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Paper Citation Record · LEDGER

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs

As of 17 August 2026, this Paper Citation Record lists 67 of 67 outbound references and 0 inbound Pith citation observations for arXiv:2506.18341.

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

pith.paper-citation-record.v1
2506.18341 v1

Coverage vector

measured 67 of 67 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:57:34.140767Z

measured 67 of 67 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

67 of 67 outbound references displayed

  • verified exact0
  • verified fuzzy45
  • unresolved19
  • parse uncertain2
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 195e894c-9cf8-4928-b7a5-23c718bb4a0b · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:35.075313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.902692Z digest=sha256:ec518fba82a9db88fe22a4970ae5dfb4860c2361475639917a19ed017a4d81e8

Observation 038452d3-eb32-431d-8531-67c19488beea · outbound

This paper cites Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:35.114951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.898423Z digest=sha256:106ed79573306becc29a5d4aaf3df269de132e920e0d51de069ead8debc14f74

Observation c01206f9-d265-4f45-b206-5c7233ef542f · outbound

This paper cites 例如, 81 是 13- 美丽的 …….

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 例如, 81 是 13- 美丽的 ……

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.918396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.939570Z digest=sha256:50a68abaa29b82fcd786d11c78ae7b3c1f6ea841666826d8e6ce4a642d2e44fe

Observation 4cbf6fc3-c46d-481e-b262-bd555cb60db4 · outbound

This paper cites So m=2n +1.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs So m=2n +1

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.439602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.057220Z digest=sha256:8608e0555bf86c85ab0ce0221d25f8d568748c1f2af189394018d982439fa6a9

Observation 9b8bfd29-38bd-48e1-bf2f-e50db6f9a7dd · outbound

This paper cites So the key is that (k^2 - k) must be divisible by (b - 1), and the result d1 must be a valid digit in base b.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs So the key is that (k^2 - k) must be divisible by (b - 1), and the result d1 must be a valid digit in base b

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:35.054040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.910091Z digest=sha256:5611c690776c308aaedb62e9b65e57ea2ea9963521b19cd03ead3847fef0ff01

Observation 05fc8127-d709-4064-9a5f-fac78926bd11 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:35.064847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.913823Z digest=sha256:4d3e8bfa163466e52c1aa4feeaa2aeb1eb313a31ea61d6234177944175d13a78

Observation a1aa3bc4-2af2-4671-8ca8-8a02512354d3 · outbound

This paper cites Therefore, combining these, for each k from ceil(sqrt(b)) to b - 1, we need: (k^2 - k) is divisible by (b - 1) and k^2 - k >= b - 1.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Therefore, combining these, for each k from ceil(sqrt(b)) to b - 1, we need: (k^2 - k) is divisible by (b - 1) and k^2 - k >= b - 1

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:35.044482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.917522Z digest=sha256:636293463325722ed201346e4d9fabfa444981c92dfeb1943542f9e13a688a46

Observation f8cf4186-ac6b-4472-b977-24e3b109716c · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:35.034767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.920879Z digest=sha256:9666ecffbaee01385b0e162a34118f6fe4aa8caef9484811604c1caa379a92f5

Observation 1c5c712a-a78b-4210-8588-8e47a92674b2 · outbound

This paper cites Therefore, for each k from ceil(sqrt(b)) to b -1, check these two conditions.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Therefore, for each k from ceil(sqrt(b)) to b -1, check these two conditions

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:35.024651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.924915Z digest=sha256:e5b8c923d712f6a976689f7056302339fddb5519806a58c0d18eae927965cc46

Observation cc685f3f-b578-42ca-b37b-eb41411aca96 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:35.013672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.928869Z digest=sha256:1c8b406e3ad061a1278b22ea94b9f690fe42ab2aca3dfccfcddd0f854981319a

Observation 248f1929-41c1-4421-8e9b-2e98397c1c3c · outbound

This paper cites Wait, we need k ≡ 0 mod4 and k ≡ 1 mod3.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Wait, we need k ≡ 0 mod4 and k ≡ 1 mod3

