# Scientific Sources — Case06

## References

Xiaoxia Wu, Linxuan Zhang, Shaofeng Zhang, and Difa Ye. 2021. *Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy*. *Physical Review A*, 104, 063121. [Source](https://doi.org/10.1103/PhysRevA.104.063121)

Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy

## Criterion-to-source crosswalk

Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.

| Criteria | Source locations, scientific use and limits |
|---|---|
| F1 | Wu et al. (2021), article p.063121-3, Eq.(11) and coupling paragraph: three-level g-a-f topology, energy gaps and transition moments; coherent physical dipole follows the stated basis convention. |
| F2, M1 | Wu et al. (2021), article pp.063121-1-2, Eqs.(1)-(4), p.063121-3 Eq.(12) and p.063121-5 Appendix A Eqs.(A1)-(A5): absorption, even frequency extension and real causal response. |
| F3 | Wu et al. (2021), article p.063121-4, Fig.2 caption specifies 50 fs decoherence scale. Applying it to the real dipole after propagation and using no extra Fourier window are explicit task conventions, not an added Hamiltonian relaxation law. |
| O1, I1, M5 | Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response. |
| O2, I2, M6 | Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary. |
| O3, I3 | Wu et al. (2021), article p.063121-4, Fig.3(d): 500 as finite-probe difference from impulse response, including late-time structure; full convolution remains faithful. |
| O4, I4, M2, M3 | Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction. |
| M4, M7, V1, V2 | Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required. |

## Formula and convention notes

The reconstruction formulas correspond to article pp.063121-2-3, Eqs.(2)-(4),(11),(12). With the source symmetric Fourier convention $\widetilde f=(2\pi)^{-1/2}\int f(t)e^{-i\omega t}dt$, the real-dipole identity requires $\widetilde d(-\omega)=\widetilde d(\omega)^*$ and the physical continuation $\sigma(-\omega)=\sigma(\omega)$. The causal inverse transform is retained only for $t>0$ before folding with the finite probe. A global convention change is accepted only when absorption sign, time direction, phases and normalization transform consistently. The 50 fs task decay is post-propagation readout processing, not a relaxation term in Eq.(11).

## Scope of the source anchors

The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.