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Source-Side Calibration Using Multi-Line Common Shifts and Invariant Ratios
V33-33.3 · F 证据节 / 显影节 ·
33.3 turns multi-line source-side calibration into the minimal axiom for TPR: within co-spatial, co-temporal line groups, a source may show a common whole-spectrum shift, but line-to-line ratios must remain invariant; if stable line-family-dependent differentials survive re-analysis, the source-side zero-point fails and the TPR/PER bookkeeping must be reopened.
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Keywords: TPR, PER, source-side calibration, whole-spectrum shift, invariant ratios, Delta z_ij, R_ij, co-spatial lines, co-temporal lines, same region same window, cross-instrument replication, zero-point constraint
Section knowledge units
thesis
33.3 freezes the source-side zero-point before later redshift bookkeeping can begin. If the source-side baseline belongs to TPR, then multiple spectral lines emitted by the same source, at the same epoch, and in the same emitting region should all share one common fractional shift while keeping their dimensionless line-to-line ratios invariant. The chapter therefore turns 'common whole-spectrum shift, invariant ratios' into a hard gate for source-side calibration. Its purpose is not to explain every redshift effect at once. Its purpose is to prevent line-family-specific behavior from quietly taking over the baseline. In V33's protocol terms, this is a source-side admissibility test that later TPR/PER decomposition has to respect rather than overwrite.
mechanism
The measurement design is built around three layers. First come the line-specific fractional shifts or redshifts for each line in the group. Second come the pairwise differential quantities: Delta z_ij, or equivalently the difference in fractional shift, and the ratio invariant R_ij, which should stay at one if the baseline is intact. Third come dimensionless shape ratios from fine-structure or hyperfine splitting, which are deliberately included because they expose line-family-specific or constant-drift-like contamination. In other words, 33.3 does not settle for saying that several lines moved in a roughly similar way. It asks whether they moved together in the only way that preserves the source-side baseline while denying special privileges to any one line family.
mechanism
To make that zero-point hard, the workflow bans casual line mixing. Lines must come from the same emitting region and the same analysis window, ideally the same velocity component; if multiple components exist, they have to be decomposed before comparison. The section also demands at least two physically different line families, frozen calibration and correction chains, blind encoding of line identities or line-family labels, and recomputation with at least two independent instruments or pipelines. This is the chapter's operational meaning of same-region same-window. It is not a poetic phrase. It is the anti-cherry-picking rule that keeps source-side calibration from being retrofitted after the reader already knows which lines look convenient.
evidence
The controls are designed to show that the procedure can recover both truth and failure. A positive control imposes a known uniform scaling or equivalent Doppler shift across multiple lines and checks that the pipeline returns near-zero differentials and invariant ratios. A negative control intentionally compares line groups from different regions or different velocity components inside the same astrophysical source and demands nonzero differential structure. A system control perturbs calibration within preregistered bounds or swaps calibration chains, and the resulting pattern has to match the known calibration change. Only by passing these controls can 33.3 claim that it is measuring a real source-side baseline rather than a blend of mixed regions, line-family quirks, or calibration accidents.
boundary
The pass line is strict. For preregistered line groups that are co-spatial and co-temporal, Delta z_ij must remain indistinguishable from zero once statistical and systematic uncertainties are combined, R_ij must remain consistent with one, the result must survive small perturbations in line choice, two independent fitting pipelines, and cross-instrument replication, and any time evolution must stay synchronized across lines while preserving ratio invariance. Failure is declared when stable line-family-dependent differential shifts persist across instrument, bandwidth, and processing changes, when R_ij departs systematically from one without a known local explanation, or when only one line family carries the structure. The chapter then names three major risk routes: calibration and line-center bias, isotope abundance or non-Gaussian line-shape contamination, and mixed emitting regions or velocity components.
summary
So 33.3 does one thing that later chapters depend on: it locks the zero-point before endpoint-path bookkeeping can start to argue about refinements. If multiple co-spatial lines show one common whole-spectrum shift while preserving line-to-line ratios and replicating across instruments, the source-side baseline survives. If stable, reproducible line-family-dependent differentials remain after the safeguards, the baseline fails and the redshift bookkeeping has to come back here before moving forward. That is why the chapter is retain under the compat bridge. It fits the existing lane directly: TPR keeps the source-side baseline, PER stays downstream as the path-side refinement lane, and later chapters such as 33.4, 33.14, and 33.70 inherit a zero-point that has actually been audited.