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Paper Citation Record · LEDGER

Analytic expressions for Debye functions and the heat capacity of a solid

As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:1908.08667.

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

pith.paper-citation-record.v1
1908.08667 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:41:22.781503Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T18:09:20.070046Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T05:25:57.889682Z

Reference resolution

21 of 21 outbound references displayed

  • verified exact0
  • verified fuzzy13
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2a0ab3c2-b6d2-48fa-bae3-11bafc6da633 · outbound

This paper cites Abramowitz and I.

Analytic expressions for Debye functions and the heat capacity of a solid Abramowitz and I

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:23.170489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.678517Z digest=sha256:1d029c97eb872dca4b2432c891ef96594d1471bbd454bffbe2e5c9d7a73e3962

Observation d7e74ead-b79d-4917-9ea4-0f49439e8945 · outbound

This paper cites Amdeberhan, O.

Analytic expressions for Debye functions and the heat capacity of a solid Amdeberhan, O

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:23.154420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.684739Z digest=sha256:9c8af164f65b7fb9746bc9be06dd104d1c168d40102a0c16d7c61038ec033bc7

Observation 126def1f-5c04-4254-b5ea-2fa074aaba71 · outbound

This paper cites Anastasiou, E.

Analytic expressions for Debye functions and the heat capacity of a solid Anastasiou, E

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:23.138714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.689783Z digest=sha256:4c5cc2f76e20e0149ca2309d27a0e193632bb22b1251783deb62f2653f8a0bcd

Observation 017866e3-48f9-4e88-9d38-f7b2b3ca1445 · outbound

This paper cites Anastasiou, E.

Analytic expressions for Debye functions and the heat capacity of a solid Anastasiou, E

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:23.122469Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.696038Z digest=sha256:8209ac3b347dc9788216ddcd96ab4262a4c37befade1751176a8070f7db35467

Observation a400bbde-cd5c-4f98-b167-ffffa0777b97 · outbound

This paper cites an unresolved cited work.

Analytic expressions for Debye functions and the heat capacity of a solid Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:23.106382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.701490Z digest=sha256:9794a824606c1fb74d2f77929ae30dbe1a3a6403af07342623b1c9eae4df84ac

Observation 74d81bb7-f428-4aab-9ee8-5f3af896d702 · outbound

This paper cites an unresolved cited work.

Analytic expressions for Debye functions and the heat capacity of a solid Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:23.090151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.706737Z digest=sha256:cd5cb783eb6d6875e6fbb45814f3746364c987845bf8dbdd29ca14c7ab945d9e

Observation 2a78688c-e946-4854-936e-4c4e8294ad98 · outbound

This paper cites an unresolved cited work.

Analytic expressions for Debye functions and the heat capacity of a solid Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:23.073430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.712121Z digest=sha256:703c862cc1656586aaa95033576b76dca7e9441a25584d91b543e821756c8adc

Observation e174260f-eea2-4a4d-b982-3c10c009d811 · outbound

This paper cites Einstein.

Analytic expressions for Debye functions and the heat capacity of a solid Einstein

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:23.052813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.717130Z digest=sha256:28959c010939db84961f67fedfb5392053db3661e8e3a6b0190160738ba9e3ef

Observation 46f488cd-790b-47c1-b119-e633cca747b2 · outbound

This paper cites Gonzalez, K.

Analytic expressions for Debye functions and the heat capacity of a solid Gonzalez, K

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:23.036677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.721901Z digest=sha256:7a0ada21c9ad37879a5ee0a2df9dc5994ab4387dbcb477fa0f844a28c83e19e2

Observation f497dc7e-9c53-4aa5-aae5-dc2dc2ad24e7 · outbound

This paper cites Gonzalez and M.

Analytic expressions for Debye functions and the heat capacity of a solid Gonzalez and M

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:23.020097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.726529Z digest=sha256:be7cb1a0151c2280ceaec06c8e18964317a845d4f685087ef6d32ee0e69383c4

Observation f3077fe1-cbf9-4ff1-aa87-2d5a1001ef00 · outbound

This paper cites Gonzalez and V.

