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Paper Citation Record · LEDGER

Taking rational numbers at random

As of 16 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:1908.06944.

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

pith.paper-citation-record.v1
1908.06944 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T12:39:07.082657Z

measured 35 of 35 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 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

35 of 35 outbound references displayed

  • verified exact1
  • verified fuzzy3
  • unresolved30
  • parse uncertain1
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bedc147f-137f-4388-8b38-f945995d55ca · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.612319Z

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=arxiv_source observed=2026-08-14T12:39:06.933418Z digest=sha256:0098e3f0ba6afea97a039a1535ffa5b5cfe21e004324a1050d4e0784f0887d9c

Observation 190c006c-11e2-464a-8e0c-5191655ceaa6 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.598371Z

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=arxiv_source observed=2026-08-14T12:39:06.938161Z digest=sha256:f6db2367f4e04dbe8e9bdf3e7f7b440a60a5e82f526240c6c0331e6b194da8ba

Observation 8e06d2bc-31e8-4465-b02f-c0749ea8ed00 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 3

Resolution
parse uncertain
raw_fallback, observed 2026-08-14T12:39:07.583641Z

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=arxiv_source observed=2026-08-14T12:39:06.942395Z digest=sha256:af1b67697cecea1397fba40b35561c1be5b921b3bbd295bbc772455a1d2b50db

Observation a40798b2-7d1e-4e3c-a1a3-b53d09b82e6c · outbound

This paper cites Gnedenko, The Theory of Probability (MIR, Moscow 1978).

Taking rational numbers at random Gnedenko, The Theory of Probability (MIR, Moscow 1978)

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:39:07.569441Z

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=arxiv_source observed=2026-08-14T12:39:06.946841Z digest=sha256:677c378b643c4edd0331bccb5cfa0c3eaed4562204006a008b257ace820528e3

Observation b309d535-aae6-4780-a904-c13b28f15be7 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.555789Z

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=arxiv_source observed=2026-08-14T12:39:06.950983Z digest=sha256:8faac871a5df3f640b317fd1f39698bb704858363bee36f311f5c1d73be70c8e

Observation d79344f8-b7a1-47fd-a076-8225c28e0196 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.542677Z

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=arxiv_source observed=2026-08-14T12:39:06.955744Z digest=sha256:aca7d629ecc8bb28564f3bcc532d5190c13df32e2968e53f08acedcb213087a8

Observation 3566719b-2f9f-48c0-9d08-7313503abecb · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.529604Z

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=arxiv_source observed=2026-08-14T12:39:06.960345Z digest=sha256:6a9e32e7cf753334aa3536865a1765c9ba015c5084e6dfa47c98871ac66c9275

Observation 2ef669cc-a08e-4669-bd41-9a28a35caeb8 · outbound

This paper cites Wiley&Sons, New York 1990).

Taking rational numbers at random Wiley&Sons, New York 1990)

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:39:07.516393Z

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=arxiv_source observed=2026-08-14T12:39:06.965024Z digest=sha256:c2235a72cb25426aa70d98ff62d1c811115d603bb775085305052f14574850bd

Observation 585c6364-1353-4c9e-9677-bd1069c705e9 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.502892Z

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=arxiv_source observed=2026-08-14T12:39:06.969506Z digest=sha256:96c8324320b9e9f3ffafbe8f73acd9fc00b9562591f13b9a2d5977b3dd850c3b

Observation f0a416df-a614-4438-83c4-4dd6c50a959e · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.489331Z

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=arxiv_source observed=2026-08-14T12:39:06.974163Z digest=sha256:0c7ef1681440d6f6e7bc020dbf525c6b9c76bc8b12604957588699d7cd1ae5ed

Observation cb3d9fcf-dafe-4e0a-9b84-3161390cd048 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.475166Z

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=arxiv_source observed=2026-08-14T12:39:06.978738Z digest=sha256:68945d53cb7924f92b6f02c975db9238676a87dfa5aec2f2b1e19055b68c2401

Observation c6586469-e8d7-4362-acee-d805e115904a · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.460476Z

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=arxiv_source observed=2026-08-14T12:39:06.984121Z digest=sha256:089377eb61c223dd3e28d38e7da2f8927d12a541c6fec07487783f028a2a485c

Observation 227194f7-91b7-41b6-abe5-6c9b89c8f935 · outbound

This paper cites Gintautas, M.I.\ Ham,.

Taking rational numbers at random Gintautas, M.I.\ Ham,

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T12:39:07.446979Z

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=arxiv_source observed=2026-08-14T12:39:06.988691Z digest=sha256:45178ac2b6b335a9b3e07201eaf18bff1b9b9bac387a128e04d9d4c732127120

Observation 4184f46a-042e-4ab6-b010-65189763841a · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.433646Z

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=arxiv_source observed=2026-08-14T12:39:06.993154Z digest=sha256:0cbcae4282e62a307ba2335443d8257a1e29153bf30c6387c80e11d8784d21e8

Observation fe7410b6-94db-479e-a811-2fb1cf0c60cd · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.419642Z

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=arxiv_source observed=2026-08-14T12:39:06.998496Z digest=sha256:1ae713496194659f8008de803d7c740c0461952197c86a63fc7a4b5fd474a939

Observation ba050c4f-06c8-4aa0-8668-2d9991184f84 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.406203Z

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=arxiv_source observed=2026-08-14T12:39:07.003137Z digest=sha256:df27dc61c893db21512b22d34b0a0e9d2fb92558deafb6cff4ff1e6401d5ddf7

Observation 53a3f116-5522-42ba-ab7a-9b841b81f615 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.393123Z

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=arxiv_source observed=2026-08-14T12:39:07.007343Z digest=sha256:0d96f35a27803b57aadf742823704be5c0f60fb3e96685124cf4726d8ce7f25d

Observation ff577808-5167-4119-be08-b56c2f69aed2 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.379906Z

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=arxiv_source observed=2026-08-14T12:39:07.011395Z digest=sha256:0b5b197a5501312af1d7ca2fbb59a5ec1273089ea2e6e1089bb15360e5823d12

Observation 15def225-2771-462e-906c-a8e60a27a9ed · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.366216Z

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=arxiv_source observed=2026-08-14T12:39:07.015560Z digest=sha256:b6a5097cd284251b91ce000697dbd21c420ae9a22d18928044fb588e3e4ca84d

Observation 8cbef3ae-d384-4a65-bfbc-9e7fa2ee3045 · outbound

This paper cites L\'evy-Schr\"odinger wave packets.

