Paper Citation Record · LEDGER

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons

As of 22 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2605.29395.

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

pith.paper-citation-record.v1
2605.29395 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-29T06:11:48.446361Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

21 of 21 outbound references displayed

verified exact4
verified fuzzy0
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 68f899fa-f4c5-43d8-a49a-1ed85053cb23 · outbound

This paper cites How arena works.https://arena.ai/how-it-works, 2026a.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons How arena works.https://arena.ai/how-it-works, 2026a

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 371314e1-cd82-4728-9da0-8b5567f94400 · outbound

This paper cites Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-06-29T14:53:32.261037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 99c92b31-9a62-4ea3-9eeb-0a40a33facfd · outbound

This paper cites Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-07-21T02:21:29.933376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0d922e7a-cdae-4511-b1aa-2e24cb3d5176 · outbound

This paper cites Uncertainty Quantification for Ranking with Heterogeneous Preferences.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Uncertainty Quantification for Ranking with Heterogeneous Preferences

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T14:53:32.251484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f98d975c-125d-4bdf-8bed-2a08ba74915a · outbound

This paper cites LLM Evaluation as Tensor Completion: Low Rank Structure and Semiparametric Efficiency.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons LLM Evaluation as Tensor Completion: Low Rank Structure and Semiparametric Efficiency

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-06-29T14:53:32.253708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e794717d-130a-4fe9-98d3-a56567fdf431 · outbound

This paper cites Dynamic Model Routing and Cascading for Efficient LLM Inference: A Survey.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Dynamic Model Routing and Cascading for Efficient LLM Inference: A Survey

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-06-29T14:53:32.256114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e8727e01-2b49-49bc-b67f-60408b787a36 · outbound

This paper cites an unresolved cited work.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c0d1b61-fc1c-46aa-89dc-f6ddc3537c8c · outbound

This paper cites an unresolved cited work.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 055c9c79-ed88-48dc-9852-c45d8c78e962 · outbound

This paper cites Fixing the taskt and lettingz(t)∈R dm be thet-th row ofH, with P m zm(t) = 0 by hypothesis, we use the elementary identity X m<m′ (zm(t)−z m′(t))2 =d m X m zm(t)2.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Fixing the taskt and lettingz(t)∈R dm be thet-th row ofH, with P m zm(t) = 0 by hypothesis, we use the elementary identity X m<m′ (zm(t)−z m′(t))2 =d m X m zm(t)2

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94cfd7af-d7c7-44df-a9f2-afad4866b92f · outbound

This paper cites an unresolved cited work.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af90234c-7da3-48a4-9ebb-3dc37a231013 · outbound

This paper cites an unresolved cited work.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be631765-07af-4d3a-858d-204309074e09 · outbound

This paper cites Each summand is mean zero (by the model) and has operator norm at most √ 2 (since∥X i∥op = √ 2 and the scalar prefactor σ(⟨Xi, M ⋆⟩)−Y i ∈[−1,1]).

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Each summand is mean zero (by the model) and has operator norm at most √ 2 (since∥X i∥op = √ 2 and the scalar prefactor σ(⟨Xi, M ⋆⟩)−Y i ∈[−1,1])

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 064799ee-a634-4547-bce4-2aa3a0a320a0 · outbound

This paper cites Stage A: initialization and right-factor construction.OnD 1, computebΘ0 by Theorem B.5.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Stage A: initialization and right-factor construction.OnD 1, computebΘ0 by Theorem B.5

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f9ef693-3547-4c19-a476-44243eb99e55 · outbound

This paper cites Define the true predictorsη ⋆ ℓ := Θ⋆ t,mℓ −Θ ⋆ t,m′ ℓ = (Θ⋆ R[mℓ])⊤θ⋆ t −o ⋆ ℓ withθ ⋆ t ∈R r thet-th row of Θ ⋆ L ando ⋆ ℓ := Θ⋆ t,m′ ℓ the opponent offset.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Define the true predictorsη ⋆ ℓ := Θ⋆ t,mℓ −Θ ⋆ t,m′ ℓ = (Θ⋆ R[mℓ])⊤θ⋆ t −o ⋆ ℓ withθ ⋆ t ∈R r thet-th row of Θ ⋆ L ando ⋆ ℓ := Θ⋆ t,m′ ℓ the opponent offset

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a697c1b-add9-44bc-b6b2-dc19b60ecf6b · outbound

This paper cites Our entrywise rateε n ≍ p ¯dpolylog(n ¯d)/nand the exact recovery margin 4ε n match these single-task minimax characterizations up to logarithmic factors.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Our entrywise rateε n ≍ p ¯dpolylog(n ¯d)/nand the exact recovery margin 4ε n match these single-task minimax characterizations up to logarithmic factors

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d15eecfd-c4e1-49cf-8a8a-fe33203f153d · outbound

This paper cites an unresolved cited work.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3e44921-455a-48fc-b823-390c532cec4a · outbound

This paper cites Step 2: the score identity.The directional score along the submodel is∂ ε logp Θε,Π⋆(Xi, Yi) 0 = sη(Yi, η⋆ i )⟨H, X i⟩(differentiating logpin the parameterε).

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Step 2: the score identity.The directional score along the submodel is∂ ε logp Θε,Π⋆(Xi, Yi) 0 = sη(Yi, η⋆ i )⟨H, X i⟩(differentiating logpin the parameterε)

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9e466813-f9ff-41d5-9df4-a46c42295c5e · outbound

This paper cites an unresolved cited work.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9546a378-92c7-4080-8436-2b8c824c63b1 · outbound

This paper cites E⋆|Zi|3 = 1 σ3 Γ E⋆[|sη|3| ⟨H⋆ Γ, X⟩ |3]≤ C3 σ3 Γ E⋆| ⟨H⋆ Γ, X⟩ |3 whereC 3 :=E ⋆[|sη(Y, η⋆)|3 |X]≤1 under Assumption A.1(iv) (since|s η| ≤1).

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons E⋆|Zi|3 = 1 σ3 Γ E⋆[|sη|3| ⟨H⋆ Γ, X⟩ |3]≤ C3 σ3 Γ E⋆| ⟨H⋆ Γ, X⟩ |3 whereC 3 :=E ⋆[|sη(Y, η⋆)|3 |X]≤1 under Assumption A.1(iv) (since|s η| ≤1)

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 123db0b0-2de9-456b-8607-6bdb33a6fa26 · outbound

This paper cites We con- dition throughout on the master good eventE n of Appendix A.8.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons We con- dition throughout on the master good eventE n of Appendix A.8

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86fc8adc-b366-4e0c-8d43-18a398ec7608 · outbound

This paper cites This is bounded in Appendix E.4 by Bernstein.

Low Rank for Rank: Uncertainty-Aware Task-Specific LLM Ranking under Sparse Pairwise Comparisons This is bounded in Appendix E.4 by Bernstein

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-29T06:11:48.446361Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.