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Paper Citation Record · LEDGER

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning

As of 4 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2605.09270.

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

pith.paper-citation-record.v1
2605.09270 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-30T22:49:29.042334Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-03T06:30:56.289259+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

29 of 29 outbound references displayed

  • verified exact0
  • verified fuzzy9
  • unresolved20
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fc858782-6316-4d8d-a752-b4c90171ae69 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.624488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

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Observation a17555c0-5391-4ca6-a6aa-4fbd7645942c · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.637453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:af5e60143a06af5c2126a82607874520a8dee84c73a47cbc063a55b35ddc4fe2

Observation 06c96f3f-7e8d-4ed0-8fd7-f51e8c3ff31b · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.612440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:5a07f72d363a617cb8cff4249f8365d31c3a9764c3bc3e4a929edd0c04769e34

Observation e4adbb80-4485-419d-afa8-b1a092936aa1 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.643849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:a828d4dbc8388c5bf5b1a7e1d7bfe743ddd383cf652d72530480fdd08f7309d5

Observation b81230cb-ca36-4be7-9cbf-5d51484bc982 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.606157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:33286902d001b73cf9259b1da4bc05af79b89d1c4310b1e1f0ffe787175dcce2

Observation cce72930-0341-4d4a-8161-65f08b4f56fd · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.640612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:5a89ff74d54d4bfa3dc5c13eec7a3fe8ffdeb4a63bd49c00eb4caec9dbd744af

Observation 5559c495-1128-4d63-a0cd-1742efa3ca05 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.603183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:469fb84e8ff80f74d9fe030cbcdd023b88840a524dd606ebebcab77cbe1451f5

Observation 2c1f5a4f-536e-435e-ae7e-1e2d6abebfc0 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.604685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:357152647452f14ae2b8aa355ad381d6088e4443be0b72eabd685a6116a0cc21

Observation d4bb77d1-abbd-484c-bb75-0156a04ba5ac · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.607661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:07e75a648a48fcb9395e2a7aab6ca8774563daa6f90c493f24cfa199cd1aa07c

Observation 5b19bd5b-fdb0-4e5d-ad83-b5ff382ba5c0 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.609197Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:c23ada44a18c1a47cc87cdc7315f35f24ac7c7a44e9bcd2106a91bb899b8905c

Observation b01f70e9-b2ff-4340-b9de-c28f0b5aab19 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.614886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:ae063a76aa085a2d028fd35da630eea1af5d1bb887d19978ed9eeb34c3ed039e

Observation c16a8c71-03f6-45bd-a6f2-fa0adb9dc3f9 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.610873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:1c9f86c6b16eff049281f9b3ade41e2779953ca2de14bddad8e3e6ddb20788c8

Observation cc9d35df-9713-4525-b7c9-91d9d481b5e1 · outbound

This paper cites x4 + 4 = (x2 + 2x+ 2)(x 2 −2x+ 2)by completing the square.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning x4 + 4 = (x2 + 2x+ 2)(x 2 −2x+ 2)by completing the square

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.627615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:8a23ee13c4d44326764ca4937e26f8f5ea770cdf273671ecf939ede01cce4bb7

Observation d2c66e3d-f891-43ee-81e0-8dd6486fddd0 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.629180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:ad7ea3672ac2290daf3e35c50b1e39ee490064dc631eda5ff0ebeeddd209926f

Observation ba1e74e8-dec1-4e65-911b-70a7fdf05e3b · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.632136Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:65e6cee607eadcb84e7bf70ef79071c0f6da8319adada0ebaef965f66d8f3723

Observation c73cb36e-f064-4839-8437-a6949ee2dcf9 · outbound

This paper cites Pythagorean Theorem.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Pythagorean Theorem

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.630694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:eaebb5f63ed2d0509317d397e6d597e0fc903eb72c28908d50eb4ca3561b66f4

Observation 1da63e19-f0e9-49ac-8dc8-c6a6b228f3da · outbound

This paper cites am) describes the action of σ on a subset of elements{a 1, a2.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning am) describes the action of σ on a subset of elements{a 1, a2

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.635702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:c5064c7cb999d75c082bc92646215cb513248c3c79c2564d1ac51aeecdc02cab

Observation 1dd10a77-51fe-45df-a795-7fcb7e2f7d16 · outbound

This paper cites That is, if Ci = (a1 a2.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning That is, if Ci = (a1 a2

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.618151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:6f0b6790a1bcd91ba4528603d87ff565f6de3eb7b8b366ebb7fa3d26a076ae6c

Observation d509678e-6d5a-4870-bc12-d0c206d36b80 · outbound

This paper cites n} , repeatedly apply σ to trace the orbit of x under σ.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning n} , repeatedly apply σ to trace the orbit of x under σ

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.616557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:334afcb9dda7a665e04bffcfa30ddf88e26bfddd13d14dfe22ba1c4bfb3845ad

Observation 6a040cb2-565a-4bcc-83f9-f3fe4da67c4a · outbound

This paper cites n} into disjoint subsets, and the action of σ within each subset is uniquely determined.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning n} into disjoint subsets, and the action of σ within each subset is uniquely determined

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.619849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:4703b424ee701a7445e167557f0e74fab7a711a3feec1f0669132c464cbedc8a

Observation a9e025aa-51a0-4367-9850-02ea7ace21d6 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.621341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:11dc9f558433165a324beb13f72b63b92660503b94ec848c1d2f2f80a716bdaa

Observation 43787266-355e-4aac-9b1d-b9d0215cb43c · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.622856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:f8d7ef78f181a9485f460395797de1852dca2d73dd1ae372be2d708d3b0082b7

Observation bb093a55-600e-4372-8f01-03baf12230f7 · outbound

This paper cites Theorem Composition.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Theorem Composition

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.633874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:bffc34f27f07fbfdb1f909765b67351b26f291b45af291ee4b25ce6c8bda9531

Observation ac149b52-1d2f-43ee-b863-e84043b9c79a · outbound

This paper cites Theorem Composition.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Theorem Composition

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.626014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:77e503d788170761ed31f14b4d819fae619af1cfa1ae753e63a0c7745bddcfde

Observation c5d3c686-22d6-483c-84b5-f51a778a1f50 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.639083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:3f45c950098a1d1500fbdc931ba0dc0f9e602ac2b425e000b7690c7d9ee7e540

Observation bdf0874b-862c-4f34-a93b-8c18c03f8ece · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.642262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:8b8f56d33b3b69ad7e64710cf55f9cef0b39452f183236c497fe83c975a3e567

Observation f2207cd5-751b-4b79-a426-0970c0d7d34c · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.645479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:ed246e80b13f6ccf9bb7398b1bcab67487382e3e1fc2c074ac8a26d1d6accf88

Observation f796ae6d-f221-45d3-80f4-8f8d9ddcfff9 · outbound

This paper cites an unresolved cited work.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-07-07T12:43:46.648511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:8198b45b3089798adc1f3ff34aa1994091ff6103ffb3924ab2b11b2b26284517

Observation 2a0447d2-674f-4ece-9bec-f39c9d13a20f · outbound

This paper cites 21 Example 1.

Memorize Theorems, Not Instances: Probing SFT Generalization through Mathematical Reasoning 21 Example 1

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-07-07T12:43:46.646967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

source=pdf_text observed=2026-06-30T22:49:29.042334Z digest=sha256:697c3968158df47d75b454ac94a965bb137d5b4ca56bba3e4471fea47d6d4140

Pith citing papers

No inbound Pith citation observations are available.