Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:18:06.589533Z
Paper Citation Record · LEDGER
Upper bounds on the theta function of random graphs
As of 16 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2506.02952.
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 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
20 of 20 outbound references displayed
- verified exact0
- verified fuzzy8
- unresolved12
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 847b32fe-3ce1-4854-969f-6ee898e7facf · outbound
This paper cites Then, LW a.s.
Upper bounds on the theta function of random graphs Then, LW a.s
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:10.145598Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 50caeddf-147e-45ed-ac20-a2ddaaf5de28 · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:09.987290Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f4bd2545-557d-4bc3-84d2-2f7112f2c94d · outbound
This paper cites In order to derive these equalities, we rely on the fact from Definition B.1 that the mixed mo- ments of centered random variances must be equal to 0.
Upper bounds on the theta function of random graphs In order to derive these equalities, we rely on the fact from Definition B.1 that the mixed mo- ments of centered random variances must be equal to 0
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:09.787533Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2ca0caa8-60d5-4399-90e0-fd9624b32d38 · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:09.591838Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 181cf599-87c7-46f1-a94f-74212c4c632b · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:09.372239Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 17d87208-1b79-4ec3-8b34-d871e1d81b67 · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:09.105934Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b5b6be8d-ad50-46d3-88dc-a246a68092b2 · outbound
This paper cites 33 Now, using the fact that a2 is free from a1 anda′ 1, we haveφ(a1a2) =φ(a1)φ(a2) and φ(a2a′.
Upper bounds on the theta function of random graphs 33 Now, using the fact that a2 is free from a1 anda′ 1, we haveφ(a1a2) =φ(a1)φ(a2) and φ(a2a′
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:08.882123Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c9075e14-45d1-4f60-bcd9-e7c32fcc6c94 · outbound
This paper cites nice enough.
Upper bounds on the theta function of random graphs nice enough
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:08.674857Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 77d6000e-4364-4ab3-986d-da3b0fca4cdf · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:08.439946Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b65e55d3-bdab-4bcd-acc8-f4ac5da3cf3e · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:08.247365Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6e7456a1-ce04-441b-84b2-5d86063d34c0 · outbound
This paper cites Letg(z) := G−1 µa⊞µb(z) = G−1 µa (z) +G−1 µb (z)− 1 z.
Upper bounds on the theta function of random graphs Letg(z) := G−1 µa⊞µb(z) = G−1 µa (z) +G−1 µb (z)− 1 z
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:08.036322Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 100843f6-b1c9-4755-9805-44ad351d258a · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:07.892571Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8973d1c3-71b8-4d1d-ab08-7cd512d5761b · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:07.751606Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b71752bc-2cd2-4c83-9e16-5208b343d881 · outbound
This paper cites This does indeed seem to be true, according to experimental results, as one can see in Fig.
Upper bounds on the theta function of random graphs This does indeed seem to be true, according to experimental results, as one can see in Fig
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:07.584627Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 43e6c7c7-b089-44fa-93e9-00f30f6ce37e · outbound
This paper cites ≥λn, then ∑ k:λk≥0 λk = 4 3πn3/2±O(n1/2 polylogn) and ∑ k:λk≤0 λk =− 4 3πn3/2±O(n1/2 polylogn).
Upper bounds on the theta function of random graphs ≥λn, then ∑ k:λk≥0 λk = 4 3πn3/2±O(n1/2 polylogn) and ∑ k:λk≤0 λk =− 4 3πn3/2±O(n1/2 polylogn)
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:07.355531Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cd88bb74-2e8d-4489-8405-d236971724b8 · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:07.189585Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ef756a42-d4d6-4c53-8f8f-82ca062a0335 · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:07.005054Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e1a5853d-0d79-47a1-baba-4035d23a8618 · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:10.561370Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4bfa7226-ac2d-493f-9872-50c062cec802 · outbound
This paper cites an unresolved cited work.
Upper bounds on the theta function of random graphs Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:18:10.368944Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 17d3794b-45b4-4dec-9c3b-81a58037a7c6 · outbound
This paper cites Theorem F.2 gives sufficient conditions for the pointwise convergence of E[LW ] to Pα for some α> 0 (after rescaling).
Upper bounds on the theta function of random graphs Theorem F.2 gives sufficient conditions for the pointwise convergence of E[LW ] to Pα for some α> 0 (after rescaling)
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:18:06.831726Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.