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.998336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.932373Z digest=sha256:992eebc20b1442f7b0f7fe47ff087a9c404298907bbb806d77c3d7521929a3d6

Observation 5a1d1401-faa6-4779-a49a-992fd4cbb7e1 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.972012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.936223Z digest=sha256:29babc8daac9ea4f0347531fc78447fbd9e8c25d6bfa6a4a0fda450f9127c57b

Observation 50331e26-3cb5-4364-b4a0-d63b1b128d5c · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.880370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.943415Z digest=sha256:bd048f04687956ca5e9cefabfc85cf0947d401223221f498ad40d5f314e502bb

Observation 69523316-5a0a-4ced-86ff-ae9e6f855a54 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.855616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.946790Z digest=sha256:fedb5b86a29417a78cf4d0b25f29b4a65b16b57c301cf49b3617cac1a6194fba

Observation 8bfa344a-bd04-4246-a7a1-c37b6fbb8d4c · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.833167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.950044Z digest=sha256:b718f60d631e44557f05c0fc2c653c0132c74920120be6fa52739ae6e2de99b0

Observation d2d0c5fe-2ae2-42f1-a16e-9871ffebb8fc · outbound

This paper cites Therefore, solutions are k ≡ 0,1,7,8 mod14.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Therefore, solutions are k ≡ 0,1,7,8 mod14

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.813981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.953283Z digest=sha256:215262f480cc017d42502ddc739740f01b263650ee8365e04e4a9b146be94850

Observation 502f8ee2-9643-4803-b360-31f7cfb63b38 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.800199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.956788Z digest=sha256:316f3c79e1c6d2aef6d612eac87b688f648fd11ce7942cb9030f1e1db7ee0186

Observation 70926f27-5375-4ded-9994-39a37093d777 · outbound

This paper cites k ≡ 1 mod7 and k ≡ 0 mod3.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs k ≡ 1 mod7 and k ≡ 0 mod3

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.787586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.960067Z digest=sha256:c523638fd30ee7050c8899a9c8bc8054877420eeb1502f8220687b719a0664d9

Observation b41dc687-65d3-48ce-8ea7-b20203835284 · outbound

This paper cites So 3m +1=7n.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs So 3m +1=7n

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.774798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.963367Z digest=sha256:c43a79ab8547f4700f00a4db288d05a72f88c0fda907e8a11359ef75725f86ef

Observation fbcbe4c1-7583-4f2c-b7f0-16357c309bad · outbound

This paper cites Therefore, solutions are k ≡ 0,1,7,15 mod21.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Therefore, solutions are k ≡ 0,1,7,15 mod21

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.763324Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.966621Z digest=sha256:b8d226dddaffcf5257a7354baeaf43e35114ee318f0e31cd82736c4153fdf80b

Observation 00721c18-697c-400d-bea0-eae593200bec · outbound

This paper cites 等等, 0 mod 4 和 0 mod 5 的解是 k ≡ 0 mod 20 。.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 等等, 0 mod 4 和 0 mod 5 的解是 k ≡ 0 mod 20 。

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.750467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.970050Z digest=sha256:584dafc41e95bdb13f3fe57235cd8cfb54e9665a2e927518f507c915ae8b9faa

Observation bd5e795a-e571-4d5b-ae69-e591a764ed5a · outbound

This paper cites Solve k=4m=5n +1.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k=4m=5n +1

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.738170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.973079Z digest=sha256:4760235fb6abd359453b8019e4cf236eff64ca8abc6568a7b16cd72ea8de80e0

Observation 008f4b57-edd4-41a8-9c52-cdd31245c2a6 · outbound

This paper cites k=4m +1=5n.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs k=4m +1=5n

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.723616Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.976499Z digest=sha256:5bf35f4eb361ae5676a48affab2201590226019e7b8bf7be359ad42a38bd76b1

Observation 838a2172-aa09-4873-9398-8c10a3e105d6 · outbound

This paper cites k ≡ 1 mod4 and k ≡ 1 mod5 =>k ≡ 1 mod20.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs k ≡ 1 mod4 and k ≡ 1 mod5 =>k ≡ 1 mod20

