Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:10:42.345844Z
Paper Citation Record · LEDGER
As of 9 August 2026, this Paper Citation Record lists 78 of 78 outbound references and 2 inbound Pith citation observations for arXiv:2507.06522.
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 2026-08-06T19:10:42.345844Z
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 2026-07-09T14:46:31.494813Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-09T14:56:17.916485Z
78 of 78 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation f45fd8a0-e7d6-40a7-ac5c-6d34b81c947d · outbound
Balanced multi-species spin glasses L., and Ruelle, D.Some rigorous results on the Sherrington-Kirkpatrick spin glass model.Comm
Reference 1
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 25b20c5f-0872-4af3-b876-29f436f1aa19 · outbound
Balanced multi-species spin glasses L.Extended variational principle for the Sherrington- Kirkpatrick spin-glass model.Phys
Reference 2
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 234b6f1a-846c-4658-9c5b-b4433d5bfe17 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 19c07f84-db8a-4d77-97d4-ed3cf209c005 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 4
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 fe39ed34-c8d7-4082-8c1a-4049b845b614 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 5
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 6cb4a71e-8cb7-48eb-970c-fd653b5918af · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 6
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 3258d205-a05e-4d33-8463-a5408e4b47b0 · outbound
Balanced multi-species spin glasses O.Free energy of bipartite spherical Sherrington–Kirkpatrick model.Ann
Reference 7
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 bd7f1383-0c2b-4ad7-97d7-3bc4132c2cf4 · outbound
Balanced multi-species spin glasses A Geometric Perspective on the Injective Norm of Sums of Random Tensors
Reference 8
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 d8b7b7f6-1856-4ed0-966d-cff07b0c7aa8 · outbound
Balanced multi-species spin glasses Rigorous Results.Ann
Reference 9
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 b39e9fff-fb26-400a-8798-c0d0e93bbb0a · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 10
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 008e947e-fa9b-46fc-b59c-1737e27d52df · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 11
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c20b647d-c2f9-45a8-892d-8fa2444551e6 · outbound
Balanced multi-species spin glasses Replica symmetry breaking in multi-species Sherrington-Kirkpatrick model
Reference 12
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 1cbf2ead-147b-41c7-a86b-289b899bd1e9 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 13
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 3e866961-6dca-4eb4-b4e0-e7785b1e6d2e · outbound
Balanced multi-species spin glasses Free energy in multi-species mixed $p$-spin spherical models
Reference 14
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 b73a2c7d-7047-490f-95e9-1fdcbfa64453 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 15
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 67abea14-4eb3-49b8-a664-9bff84e7b6af · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 16
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 6253c439-0c49-4062-9cac-b95c7f146187 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 17
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 97ce2c6c-b592-4423-961e-639b10ce3a15 · outbound
Balanced multi-species spin glasses Injective norm of random tensors with independent entries
Reference 18
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 311d1e28-b2de-4c5d-b5dc-002a7a97ce62 · outbound
Balanced multi-species spin glasses Oxford University Press, Oxford, 2013
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 46ba5e3b-4d05-420b-ab0f-5f841e80a861 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 20
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 ffda38df-0eca-406f-85a6-61ec52a9bc13 · outbound
Balanced multi-species spin glasses On free energy of non-convex multi-species spin glasses
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4409fbe4-986e-47eb-9940-97536fd31157 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 22
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 e1a69c2e-bf5d-489c-b54e-8792548c6df7 · outbound
Balanced multi-species spin glasses Envelope representation of Hamilton-Jacobi equations from spin glasses
Reference 23
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 32621c95-6ef1-4ec0-aa58-ed2698347a5e · outbound
Balanced multi-species spin glasses Uniqueness of Parisi measures for enriched convex vector spin glass
Reference 24
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 150067d3-9c67-4cea-bc97-3b0ad455dac4 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 25
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 99aa9eff-c72c-4d5c-9273-e2bf75753980 · outbound
Balanced multi-species spin glasses Electron
Reference 26
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 e8016cd6-3aa7-479d-8a59-55b5ea89ca4f · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 27
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 cd93e757-3909-4db4-99cc-d7585f68c7f9 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6922a2d0-c9e8-4ace-bdaf-d91a6b5b5f09 · outbound
Balanced multi-species spin glasses Injective norm of real and complex random tensors I: From spin glasses to geometric entanglement
Reference 29
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 663f6037-48ba-4b8c-a66c-c4b14a8f3396 · outbound
Balanced multi-species spin glasses S., and Wu, Q.Fluctuation Results for Multi-species Sherrington-Kirkpatrick Model in the Replica Symmetric Regime.J
Reference 31
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 116d25c4-5adf-4d36-9b6f-1f887872c83f · outbound
Balanced multi-species spin glasses 2024, vi+361.https://doi.org/10.4171/zlam/32
Reference 32
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 2fd93106-39d3-44b4-bee3-ab4969c403d6 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 33
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 894c4b6a-375b-4867-95c5-8d9872f74e2c · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 34
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 c09f09c8-6a1d-4466-b0d0-2ba30cc319ff · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 35
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 99349029-3834-40f9-9164-6d3a1e6a4d5d · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 36
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2d4af970-e4e0-4fa1-9ef4-fa6a28a71c11 · outbound
Balanced multi-species spin glasses Towards Parisi ultrametricity.J
Reference 37
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 7f6f3a85-66ef-41dc-b591-d2a4002156b5 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 38
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8f2449fc-ea4a-4098-9276-59fd32b1cfa2 · outbound
Balanced multi-species spin glasses Algorithmic Threshold for Multi-Species Spherical Spin Glasses
Reference 39