Taking rational numbers at random L\'evy-Schr\"odinger wave packets

Reference 20

Resolution
verified exact
local_arxiv, observed 2026-08-14T12:39:07.126337Z

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=arxiv_source observed=2026-08-14T12:39:07.019803Z digest=sha256:3bfc7ae129ae8d3abfd16680d7d6386f2345ed6d9fafeed0c1aedf076d2d0511

Observation 9a503d7d-f1ed-4c9c-b579-b35f85d96671 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.351081Z

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=arxiv_source observed=2026-08-14T12:39:07.024203Z digest=sha256:e0f6fa6bbd901163cc08a19ee2a9a46c77b8fc501c5fd0826a8926d3afe5b238

Observation 2c38da4f-63d3-4423-8dec-92c80e4fee3d · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.336660Z

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=arxiv_source observed=2026-08-14T12:39:07.028145Z digest=sha256:a23103cb7cf3d7410f29b45c6da97c6283316bf5a24663c303ceb1c183879cdb

Observation bec026f8-25c2-4a64-9903-689f11effcd2 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.323010Z

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=arxiv_source observed=2026-08-14T12:39:07.032196Z digest=sha256:5cc9bcb3fe7d0e06634ed2797903d88507be2a74340a6412d56d11281e1c84f6

Observation 8892fc81-eb62-416b-a662-5c3f558f958b · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.307922Z

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=arxiv_source observed=2026-08-14T12:39:07.036463Z digest=sha256:629a7e9fe0cb8789a48c4c426be5fa851948a7601cba952ffbd94d5099e4c184

Observation b5c0b033-7427-4a1b-a7c3-78d6fbe6ebd4 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.294208Z

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=arxiv_source observed=2026-08-14T12:39:07.040464Z digest=sha256:1c3ac26635f77800b0884d4fe1c73f0a9157f541f20f535dbfefbbabaa17ad7a

Observation 4462aaaa-7c6e-453e-886a-bb64273466d6 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.279919Z

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=arxiv_source observed=2026-08-14T12:39:07.044592Z digest=sha256:1d2ee65558496bde3fd02d5fdd39077c9a398762b25b2f3aad1f7f9ac1f4daef

Observation 8d2c807e-4412-4596-8cd8-0d590d05c4fd · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.266263Z

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=arxiv_source observed=2026-08-14T12:39:07.048640Z digest=sha256:40ba26305979b1f8867b9874fd176ab8b9d18f71c416c459bb3af0bdd108ea95

Observation 73ddda50-3d4f-43be-bb6e-0cf17d42d5ad · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.252322Z

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=arxiv_source observed=2026-08-14T12:39:07.052856Z digest=sha256:39f1861178421756b8bd783f3813aaafb03c40297404aa8624abf34e0feb0d43

Observation 31f5cdfd-2ffc-4973-a179-febcdb1435b9 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.237416Z

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=arxiv_source observed=2026-08-14T12:39:07.057496Z digest=sha256:bcc817f9369d1b39bb2ef2aaa18fac90c03156505f428896e4c7b328013f840c

Observation 1b7c3d93-b9fb-45b8-afa0-000ba00ed1f1 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.223246Z

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=arxiv_source observed=2026-08-14T12:39:07.061644Z digest=sha256:dd33cb1a9badc9e728b8e64f463f8802464207992926b1c1777ef6bc69b02e11

Observation 847fa64d-c2df-4484-a3e9-463215c799a8 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.207029Z

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=arxiv_source observed=2026-08-14T12:39:07.065678Z digest=sha256:9b79fc4cad28233291773ccc2e72d0bd59b859209f032187d8c9f536c82c2801

Observation 938b682c-3f92-4a0e-8c86-8d452e0899cc · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.192819Z

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=arxiv_source observed=2026-08-14T12:39:07.070086Z digest=sha256:c6eee49ea0f1dab5dceeaf44acaa4952500b9cc440002c9dc303e94337f5180b

Observation b326929f-6c00-40b9-b8c1-ec4fe047fbd9 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.176923Z

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=arxiv_source observed=2026-08-14T12:39:07.074217Z digest=sha256:69e021ad4623968b243f20cb3e88b8fa22b379fa58dcb5a3f21c61a61a95a5c8

Observation cf4d2aa6-bb84-499e-982e-7d2f9ce01079 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 34

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.159097Z

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=arxiv_source observed=2026-08-14T12:39:07.078316Z digest=sha256:403c2a5a5ef8f32df834b6afd869cbdd07b85851aa278e9fdd102b428128a772

Observation c12320b9-fae6-4767-92f7-65ddda79cf61 · outbound

This paper cites an unresolved cited work.

Taking rational numbers at random Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-14T12:39:07.142916Z

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=arxiv_source observed=2026-08-14T12:39:07.082657Z digest=sha256:93ac7ea8f3ee6f2d5c7fb55d7e3d746b5fdd9b9607f727102ca932f52308fe5e

Pith citing papers

No inbound Pith citation observations are available.