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.710470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.979823Z digest=sha256:89c1c051df36425f4a4b3d5ff011728e5702c02199b709912bcf26ee84565c97

Observation 055e9d3f-de5e-4f56-ab25-d776f90fa916 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.698014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.983034Z digest=sha256:a2984a17fdeab522de4aee5fa92b2ab4844a520f21a260a82a06175abdb96902

Observation c06f8c2f-c246-490d-8dff-e1ac39d16ded · outbound

This paper cites 3m ≡ 1 mod5.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 3m ≡ 1 mod5

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.684367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.986443Z digest=sha256:648b037d0d53c94e2ee8aa4e645d9ddc36bf539b8437a7e237b1eec6d73a19d2

Observation 248a8d6a-467b-4fdb-ac39-68cdddd43033 · outbound

This paper cites 3m +1 ≡ 0 mod5 =>3m ≡ -1 ≡ 4 mod5.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 3m +1 ≡ 0 mod5 =>3m ≡ -1 ≡ 4 mod5

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.672262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.989659Z digest=sha256:d327bbe4f78f09ffcca993c3667246933fba3cbefe64c0f1c3940d365f596682

Observation 0cdc4d25-71ca-49ef-bcc3-34b817290074 · outbound

This paper cites Thus, solutions are k ≡ 0,1,6,10 mod15.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Thus, solutions are k ≡ 0,1,6,10 mod15

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.659354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.992774Z digest=sha256:90cfd648b8d85ee2f06067d274b11b399f67f8cbbbcdfb15b1df7d9c6950fccb

Observation 946103fe-182d-46c4-b986-4e9dd44c92b5 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.646906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.996078Z digest=sha256:e1e17e732ef7cca6679fa9fe24768bf40a5ddff39937a447d6639cb02e385275

Observation d10f36c0-c4e3-497a-b2e9-f72c8efa4cec · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.634989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.999488Z digest=sha256:dc5421d84d49a76e356477979807c45e62417cd527cf9d9709b7a7d09c6d53b4

Observation 40218d17-086c-453a-aeac-844e092887b7 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.622658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.002543Z digest=sha256:e49f327c6a93d788e10f5a7da6f56e5414cae83040b01b168dedbb2f7c8d2586

Observation 8fd1eba1-e5f9-4ad9-b067-8e51b3d23da1 · outbound

This paper cites 20 / 35 Thus, solutions are k ≡ 0,1,3,4 mod6.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 20 / 35 Thus, solutions are k ≡ 0,1,3,4 mod6

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.610672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.005726Z digest=sha256:4b6cf2111cce751648bcd6d019519e18e4d544aedb95f2f470a7e4485c7547bb

Observation f3091989-5d62-4397-95ad-871974525e4d · outbound

This paper cites So k=0 mod210.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs So k=0 mod210

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.597861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.008936Z digest=sha256:acaf35219a07e21320e2a6443ad0f0913cf4ab7e1820a8da2da39d5a4ebba1d7

Observation 188b4cd6-d787-420b-b5a3-dd6e69083ba4 · outbound

This paper cites So k=30m ≡ 1 mod7.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs So k=30m ≡ 1 mod7

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.584901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.012517Z digest=sha256:cb792f8020587ac31254294b16e044537e192ac75d18a4c893a393f5d08b2ec8

Observation a6d21dfc-aa6c-4226-b12b-dd7dd41f7e20 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 37

Resolution
parse uncertain
raw_fallback, observed 2026-08-15T18:57:34.571468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.015886Z digest=sha256:1285a0979214e0fe1659e9e696e627418b2a1c24f5b04d7f2c4688a80bbc452d

Observation 03cbc1fe-8171-4fec-869e-c18f46703847 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.559859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.019557Z digest=sha256:5f2bcc79615178e4d41093bcf36a43f21b15a96ed89ff92eadb06d2add439f3f

Observation 19764299-d285-48e4-a408-491f5cac0ca0 · outbound

This paper cites 等等,也许我们可以枚举所有可能的组合: For each prime factor, choose k ≡ 0 or1 modp.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 等等,也许我们可以枚举所有可能的组合: For each prime factor, choose k ≡ 0 or1 modp

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.547020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.022892Z digest=sha256:24ea26f4eaed31cc896848ae02667dc4f07e28d564f05011228902b4aaf1cad8

Observation 8762ffad-f31e-4643-82f4-c73416412d36 · outbound

This paper cites k=0 (excluded).

