Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T20:15:10.153779Z
Paper Citation Record · LEDGER
As of 20 August 2026, this Paper Citation Record lists 51 of 51 outbound references and 1 inbound Pith citation observation for arXiv:2505.13664.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T20:15:10.153779Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T13:10:46.726958Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-06T13:10:48.983847Z
51 of 51 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 1a5ec224-3049-44be-9113-2ed5cc348351 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading This does not change the number of trees in the forest
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dd1ab62e-1eb6-4911-ad89-55cbb6c44ea3 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading F ∈F n,k =⇒ F ∈T n,k: Assume towards a contradiction that ∃F : F ∈F n,k∧F /∈T n,k
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b8b6fe2e-fe0e-4a5e-8552-87c2c00c8da5 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading F∈T n,k =⇒ F∈F n,k: We can argue inductively that all our F∈T n,k are valid
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 97806c79-d133-4988-a70f-da7842c37bee · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading At each step, we ensure that the runs maintain sizes that are powers of two and that there is at most one run of any given size
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 253325de-c3ca-426f-992f-9d16f6beeac2 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading zero or more
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 925bc67d-3b9e-4ae6-aa77-527c4ad927ab · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation da02a2f4-5023-4a0f-a8a2-22b177fa67ee · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading vertical strip
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 210e127f-5e43-4ea3-8c98-c9d83bbdf908 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading The prepro- cessing time is O(log 1) =O(1)
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d782f865-a30f-4e14-922c-8db389260da8 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading We rebuild the static data structure for this new run, which takes O(2 log 2) =O(2) time
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d551dd6d-12dd-4e27-9c3c-b9688d545470 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0adc9d39-7753-4d36-a418-199b36d755e7 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2c8e8280-db00-419d-b3d4-99c62e2c44ac · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading We implement the operations as follows
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0fdddf0f-1585-4e65-89f8-11916b65ef8a · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4ea5d465-062a-47d4-81da-a745455189f3 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading This adjustment en- sures that deleted elements do not contribute to the final count
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3ec5b709-c0c3-445d-af16-9b9d36f453e9 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading This can be rewritten as: ( P⊤−I)x = 0, where I is the identity matrix
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 0fdb6c34-dc45-43b2-aea2-3a38f9c7b8c4 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 127dcc04-a31d-4f32-8512-ccaa587473bf · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Therefore, the LP is: Minimize 0 Subject to ( P⊤−I)x = 0, x≥ 0, 1⊤x = 1
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f515f117-5203-4785-b494-ce660e29ef22 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 06d254e4-3a82-4492-adc7-f7894a3223cf · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Since the first condition is assumed false (the LP is infeasible), there must exist a vector y satisfying the second condition
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3b7fa4b0-91bb-4437-bb41-1c65b462328b · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Master Solution Assign the value 0 or 1 with probability 1/2 independently to each input wire
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3b21a65c-2c12-4bc7-acca-b5c80d748632 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading For each OR-gateCj, the probability that all of its 5 input wires are 0 is: Pr(all inputs to Cj are 0) = 1− 1 2 5 = 1 32
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation febd8267-338f-4c47-9ac9-198651e6b366 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading And the probability that Cj outputs 0 is: P (Cj = 1) = 1−P (Cj = 0) = 1− 1 32 = 31 32
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4977e03f-1ec6-4476-861b-3195cc961672 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Let this output be T0
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation dc24be93-5b44-44da-9264-6971f59b7579 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Let this output be T1
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a1745a55-be42-42e8-8c92-72fb88c5316d · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Proof of correctness: Consider any input configuration S and its nega- tion ¯S (where each input is flipped)
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4de5ff3e-f1e8-4f57-ba44-f0f206ed94bc · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading An edge (m,p )∈E exists if square m (a mushroom) and square p (a pepper) are adjacent in the pizza
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 58c45c03-dbf7-4b26-a1b0-0ad7e490ea92 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Each perfect matching corresponds to a valid way to slice the pizza
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation c2f7f514-7fdb-4409-997e-7d94e8ed71a8 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Let P be the set of squares topped with peppers
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 28218c81-5fbf-4f72-8408-2e47682e228b · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading We can use the Kasteleyn’s algorithm or Pfaf- fian orientation to compute the number of perfect matchings
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 3b2e008b-66c0-40f5-994f-666bfb41e133 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Use existing algorithms for counting match- ings in planar graphs
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation bc9d4ff2-26f7-46ac-83ed-0a92f1cd0bee · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading The toppings partition the vertices into two disjoint sets: • M ={Squares topped with mushrooms} • P ={Squares topped with peppers}
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation e19095bb-ba34-4f24-98a4-1bd2a37e64d6 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading However, for pla- nar graphs, and specifically for bipartite planar graphs, there exist polynomial-time algorithms
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d0ff4182-49b1-42b9-8a0d-8ee8f3087f13 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 6b41e660-d55b-4133-b64e-540685fb2a8c · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Complexity: • Constructing the graph G: O(nm) (each cell checks adjacency)
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ed30b7c1-2cd6-4343-8459-8d94f80ac592 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Orient the edges to satisfy Kasteleyn’s condition
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ffa03cfa-450e-4e7c-b575-3b96b970cbf4 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading If the edge is directed fromv tou, setAuv =−1 and Avu = 1
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8317e7c8-4216-4fcf-a8c8-6172c4f4c609 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading The number of perfect matchings is p | detA|
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation cb382314-28f0-40ae-8592-a992360768b6 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b4b881e2-e741-453b-b56e-e35b958a244d · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Substitute xij = 1 for all edges ( i,j )∈E to obtain the polynomial: q(y) =p(1,y )
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f12ec892-0939-4acc-af39-d62b8388d623 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Perform polynomial interpolation to recover the coefficients of q(y) and determine the smallest degree dmin
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 9b022ad7-513d-4326-b1ba-7ecef3bea4e2 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Correctness: The determinant det(C +I) sums over all walks in the graph
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation cf7d3006-2f52-424b-b16c-131680c1a5fe · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Set klow = 1, khigh =Dmax
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f844e1d9-6b75-47c6-89d9-71d78b516494 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading (b) Compute qk(y) =q(y) mod yk
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation b22d4806-46fa-4f31-b2b9-117e862c14a0 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Since the minimal cycle is unique, dmin correctly represents the minimal cycle weight
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 32d06b76-e7a9-4599-a7b0-5982e17df2f5 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation d9366b45-96f8-4ae7-985f-63c0c0e6e732 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading [Mathematical Errors : You need a finite field to use the theorem.]
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 88f38707-dd95-47f9-9dda-226eb34514ad · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Unresolved cited work
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation acb8d391-b102-450e-85a6-9481e56c1d3f · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading X π sign(π) Y i ai,π(i) # = X π sign(π) E
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4c2c0d61-94b1-43ef-89b1-1b416793e61d · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading 1 N NX i=1 detAs(− →Gi) # = 1√ N r var h detAs(− →Gi) i . By Chebyshev’s inequality: Pr E h detAs(− →G) i − 1 N NX i=1 detAs(− →Gi) ≥k vuut var
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4b8165f0-e409-4a2d-8543-8181818d7812 · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge
Reference 2018
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f99a4cba-1b40-41f1-a3f0-a1216c8ec41b · outbound
Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading Can OpenAI o1 outperform humans in higher-order cognitive thinking?
Reference 2024
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 17035d1f-e229-4cb7-8a66-a947fda985d2 · inbound
VArsity: Can Large Language Models Keep Power Engineering Students in Phase? Assessing GPT Performance in a Proof-Based University-Level Course Under Blind Grading
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.