Paper Citation Record · LEDGER

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution

As of 22 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2602.20907.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2602.20907 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T21:16:13.101620Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

26 of 26 outbound references displayed

verified exact0
verified fuzzy0
unresolved26
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4a4c72dc-cc6f-44e8-8859-303b249f7799 · outbound

This paper cites Let u(t) ={u aα(t)} denote the Cartesian displacement vector, whereu aα is the displacement of atomaalong Cartesian directionα∈ {x, y, z}.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Let u(t) ={u aα(t)} denote the Cartesian displacement vector, whereu aα is the displacement of atomaalong Cartesian directionα∈ {x, y, z}

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:11.606862Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 341356fc-e27c-4eb2-a75e-4d72bed26750 · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:11.690668Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b834026-cefd-4b28-8adb-e3eb8b4c4c51 · outbound

This paper cites This induces a perturbation of the dynamical matrix D→D+δD,(A12) through the mass-weighting in Eq.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution This induces a perturbation of the dynamical matrix D→D+δD,(A12) through the mass-weighting in Eq

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:11.730798Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11edc25d-e03f-431e-9d57-2ec1cf43c2ec · outbound

This paper cites (A9), we write D(M) =M −1/2 Φ M−1/2.(A13) UnderM→M+δM, the first-order change is δD=δ(M −1/2)Φ M−1/2 +M −1/2 Φδ(M −1/2),(A14) where we have usedδΦ= 0.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution (A9), we write D(M) =M −1/2 Φ M−1/2.(A13) UnderM→M+δM, the first-order change is δD=δ(M −1/2)Φ M−1/2 +M −1/2 Φδ(M −1/2),(A14) where we have usedδΦ= 0

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:11.798936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22c7ab29-021e-4331-b554-d06768785222 · outbound

This paper cites (A19) Substituting into Eq.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution (A19) Substituting into Eq

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:11.880430Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54049cbe-9ad9-4a11-b15e-0f24ceb4f269 · outbound

This paper cites (A26) The corresponding first-order mixing amplitude is de- fined as aji = Nji ω2 i −ω 2 j.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution (A26) The corresponding first-order mixing amplitude is de- fined as aji = Nji ω2 i −ω 2 j

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:11.932130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d65c9ced-650d-4bf9-a9d4-89639bad2f80 · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:11.978884Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e96a51f-ffae-4487-ace0-248dca659029 · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.049343Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9a137bc-699c-41c0-b11a-0d2211e3a26b · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.112452Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 61dc41e1-f4ee-4b95-b157-727726f1edbd · outbound

This paper cites Colognesi, S.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Colognesi, S

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.183625Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4b959db7-43d1-47dc-b7ce-7af698a62638 · outbound

This paper cites Armstrong, S.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Armstrong, S

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.235830Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a095feb0-bdf6-4584-a83f-e8e54c9e7ef0 · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.306820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f7ef6d4-4bab-4d88-8b2c-b79c382cf9ef · outbound

This paper cites Bahadur, S.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Bahadur, S

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.359415Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c02c9d8-9703-4017-bf98-85e29d187857 · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.414081Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7befbcbb-d54b-47cc-adf6-978faf47ddc8 · outbound

This paper cites Filippov, J.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Filippov, J

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.499535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79a4126f-1de0-469c-b529-794fcb1162d9 · outbound

This paper cites Kieslich, J.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Kieslich, J

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.565573Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8279d112-7d94-4b98-92db-715b30c77f7e · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.614759Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bca0d613-c82d-4f7b-8068-f738f32092be · outbound

This paper cites 5286/isis.instrument.2527(2026), instrument DOI for TOSCA, ISIS Neutron and Muon Source.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution 5286/isis.instrument.2527(2026), instrument DOI for TOSCA, ISIS Neutron and Muon Source

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.663938Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58fb46cd-a5b8-4d98-9ffc-78a38b04ba7e · outbound

This paper cites Arnold and et al., Nucl.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Arnold and et al., Nucl

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.719365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 096d55df-a389-461e-a39d-72fe17e5d2f8 · outbound

This paper cites Kresse and J.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Kresse and J

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.764600Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57fe8020-460e-41ab-9a30-6c4e04e0ecea · outbound

This paper cites Kresse and J.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Kresse and J

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.827791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f20b2a2b-a335-4033-b493-c330c0ea988c · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.881261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fac63f6e-195c-4966-9cf4-d6f4cc1e28f8 · outbound

This paper cites Kresse and D.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Kresse and D

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.937140Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62635e43-7762-43f3-9cec-c5bb3699777d · outbound

This paper cites Grimme, S.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Grimme, S

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:12.989410Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eecd99df-150a-4a18-bb00-103a2a20eaf1 · outbound

This paper cites Dymkowski, S.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Dymkowski, S

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:13.036510Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d383da2-eca8-4641-af45-3e55f2007f7b · outbound

This paper cites an unresolved cited work.

Collective Phonon Mixing and Eigenvector Transport Under Isotope Substitution Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-02T21:16:13.101620Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.