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs k=0 (excluded)

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.536119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.026145Z digest=sha256:0d8f45c3acb0174c5b9a64edc0554956e6292040be14209107e612343f0380be

Observation 1decb30d-4a58-4506-a573-2bc5eb116772 · outbound

This paper cites k=1 (excluded, <15).

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs k=1 (excluded, <15)

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.524227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.030049Z digest=sha256:4cdda58d6b445c5878f86a31a7d592c2e7e2cb58a4300ce61b370f2de2c3e427

Observation 344ceb91-c951-4f68-80c3-8d79b8c6667a · outbound

This paper cites Similarly, compute others.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Similarly, compute others

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.512143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.033795Z digest=sha256:8f14cf75c8e751e4e3e69f6de14f0a543d5973fa69a37dd6a5c14f10380f9768

Observation 5b98493c-2e18-4a9b-a62b-f6cb15ec0c4f · outbound

This paper cites 等等, 120 。 Similarly, other combinations will result in numbers like36, etc.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 等等, 120 。 Similarly, other combinations will result in numbers like36, etc

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.499651Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.037627Z digest=sha256:d45a00a64eb49727937d5cbc01f660b9e26df5283307207749613ca6b432a374

Observation 37d6be25-e869-4962-8d1c-0af4ba31a8d1 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.485589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.041717Z digest=sha256:9c7e2149bf361e526172545d5ac3fda725656a87333a2f4fcc263d0848a5d8ca

Observation af1a836f-e8c5-453a-baad-16a487d624ae · outbound

This paper cites Solve k=6m ≡ 1 mod5 =>6m ≡ 1 mod5 =>m ≡ 1 mod5.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k=6m ≡ 1 mod5 =>6m ≡ 1 mod5 =>m ≡ 1 mod5

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.473738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.045748Z digest=sha256:4ece2453d2fe248eeb1a4a8944c27301e00cc7992eef7248596c221cc65e765a

Observation a848f3e1-0c25-44b2-b497-f4c4e94f2432 · outbound

This paper cites Solve k=10m ≡ 1 mod3 =>10m ≡ 1 mod3 =>m ≡ 1 mod3.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k=10m ≡ 1 mod3 =>10m ≡ 1 mod3 =>m ≡ 1 mod3

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.462294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.049510Z digest=sha256:a13437d7bbd88dbabb6a83223f14ab765ce6a8008582f6a255f5a644de612433

Observation dd15de78-c531-43de-b694-a900137b5b7e · outbound

This paper cites Solve k ≡ 1 mod3,5 and ≡ 0 mod2.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k ≡ 1 mod3,5 and ≡ 0 mod2

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.450663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.053366Z digest=sha256:271b39f19634d920cc58c448311a3a4c46c94225c48339927ba035b6c5d9cc52

Observation b765e486-ce68-4999-a3bf-954cccea279c · outbound

This paper cites Solve k ≡ 1 mod2,5 and ≡ 0 mod3.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k ≡ 1 mod2,5 and ≡ 0 mod3

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.428168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.060747Z digest=sha256:f6bc431a7dc5c07140616f4691a9b825dee0bf2c387aa4ff9293ed220d211b7e

Observation 2d9820ea-b66c-4ca1-b381-d621e5726295 · outbound

This paper cites Solve k ≡ 0 mod5 and ≡ 1 mod6.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k ≡ 0 mod5 and ≡ 1 mod6

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.416584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.064401Z digest=sha256:d8938ed306e2cdb1e15c8dcc7b9469f187f9d60fb851e122ebff3822ebf89b8f

