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Paper Citation Record · LEDGER

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum

As of 6 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2510.00526.

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

pith.paper-citation-record.v1
2510.00526 v3

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-25T07:41:38.513152Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T18:28:58.515666Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T00:30:53.546973Z

Reference resolution

22 of 22 outbound references displayed

  • verified exact0
  • verified fuzzy6
  • unresolved16
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 182d7cb3-a1ed-4877-9687-437534648298 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.866521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-25T07:41:38.513152Z digest=sha256:8ed36462932eff8f0871e7e8016865d0147f9f531f3bf4e37b0b9575f66670be

Observation 2ef103cc-a80e-4da6-ab6a-89a689c08c9e · outbound

This paper cites Then max q∈∆V−1 F(q) = 11 √ 33−59 768 ≤0.00546, and the maximizer is attained by a vector with qi =q j = 9− √ 33 24 ,all remaining mass1−2q i placed on one coordinate.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Then max q∈∆V−1 F(q) = 11 √ 33−59 768 ≤0.00546, and the maximizer is attained by a vector with qi =q j = 9− √ 33 24 ,all remaining mass1−2q i placed on one coordinate

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T07:46:43.910694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 7acf9f7a-8f61-4cd7-8d13-b4ea4fd095a8 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.923047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 5f453720-012b-407b-80c7-d96696c94cf8 · outbound

This paper cites Substituting and simplifying, max q∈∆V−1 F(q) =G(x ⋆) = 11 √ 33−59 768 ≤0.00546.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Substituting and simplifying, max q∈∆V−1 F(q) =G(x ⋆) = 11 √ 33−59 768 ≤0.00546

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T07:46:43.935938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation c226ba57-eb42-40e3-953c-2f4b1633565b · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.939570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 21a36db4-d6fc-44cb-b564-cec8a4123560 · outbound

This paper cites • ˙R(θ(1) t ) t=0 ≤ ˙R(θ(2) t ) t=0 in Model Weak End.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum • ˙R(θ(1) t ) t=0 ≤ ˙R(θ(2) t ) t=0 in Model Weak End

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T07:46:43.944845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation f2de253f-1c32-4b15-8560-809be80ea72b · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 7

Resolution
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raw_fallback, observed 2026-05-25T07:46:43.927303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation f32419b0-1819-400c-b7f8-9c6d977deb55 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 8

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raw_fallback, observed 2026-05-25T07:46:43.856090Z

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No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 22218665-224b-4281-8d29-7cb8c03a7027 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 9

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raw_fallback, observed 2026-05-25T07:46:43.917368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation aeca0771-0669-4902-ad6e-1ef76609097d · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 10

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raw_fallback, observed 2026-05-25T07:46:43.880111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation ad5e230b-1b7a-4b92-aa48-ad5e2e135041 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 11

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unresolved
raw_fallback, observed 2026-05-25T07:46:43.883811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 74446913-8880-475c-8ffa-fbee1110b7b3 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.905949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 6c45d53e-2e27-494a-80a9-91aefea34454 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 13

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unresolved
raw_fallback, observed 2026-05-25T07:46:43.895821Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-25T07:41:38.513152Z digest=sha256:0a9a53e8ffa7a12975d683402a47125e3d805906ff3db64ec4b5a3f3786f03a6

Observation e7590d63-aac1-40bb-bc43-e85d8ba9c4e8 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 14

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raw_fallback, observed 2026-05-25T07:46:43.907530Z

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No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 6ed42eb2-0cc9-45c8-9215-2133b67a383e · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.893510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 3b5dd3a2-a958-420f-85f5-750a9d35456c · outbound

This paper cites Denote the label noise rate to beE.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Denote the label noise rate to beE

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T07:46:43.911338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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Observation 3ab523ca-ae29-49d6-a372-9f36e6baf09b · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.898493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-25T07:41:38.513152Z digest=sha256:97a8c38459142e03bcb5712f57e078e14c1e6cd7355be2e1bc453500ea67e53f

Observation 0a6dd900-6202-4501-a53c-8093edc1b9ff · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.949181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-25T07:41:38.513152Z digest=sha256:9f534e78deb5748d0c446d31761517fa2bf0d017ae95ead4524e1a341ea9bada

Observation 8d418451-5bbb-4015-a807-065976140735 · outbound

This paper cites 1 E Ex h q˜yqy∗ (f ′ 2 −f ′.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum 1 E Ex h q˜yqy∗ (f ′ 2 −f ′

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T07:46:43.870721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-25T07:41:38.513152Z digest=sha256:6af73793ae4213cfd9a48a6530b0ce2c314a083a5f0a5e2b75b0122993026f7b

Observation 7a2d0e4f-0735-45b2-a039-974997f72089 · outbound

This paper cites 5, we have that givenQ <0, min 0.95≥q ˜y+qy∗ ≥0.55 |Q| ≤ −max 0.95≥q ˜y+qy∗ ≥0.55 1 + 2(q˜y+q y∗)2 −3(q ˜y+q y∗)≤0.045 Also by Assumpion.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum 5, we have that givenQ <0, min 0.95≥q ˜y+qy∗ ≥0.55 |Q| ≤ −max 0.95≥q ˜y+qy∗ ≥0.55 1 + 2(q˜y+q y∗)2 −3(q ˜y+q y∗)≤0.045 Also by Assumpion

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-05-25T07:46:43.931873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-25T07:41:38.513152Z digest=sha256:8b09687a39ad7e2e4f1dbaed1d5c65b15faa1f8063cccea1c7028e57585a083d

Observation 4fc04d83-0db5-49a0-9dd6-50f12af0f7f5 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.875667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-25T07:41:38.513152Z digest=sha256:81ff8a8493293ff548d563ae8e09faa2ed8f064c1547a425197e8d3ff436c100

Observation 8c4a213e-a27b-447e-bf85-63c9217764d1 · outbound

This paper cites an unresolved cited work.

Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-05-25T07:46:43.875455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-25T07:41:38.513152Z digest=sha256:d84fe4f55ac5d985f682245b3862ffcc37d1b00db19ab9d5e33a9ff5df2ca664

Pith citing papers

Observation 68d7d5b9-93b3-4089-8a19-d8225f32db37 · inbound

Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning cites this paper.

Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum

Reference 129

Resolution
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arxiv_id, observed 2026-05-25T03:01:06.856807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

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