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 866c9be5-aea4-4699-abb3-74a615a83d7a · outbound
Balanced multi-species spin glasses A Constructive Proof of the Spherical Parisi Formula
Reference 40
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 296dfa8f-1175-4538-89c0-b6094dd839bb · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 41
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 a546626c-9e85-4d8b-a82f-c5d76d1b2ed5 · outbound
Balanced multi-species spin glasses Existence and Uniqueness of Permutation-Invariant Optimizers for Parisi Formula
Reference 42
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 80a87692-cf63-4f63-9d39-01ab14b7e609 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 44
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 caa6fb74-7855-4dae-80f5-89102c884a2c · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 45
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 3090f962-d5de-4930-9f54-31af9c23918e · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 46
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 bd6c411f-7aa7-4fd2-a862-f528ae56704a · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 47
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 da4cc5e9-ca34-498b-87c8-4728a5155ec0 · outbound
Balanced multi-species spin glasses M., Thouless, D
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39648c3c-2747-4496-b858-9a8d85989b1d · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 49
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 98aaa1ef-f364-45d8-b675-ff5fa592d159 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 50
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 52b2991a-8ab8-4e3c-96fd-a97aebb11a6a · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 51
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 b584f021-117a-44da-9de0-0234e0e37774 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 52
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 f6555b3e-0319-425c-9c83-5fcb29a36253 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 53
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 a6750faa-c6e2-46a1-8229-98693e16c8d8 · outbound
Balanced multi-species spin glasses H., Drineas, P., and Tran, T
Reference 54
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 7069d47a-d120-4604-9a34-8351efac6994 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 55
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 ac3605ee-c4f7-4821-801f-edf08464e992 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 56
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 28e79918-f4b0-4311-a884-bd20259fbc3a · outbound
Balanced multi-species spin glasses Springer Monographs in Mathematics
Reference 57
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fb87f954-9a93-47a7-8b8a-1ab6567c6803 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 58
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 fcf8d633-8b28-4a71-8897-a05379f133af · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 59
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f66c238b-5b86-4c32-a8ab-939992fef01c · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 60
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3e473fff-c4ef-4ed4-a60b-e10ad3b1f366 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 61
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 f600dda2-135a-4731-9a81-b49da7db9819 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 62
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f6a2f5cf-468a-4dd3-8bb1-266b01ca558e · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 63
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8b00193b-58ee-4215-a8f4-a94988bfc8d6 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 64
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 76a10272-d47a-4578-b531-49801618d685 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 65
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e0add2a4-5ebe-4c43-a03c-9b7753f409d9 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 66
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e232dea9-98f4-493e-9996-0ae8f3d7cd2b · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 67
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5eaecd45-8f42-45e9-aa98-527ae6a81f01 · outbound
Balanced multi-species spin glasses Theory Related Fields 186, 3-4 (2023), 715–734.https://doi.org/10.1007/s00440-023-01200-0
Reference 68
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 082b5b23-eddb-4e30-a949-6b14657b84f0 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 69
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 4060efdb-b26e-40be-b509-310c0a65afff · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 70
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 d99ad7d6-92c9-40af-a40a-75bc55860e2f · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 71
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 86a98e86-584f-45d4-ab72-4f5572cb8925 · outbound
Balanced multi-species spin glasses Theory Related Fields 134, 3 (2006), 339–382.https://doi.org/10.1007/s00440-005-0433-8
Reference 72
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 4ad1485d-a8ab-47ad-89c4-42416f578184 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 73
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 954a0e30-f031-466b-a39d-de0b3b3d8466 · outbound
Balanced multi-species spin glasses Volume II: Advanced Replica-Symmetry and Low Temperature, vol
Reference 74
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e4d062ee-b8b5-438e-922f-5eb0edf38ead · outbound
Balanced multi-species spin glasses 60 ofErgebnisse der Mathematik und ihrer Grenzgebiete
Reference 75
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f013a50d-ab51-4598-af71-4c4f69896d4d · outbound
Balanced multi-species spin glasses Spectral norm of random tensors
Reference 76
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5124aaf9-6236-4157-b714-85cbbcdd768e · outbound
Balanced multi-species spin glasses L.About the Almeida-Thouless transition line in the Sherrington-Kirkpatrick mean-field spin glass model.Europhys
Reference 77
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 cee49c43-e43a-4746-9ee4-44bdf00a0e77 · outbound
Balanced multi-species spin glasses 47 ofCambridge Series in Statistical and Probabilistic Mathematics
Reference 78
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6cf34877-00ce-4b97-bb51-753f5591fdb6 · outbound
Balanced multi-species spin glasses Q., Bai, Z
Reference 79
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d67ec322-35f3-4d3d-a204-dbb711eea917 · outbound
Balanced multi-species spin glasses Unresolved cited work
Reference 80
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 7c6949fe-1ad9-4e61-897e-fbca377383fa · inbound
The SK model with a sparse variance profile: free energy and AMP algorithm for TAP equations at high temperature Balanced multi-species spin glasses
Reference 7
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 ffb1a1f3-58f7-4b67-ac67-72c7db8bb3f7 · inbound
Norm Bounds for Sparse Random Tensors and Spectral Gap of Random Hypergraphs Balanced multi-species spin glasses
Reference 24
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.