Observation 5ed6446e-4ce4-441f-a261-9102f7ce9eec · outbound

This paper cites Thus, the8 solutions mod30 are0,6,10,15,16,21,25,30.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Thus, the8 solutions mod30 are0,6,10,15,16,21,25,30

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.405231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.068175Z digest=sha256:bdd43c584d0a1f23ee7cd4fce57bac9a25a7df1839c4440173c92caa6d3ec36e

Observation 9841f53d-ab96-43b5-8712-3048158163aa · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.393373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.072382Z digest=sha256:5ea6630a4f367cd939147ea304ffc8261bab4bfa10990889368c6dbaa8fd7a90

Observation efa3fa40-43cd-421b-b0af-53dc1057de83 · outbound

This paper cites 等等,这样会得到以下 8 种组合: For each prime, choose 0 or1: 0,0,0:0 mod42.● 等等,这会引发⼀些疑惑。我们来枚举所有组合吧:.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 等等,这样会得到以下 8 种组合: For each prime, choose 0 or1: 0,0,0:0 mod42.● 等等,这会引发⼀些疑惑。我们来枚举所有组合吧:

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.381453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.076277Z digest=sha256:3936d97bf3074dd3edf89afa047c7a434ac173fea7f371897eefecae368f91a7

Observation e15e20bf-b71b-46d9-b9a8-19a6894b08ca · outbound

This paper cites 等等,这⾥可能需要同时满⾜以下条件: k mod 2 = 0 , k mod 3 = 0 , k mod 7 = 0 。因此, k ≡ 0 mod 42 。.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 等等,这⾥可能需要同时满⾜以下条件: k mod 2 = 0 , k mod 3 = 0 , k mod 7 = 0 。因此, k ≡ 0 mod 42 。

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.369798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.080192Z digest=sha256:272116e7596db8687aed7e162b71c35524d1c8efb66334cd6e8452c9362dd1b6

Observation 311bcd3b-dc54-403f-a06e-f3db97069bc3 · outbound

This paper cites Solve k=6m ≡ 1 mod7.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k=6m ≡ 1 mod7

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.357922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.084179Z digest=sha256:353342b7e5948e9c8d61604337756c8e5e118d7795094e34404cbbbc123fb09f

Observation 34738ff1-3585-4272-bea6-36359957a23c · outbound

This paper cites So k ≡ 0 mod14.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs So k ≡ 0 mod14

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.346490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.088236Z digest=sha256:cfb1549db2d4e9cbe7d8245a07ecb97ba2b2c00f22c441ab5d68487a375c417f

Observation 316f606e-9229-4c92-b8fe-f551985ea46c · outbound

This paper cites Solve k ≡ 1 mod3,1 mod7, and0 mod2.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k ≡ 1 mod3,1 mod7, and0 mod2

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.334505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.092577Z digest=sha256:89997634de96791d7f5182ca36bd6993242802eb422f688c50b67f51cbe20483

Observation e263fa6f-6250-4857-9a6c-f3476f137703 · outbound

This paper cites Similarly, impossible.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Similarly, impossible

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.322915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.096553Z digest=sha256:6f4b0371fb0e8d3e6aba320bbd75f6f39a312c95abd93b6ea1373becc4c124a5

Observation d6e9bc17-688a-4dc2-b48d-86b454ff1a56 · outbound

This paper cites Solve k ≡ 1 mod2,0 mod3,1 mod7.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k ≡ 1 mod2,0 mod3,1 mod7

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.310434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.100765Z digest=sha256:cf0f731dd0c60a44d28090d780c1328362d2e9f86c50f6d3eb50c1e7578db115

Observation 3a28628f-651a-44f3-9c83-232aac8af86e · outbound

This paper cites Solve k ≡ 1 mod2,1 mod3,0 mod7.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k ≡ 1 mod2,1 mod3,0 mod7

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.298542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.105837Z digest=sha256:1ebade4743c6c97803b56342ae7e3dd43135f93b5ed32dde3be56da2d966200c

