta is approximately equal to z. At moderate or large redshift, direct addition of z terms is generally incorrect. The USP gravitational interpretation is synchronized with the calibrated resonance-potential framework: Psi_USP = alpha_g [Delta f_proxy - Delta f_infinity]. The potential is decomposed as: Psi_USP = Phi_standard + delta Psi_USP. In the weak static limit: zeta_grav^USP approximately equals [Psi_USP(o) - Psi_USP(e)] / c squared. This gives: zeta_grav^USP = [Phi_standard(o) - Phi_standard(e)] / c squared [delta Psi_USP(o) - delta Psi_USP(e)] / c squared. The standard term is mandatory. The additional USP term is optional, bounded, and tested as an endpoint residual. If Delta f_proxy is reported in hertz, the calibration alpha_g must carry the units required to make Psi_USP a specific potential with units of metres squared per second squared. A calibration obtained from one system is not assumed universal unless the same proxy definition and coefficient recover independent gravitational and clock datasets. The cosmological USP translation is similarly restricted. An operational background scale A_USP may be introduced only through: A_USP(t) / A_USP(t_0) defined to equal a(t) / a(t_0). Until independent dynamics and new predictions are derived, this is a relabeling of the standard scale factor rather than an alternative cosmology. The professional residual framework is: zeta_obs = zeta_standard + delta zeta_USP, with the null hypothesis: H_0: delta zeta_USP = 0. Allowed residual templates must be: dimensionless, predeclared, independently generated, normalized before fitting, smaller than the applicable systematic uncertainty unless detected, and transferable across withheld datasets. Possible residual channels include: higher-order endpoint-potential templates, time-varying-potential templates, localized material or plasma environment templates, and predeclared anisotropy templates. Pure empty-space path length is not an admissible foundation predictor. A possible spectral-transfer residual may be written through: K_USP = K_standard + delta K_USP. The default foundation value is: delta K_USP = 0. A nonzero transfer residual is rejected if it: broadens or distorts lines without evidence, spoils the CMB blackbody spectrum, violates supernova time dilation, breaks distance duality without a full photon-transfer model, or fails to reproduce across frequencies, instruments, or source classes. The document defines a complete source–path–observer inference chain. The source layer includes: transition identification, rest frequency, temperature, pressure, magnetic and electric fields, line blending, rotation, outflow, and source variability. The path layer includes: metric geometry, cosmic scale evolution, lensing, plasma, dust, inelastic interactions, and time-dependent potentials. The observer layer includes: local velocity, local potential, time standard, barycentric correction, wavelength solution, line-spread function, point-spread function, template fitting, and calibration covariance. Only after the complete standard chain is fitted may a USP residual be tested. A statistically nonzero leftover is first treated as evidence of incomplete source modeling, covariance, calibration, or environmental physics. It is not automatically evidence of new physics. The observational and experimental program includes: laboratory and clock gravitational-redshift tests, reversed endpoint comparisons, rotating-galaxy odd/even velocity decomposition, cluster gravitational-redshift studies, multiple-image gravitational-lens spectroscopy, cosmological transient time-dilation tests, distance-duality and surface-brightness tests, CMB spectrum and temperature-scaling tests, and long-baseline redshift-drift measurements. For rotating systems, the leading kinematic red/blue pattern is separated into odd and even components: z_odd(x) = [z(x) - z(-x)] / 2, z_even(x) = [z(x) + z(-x)] / 2. The odd component primarily tracks rotation. The even component may contain systemic, gravitational, symmetric source, and calibration effects. Warps, bars, inflows, outflows, dust, source morphology, inclination, and beam smearing remain mandatory nulls. For gravitational lenses, static vacuum lensing remains achromatic at the leading geometric-optics baseline. Image-to-image spectral differences must first be tested against: time delays, source variability, microlensing, source-region size, dust, plasma, extraction aperture, point-spread function, and wavelength calibration. Static lensing alone does not create a headline optical-frequency shift. The project’s acceptance conditions require that a residual: is predeclared or clearly labeled exploratory, includes zero as a physically meaningful null, improves model selection after parameter penalties, retains compatible sign and amplitude in withheld data, survives line, instrument, calibration, and source-model variants, and predicts at least one new observable not used in the fit. A project-level threshold such as: Delta AIC greater than or equal to 4 may be used as a minimum screening