Paper Citation Record · LEDGER

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning

As of 9 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2506.06877.

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

pith.paper-citation-record.v1
2506.06877 v2

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:50:52.589230Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

40 of 40 outbound references displayed

verified exact0
verified fuzzy26
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c0ffd5a8-9653-4055-bf8c-fc097a49193c · outbound

This paper cites - For n = 1: (21 − 1)(31 − 1) = (2 − 1)(3 − 1) = 1 · 2 = 2 Since 2 is not a perfect square, n = 1 is not a solution.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning - For n = 1: (21 − 1)(31 − 1) = (2 − 1)(3 − 1) = 1 · 2 = 2 Since 2 is not a perfect square, n = 1 is not a solution

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:58.815811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bf2401fd-78dd-4c80-af59-37c836414f9c · outbound

This paper cites Then A · B = m2.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Then A · B = m2

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:58.796164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d40f91b3-e126-439c-b9a1-f1761660bd8d · outbound

This paper cites DeepSeek-V3 Technical Report.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning DeepSeek-V3 Technical Report

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T05:50:49.397263Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e104101e-e157-47ab-9789-edbe58235f57 · outbound

This paper cites LLM Evaluators Recognize and Favor Their Own Generations.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning LLM Evaluators Recognize and Favor Their Own Generations

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T05:50:49.513946Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b12c2113-dbc3-4f3b-bc7e-d081fa75d0cf · outbound

This paper cites Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T05:50:49.653031Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 014abebb-2fdf-47f5-bc04-04ebbe0dca09 · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:57.716737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5b9a4e03-f542-4d12-93dd-ee10dfbb1637 · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:57.305382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fd780392-8395-4b35-b06a-a35cd21a1e5c · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:58.777450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 07602c5b-5dc9-414b-9b3e-64a282e323ca · outbound

This paper cites Here, a + b + c = 3 and ab + bc + ca = 3, which satisfies the given condition.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Here, a + b + c = 3 and ab + bc + ca = 3, which satisfies the given condition

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:58.753465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation faf7d601-2cd0-4203-b353-46b01b3735a6 · outbound

This paper cites The condition a + b + 0 = ab + 0 + 0 simplifies to a + b = ab.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning The condition a + b + 0 = ab + 0 + 0 simplifies to a + b = ab

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:58.735991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dd6edfbc-b5f5-41fd-b906-a909b66e024a · outbound

This paper cites For instance, if we take a = 1.5, b = 1.5, and c = 0.375, the inequality still holds for k = −3+ √ 13 2.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning For instance, if we take a = 1.5, b = 1.5, and c = 0.375, the inequality still holds for k = −3+ √ 13 2

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:58.711178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9c4fa524-a07c-40ab-9148-de18db3cb993 · outbound

This paper cites - Place E at (3, 0) since AE = 3.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning - Place E at (3, 0) since AE = 3

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:58.679150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a1c6314a-986e-4d59-973b-a4f141a452dc · outbound

This paper cites Let AC = x.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Let AC = x

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:58.657511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e56727e8-ec6b-4fe0-8707-2e782bb11311 · outbound

This paper cites The coordinates of D are given by: D = 5 · c_x + x · 3 5 + x , 5 · c_y + x · 0 5 + x where C = (c_x, c_y).

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning The coordinates of D are given by: D = 5 · c_x + x · 3 5 + x , 5 · c_y + x · 0 5 + x where C = (c_x, c_y)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:58.642103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 86dc26a5-da7a-43e4-941a-da904bf9c723 · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:58.559012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f6bb27b5-430a-4f9f-9367-8bdd1176d4c9 · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:58.191135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 55aeae37-b152-403a-9373-1abc62579bf7 · outbound

This paper cites This simplifies to 8ax + 16a + 4b ≤ 2x + 2.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning This simplifies to 8ax + 16a + 4b ≤ 2x + 2

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:56.911498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 289c1374-d442-4030-9cec-cbe024d6c7d7 · outbound

This paper cites This simplifies to 24ax + 144a + 12b ≥ 6x + 30.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning This simplifies to 24ax + 144a + 12b ≥ 6x + 30

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:56.627631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7d4e40ab-da9c-4bc0-9168-0d4d3059e39a · outbound

This paper cites Therefore, the function is: f (x) = 1 4 x2 − 1 2 x + 1008.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Therefore, the function is: f (x) = 1 4 x2 − 1 2 x + 1008

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:56.396319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9454a065-9de6-424e-8d77-e73dee526392 · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:56.211585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6f242a36-863c-48e6-be22-eebf87ada026 · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:56.016861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d3613f5b-b374-4b9a-ae9a-c1f7bbe40792 · outbound