Analytic expressions for Debye functions and the heat capacity of a solid Gonzalez and V

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:23.002093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.731471Z digest=sha256:3e6044a514c6b0916aeaeb0f2aceeb085669e939e3fa6a18e611f401de67d99e

Observation 1465a59d-2770-44ef-b6d3-6e4832535d9a · outbound

This paper cites Gonzalez, V.

Analytic expressions for Debye functions and the heat capacity of a solid Gonzalez, V

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:22.985064Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.736199Z digest=sha256:4888c40be7a0a169235be428e961218873c97c8fa787db9a56673d412fff1cff

Observation 79dd5e28-e446-4050-98f3-4e1031cee69e · outbound

This paper cites Gonzalez, V.

Analytic expressions for Debye functions and the heat capacity of a solid Gonzalez, V

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:22.969268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.742165Z digest=sha256:d3ec204674e787927ca7c4fdc560d9c94cfbaff5ae480a21622b18479fa32d6f

Observation 7cd3e4cb-1b27-4072-8b01-7c223f992902 · outbound

This paper cites Gonzalez and I.

Analytic expressions for Debye functions and the heat capacity of a solid Gonzalez and I

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:22.952796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.747249Z digest=sha256:0202372335c73b5781286ff6ac3c7532e7c394d2a9297aff1e7df75cacc9a3af

Observation 46e14dca-31a2-472c-9511-39d24ee0a95f · outbound

This paper cites Gonzalez and I.

Analytic expressions for Debye functions and the heat capacity of a solid Gonzalez and I

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:22.933721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.752096Z digest=sha256:377baf9d275bbf2956abfacccebd0c7215c0bed612a328e9e1ed6fea14b9f660

Observation 3303b251-4f7d-4532-81a1-8ca81d3ac597 · outbound

This paper cites Gonzalez and I.

Analytic expressions for Debye functions and the heat capacity of a solid Gonzalez and I

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:41:22.917514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.757021Z digest=sha256:a8501d9294a157b76796d9cd34cb0d7a676306f68375b87190bb171faf4ea9a1

Observation 41e615f7-e4d9-41c2-9f66-64ab925bfb42 · outbound

This paper cites an unresolved cited work.

Analytic expressions for Debye functions and the heat capacity of a solid Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:22.898634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.762639Z digest=sha256:f3bcb10371b6bf79dedc0e0ee8c5a529218d786536d1ecd299ed79d789887809

Observation b78b75ac-2198-4abe-9351-30946da88b36 · outbound

This paper cites an unresolved cited work.

Analytic expressions for Debye functions and the heat capacity of a solid Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:22.882179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.767343Z digest=sha256:e385a21c6a5711cdfda6b48d5774fd26874ea72b49a33082bf1bb122ad87bde8

Observation 0a45e5d9-8f4a-40a8-ae09-fd1de2ac12af · outbound

This paper cites an unresolved cited work.

Analytic expressions for Debye functions and the heat capacity of a solid Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:22.864235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.772023Z digest=sha256:3a29328e18ec9e79f6d091d178be56b1a7c818f5a2912b22fd1e23c41ffda78f

Observation 46d171ec-861d-4bc0-b532-57f2e72668db · outbound

This paper cites an unresolved cited work.

Analytic expressions for Debye functions and the heat capacity of a solid Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:22.845761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.776723Z digest=sha256:93e5e9a28ec705b5fb5245d5547cad8be740bd1b691f0378fa4dc89d77181e16

Observation 8d45878e-13e5-4cf4-9f69-7ca43fe8ddf9 · outbound

This paper cites an unresolved cited work.

Analytic expressions for Debye functions and the heat capacity of a solid Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:41:22.820034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T11:41:22.781503Z digest=sha256:642b8426252a0d66caa85d9905fbcb5e814c81aed9863f97392500a21f986f3e

Pith citing papers

Observation 5e2868de-2902-419b-b1e1-126b02d7f218 · inbound

Inverse Laplace and Mellin integral transforms modified for use in quantum communications cites this paper.

Inverse Laplace and Mellin integral transforms modified for use in quantum communications Analytic expressions for Debye functions and the heat capacity of a solid

Reference 19

Resolution
verified exact
arxiv_id, observed 2026-05-11T05:25:57.894687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-05-10T18:09:20.070046Z digest=sha256:60d5ed7aa49672cdcfafe2832b2a0714e12a29bed3d22b43650b7166a20a13d6