Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:16:51.920045Z
Paper Citation Record · LEDGER
Non-Asymptotic Length Generalization
As of 9 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2506.03085.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-14T03:23:31.727605Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
29 of 29 outbound references displayed
- verified exact0
- verified fuzzy19
- unresolved7
- parse uncertain3
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 22e898fd-9973-45d2-9258-e9d26dfc2503 · outbound
This paper cites A outputs ˆp at least for one N ∈ N.
Non-Asymptotic Length Generalization A outputs ˆp at least for one N ∈ N
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:57.630509Z
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 abd59e88-eee0-4cc2-88e1-b2b503e6fe36 · outbound
This paper cites equivalent.
Non-Asymptotic Length Generalization equivalent
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:57.446627Z
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 39f83fef-a94b-48a0-bf45-aa11c8df0b89 · outbound
This paper cites , m− 2}, Y restricted to the interval [ Ti, Ti+1] can be rearranged into an equivalent monotone curve by Lemma D.13.
Non-Asymptotic Length Generalization , m− 2}, Y restricted to the interval [ Ti, Ti+1] can be rearranged into an equivalent monotone curve by Lemma D.13
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:54.786993Z
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 34e2a6ad-b77c-4c8d-b63b-f8c8bf78fa29 · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:16:57.232097Z
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 ed1cea82-f20b-48d3-8c2b-8f625d04c672 · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:16:56.993421Z
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 71116b9d-dcca-493a-b0c5-ec06113151d1 · outbound
This paper cites functions.
Non-Asymptotic Length Generalization functions
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:56.800713Z
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 24be3c23-8f04-4869-a4a6-be27a41f331e · outbound
This paper cites S is 1-Lipschitz and monotone non-decreasing.
Non-Asymptotic Length Generalization S is 1-Lipschitz and monotone non-decreasing
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:56.609495Z
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 9d914eb2-38fa-4c7d-ad98-a021091fbcd0 · outbound
This paper cites minimal segment.
Non-Asymptotic Length Generalization minimal segment
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:56.388556Z
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 ff8c5179-b2fc-4d4a-bf9b-ddd569e6f7c5 · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:16:56.160012Z
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 e71a2aaa-7b75-49a1-85ea-0de7f104a6aa · outbound
This paper cites Corollary D.14.
Non-Asymptotic Length Generalization Corollary D.14
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:55.941248Z
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 52cf3ea0-4d8c-4ea7-a256-f7cd4107b13a · outbound
This paper cites The 1st monotone curve has start-point at the origin, (0, 0).
Non-Asymptotic Length Generalization The 1st monotone curve has start-point at the origin, (0, 0)
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:55.474938Z
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 6cdc2290-7a75-4b8b-9f91-ec7913d8b6c6 · outbound
This paper cites Finally, note that each monotone curve consists of multiple segments.
Non-Asymptotic Length Generalization Finally, note that each monotone curve consists of multiple segments
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:55.229252Z
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 7d529402-f1c9-45b8-9ab1-3746dd96bf3b · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 14
- Resolution
- parse uncertain
- raw_fallback, observed 2026-08-07T11:16:55.084566Z
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 95a7fad2-24d3-4ea3-abbb-d4097dff3ec4 · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:16:54.973364Z
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 893848f4-3179-4e1c-b33d-edcdb5e5475e · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 17
- Resolution
- parse uncertain
- raw_fallback, observed 2026-08-07T11:16:55.700521Z
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 b4220b5c-f009-4416-b5b2-238e3d4757bd · outbound
This paper cites The last issue about ensuring YPairs satisfies the property that ( y1 1, y1.
Non-Asymptotic Length Generalization The last issue about ensuring YPairs satisfies the property that ( y1 1, y1
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:54.584557Z
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 d2a6660c-3cf1-4e95-ac4f-a464f1184428 · outbound
This paper cites The issue arises when Span(Y) ⊊ [k], so that Y does not span all k lines.
Non-Asymptotic Length Generalization The issue arises when Span(Y) ⊊ [k], so that Y does not span all k lines
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:54.238691Z
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 fe953422-4e47-4a1d-a4ee-1ae1cef2639c · outbound
This paper cites positive.
Non-Asymptotic Length Generalization positive
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:54.082823Z
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 b26814ef-eee7-4cc0-98e6-3280d1c90efc · outbound
This paper cites , O(T d)}M −1.
Non-Asymptotic Length Generalization , O(T d)}M −1
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:53.891518Z
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 fc03f7cb-c861-47ef-9773-528312f48164 · outbound
This paper cites crossing points.
Non-Asymptotic Length Generalization crossing points
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:53.700867Z
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 ab6bfda1-1b4d-4dd7-878e-7cb2101d2b97 · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 24
- Resolution
- parse uncertain
- raw_fallback, observed 2026-08-07T11:16:54.435708Z
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 07db6190-43b6-4d33-8fcf-5240d8f0c713 · outbound
This paper cites adjacent.
Non-Asymptotic Length Generalization adjacent
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:53.513583Z
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 5402cb01-18b3-4144-b8c7-19c79e274741 · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:16:53.325993Z
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 d648edcb-c058-40df-a28d-001f757d2929 · outbound
This paper cites an unresolved cited work.
Non-Asymptotic Length Generalization Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:16:53.135140Z
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 5498339e-9ed4-4c02-ad8a-8ec5457ba134 · outbound
This paper cites Lemma D.34 implies that either all Aj are type II or all Aj are type III, which can be seen as follows.
Non-Asymptotic Length Generalization Lemma D.34 implies that either all Aj are type II or all Aj are type III, which can be seen as follows
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:52.936995Z
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 e2bf0045-844e-462c-bdd1-2c6566cfa8a5 · outbound
This paper cites Thus, O is disjoint from S j∈[Nk] int(Aj).
Non-Asymptotic Length Generalization Thus, O is disjoint from S j∈[Nk] int(Aj)
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:52.712088Z
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 f7405b54-b945-434d-8d19-761a43e51663 · outbound
This paper cites x + y >2, x+ y >1.
Non-Asymptotic Length Generalization x + y >2, x+ y >1
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:52.393386Z
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 16521e21-b34d-403b-adbe-232462d0bbfd · outbound
This paper cites Once again, {Aj}j∈[Nk] are either all type II or all type III, contradicting that z, z′ > 0, and PK i=1 λi > z andPK′ i=1 λ′ i > z′ respectively.
Non-Asymptotic Length Generalization Once again, {Aj}j∈[Nk] are either all type II or all type III, contradicting that z, z′ > 0, and PK i=1 λi > z andPK′ i=1 λ′ i > z′ respectively
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:16:52.114933Z
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 65efd611-76cd-4376-9fbd-0125e9f514c9 · outbound
This paper cites Investigating the Limitations of Transformers with Simple Arithmetic Tasks.
Non-Asymptotic Length Generalization Investigating the Limitations of Transformers with Simple Arithmetic Tasks
Reference 2021
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T11:16:49.682246Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation 9af35948-d31e-4e0c-81b3-44c16424fe67 · inbound
From Expressivity to Sample Complexity: Narrow Teachers for Transformers via C-RASP cites this paper.
From Expressivity to Sample Complexity: Narrow Teachers for Transformers via C-RASP Non-Asymptotic Length Generalization
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-07-14T03:23:31.727605Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.