This paper cites These roots satisfy the sum of roots being 0 and the sum of the products of the roots taken two at a time being -10, which matches the conditions.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning These roots satisfy the sum of roots being 0 and the sum of the products of the roots taken two at a time being -10, which matches the conditions

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:55.841160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fb00a21a-5873-4ac6-92ff-a9efe1bc070e · outbound

This paper cites Discriminant analysis shows that a larger m cannot be constructed.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Discriminant analysis shows that a larger m cannot be constructed

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:55.633729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0aa2b747-7e29-4bb0-b744-4e68cdd007a9 · outbound

This paper cites We can also verify the result by solving for the general formula of the recurrence relation.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning We can also verify the result by solving for the general formula of the recurrence relation

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:55.453832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b6aa4ce1-474e-4615-ac2d-6529602585b9 · outbound

This paper cites The left side, sin(πx), also has a period of 2.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning The left side, sin(πx), also has a period of 2

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:55.308672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation be5347b0-2237-4fb2-a614-97af45307c06 · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:55.138238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d0e9b299-f5b5-417b-8b47-358514efe451 · outbound

This paper cites Let x = 2k + t (where t ∈ [0, 2)).

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Let x = 2k + t (where t ∈ [0, 2))

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:54.961296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4bef746c-19e8-428c-bd49-d331e936f3c1 · outbound

This paper cites Therefore, the sum of the corresponding x solutions is: (2k + t1) + (2k + t2) = 4k + (t1 + t2) = 4k + 1.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Therefore, the sum of the corresponding x solutions is: (2k + t1) + (2k + t2) = 4k + (t1 + t2) = 4k + 1

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:54.788106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1761d0af-0f83-4dd7-9127-4642b0139f21 · outbound

This paper cites — Final Answer 12 C.3 IMO Case Study – IMO: Inequality Manipulation Errors Problem Description: Let R>0 be the set of positive real numbers.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning — **Final Answer** 12 C.3 IMO Case Study – IMO: Inequality Manipulation Errors Problem Description: Let R>0 be the set of positive real numbers

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:54.584236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6c5d672d-aaf0-4d0e-94e9-c5340ab04cbc · outbound

This paper cites - Simplifying both sides by dividing by f (x) + f (f (x)) (which is positive), we get: x ≥ f (f (x)).

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning - Simplifying both sides by dividing by f (x) + f (f (x)) (which is positive), we get: x ≥ f (f (x))

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:54.379042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 694f994e-7e1b-4c85-a90a-9743c07870df · outbound

This paper cites - Simplifying both sides by dividing by f (y), we get: f (f (y)) + f (y) ≥ f (f (f (y))) + y.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning - Simplifying both sides by dividing by f (y), we get: f (f (y)) + f (y) ≥ f (f (f (y))) + y

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:54.164443Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 51a5b865-8fcf-423c-b573-5ff221bd95c5 · outbound

This paper cites Combining these, we conclude: f (f (x)) = x - This shows that f is an involution, meaning f (f (x)) = x for all x >0.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Combining these, we conclude: f (f (x)) = x - This shows that f is an involution, meaning f (f (x)) = x for all x >0

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:53.988984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d7514281-8653-48ee-97cb-f5481e65009f · outbound

This paper cites an unresolved cited work.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:50:53.828655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9c273267-f51c-4c7d-9b70-3b4eb9ad90a8 · outbound

This paper cites similar contradictions arise.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning similar contradictions arise

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:53.641272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6668bfe9-d5a4-4214-a8d6-417590bf2b7a · outbound

This paper cites - p = k2 − 1 = (k − 1)(k + 1).

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning - p = k2 − 1 = (k − 1)(k + 1)

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:53.498411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3ad56bfd-fd89-4ef7-8318-ce85c9bb3218 · outbound

This paper cites - Factoring: (k − p)(k + p) = 16.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning - Factoring: (k − p)(k + p) = 16

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:53.326381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6ece6ff5-4395-4e32-a5f5-b4d7135aa932 · outbound

This paper cites - This factors as 34 · (32 + 24) = 81 · 25 = 452.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning - This factors as 34 · (32 + 24) = 81 · 25 = 452

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:53.169137Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8d4459b3-f778-42b8-925d-a1987daaf1ec · outbound

This paper cites - This factors as 38 · (3 + 1) = 6561 · 4 = 1622.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning - This factors as 38 · (3 + 1) = 6561 · 4 = 1622

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:50:53.038669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2a9535f2-ad84-43ff-aad2-9dc73c1ddeef · outbound

This paper cites LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning LLMs-as-Judges: A Comprehensive Survey on LLM-based Evaluation Methods

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-07T05:50:49.311179Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ade5b51c-9d19-431a-80a4-3a90f6739eeb · outbound

This paper cites DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning.

Right Is Not Enough: The Pitfalls of Outcome Supervision in Training LLMs for Math Reasoning DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-07T05:50:49.203073Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.