Observation 82a0445f-cd64-49dd-8a03-309e2183de3a · outbound

This paper cites Solve k ≡ 1 mod2,1 mod3,1 mod7.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Solve k ≡ 1 mod2,1 mod3,1 mod7

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.286659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.110512Z digest=sha256:9ae3da71d27d5ba6f139fe1a921b591fde086e02dabfeb030a6e76954a4ee19b

Observation 596f93fa-4933-4441-b29f-1d9ad4777ada · outbound

This paper cites 等等,第四种组合是⽆效的。.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 等等,第四种组合是⽆效的。

Reference 62

Resolution
parse uncertain
raw_fallback, observed 2026-08-15T18:57:34.275098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.114966Z digest=sha256:018e4484e639b3b1b042c901a0f5ac61f2e399a073a5bdb03ee46286d20eb900

Observation a7d10471-0e5f-4e05-906f-ada0d3640dd5 · outbound

This paper cites 6.15 mod42.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 6.15 mod42

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.263113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.120438Z digest=sha256:2d80261863cd486a97b9978318f06aa558c903094c05c4e6a300959d3e7d527f

Observation 8909d207-ea1f-41fd-b8ba-80b495878b51 · outbound

This paper cites 2.1 mod210.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs 2.1 mod210

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.250174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.124557Z digest=sha256:2a520bd25100e31956bd3ffed7fb59a9336f6cabc61efa86e917c05bb3b94003

Observation 85ff7e1e-a02e-4a65-af69-1bb92b30f8fb · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 65

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.237144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.128630Z digest=sha256:141c62110f2441575b460c6e3692f81fd426d56e2344df5f5956f4b45776b9f6

Observation 5f5cb941-c5d7-4d7f-84cb-c5046c7fae91 · outbound

This paper cites Key steps:.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Key steps:

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.224800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.132649Z digest=sha256:91a10570f4adeee02d76b3329d0031dfb641197c90e2a39a1045f00994bd30da

Observation 13e7f42c-317d-46f7-befb-f535bb6b9c89 · outbound

This paper cites an unresolved cited work.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs Unresolved cited work

Reference 67

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:57:34.212584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.136444Z digest=sha256:d7a741b74c3e2c10924b2e7479c8ec35ae26042bb63bba34acd03b8efff8fd79

Observation 92150efe-b075-4a44-a279-3ab8943895ae · outbound

This paper cites This translates to the condition that \( (k^2 - k) \) is divisible by \( (b - 1) \).

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs This translates to the condition that \( (k^2 - k) \) is divisible by \( (b - 1) \)

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:57:34.200504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:34.140767Z digest=sha256:7852a91900ab00210838598fcbbb75d43663c74c941a5000648487ad4c9dec40

Observation 451a9eb7-57db-44d8-bfbc-28c0b2d9d3db · outbound

This paper cites AdaMCoT: Rethinking Cross-Lingual Factual Reasoning through Adaptive Multilingual Chain-of-Thought.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs AdaMCoT: Rethinking Cross-Lingual Factual Reasoning through Adaptive Multilingual Chain-of-Thought

Reference 2023

Resolution
unresolved
no resolver link, observed 2026-08-15T18:57:33.889939Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T18:57:33.889939Z digest=sha256:28369402f22941257c0245146271ad90e1e66ad7dbed1752e0bec7b3b157fe57

Observation 599a168f-a068-4c6c-a4ea-40bd99d1e5f8 · outbound

This paper cites LayAlign: Enhancing Multilingual Reasoning in Large Language Models via Layer-Wise Adaptive Fusion and Alignment Strategy.

Less Data Less Tokens: Multilingual Unification Learning for Efficient Test-Time Reasoning in LLMs LayAlign: Enhancing Multilingual Reasoning in Large Language Models via Layer-Wise Adaptive Fusion and Alignment Strategy

Reference 2025

Resolution
metadata mismatch
local_arxiv, observed 2026-08-15T18:57:34.177316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-15T18:57:33.894347Z digest=sha256:1dd7a9c5634a0c7d05aacab96d242fb52d6a66d5bb32f565eb3445091fa3a38c

Pith citing papers

No inbound Pith citation observations are available.