{"as_of":"2026-08-10T12:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b32b150ae335a10ac991750c8ed1c9b96a4282738c9214890ad8305b0f05d72f","coverage":[{"denominator":121,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:23:42.696268Z","state":"measured"},{"denominator":101,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":101,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-26T07:51:39.666050Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-04T11:39:46.652447Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"cited_work":{"arxiv_id":"2507.05923","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05923","snapshot_observed_at":"2026-07-04T11:39:46.652447Z","title":null,"venue":null,"work_id":"e5bd4013-3c01-4aaf-b4f7-82a0ce03c421","year":2025},"citing_paper":{"arxiv_id":"2606.23088","last_updated":"2026-06-22T09:33:56Z","snapshot_observed_at":"2026-08-02T02:29:26.761582Z","submitted_at":"2026-06-22T09:33:56Z","title":"On background fields and a cutoff in sigma models","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-26T07:51:39.666050Z"},"links":{"cited_paper":"/paper/2507.05923","citing_paper":"/paper/2606.23088"},"observation_digest":"sha256:d6a655cfa6fbf07776f9c74e90133ee96b55241bbf20f0018eb3666a1ece19b0","observation_id":"baeee157-356a-4aad-aeea-721e8e836d6f","resolution":{"observed_at":"2026-07-04T11:39:46.653947Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.05923/citation-record","integrity":"/paper/2507.05923/integrity","json":"/paper/2507.05923/citation-record.json","paper":"/paper/2507.05923"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:31.286646Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:31.286646Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:3e2f6df293681532467b6f9a692f37bb7430316d151ec3b20a9b8aa23c936176","observation_id":"bc68f4dd-93da-4326-9e0f-76cf087a7596","resolution":{"observed_at":"2026-08-06T19:23:31.286646Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:31.196576Z","title":"Let us consider all four terms separately","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:31.196576Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:966a2df5388bf31c9e15f07888a3c104c31ca6b21abdc8b6c41a23c2fb5688bd","observation_id":"9107a37c-f1a4-4c83-84c8-df42971030b9","resolution":{"observed_at":"2026-08-06T19:23:31.196576Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:31.116913Z","title":"=H sc 0 Hc 2(Γ2","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:31.116913Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:c60eea5fcd5e3bdd6dd79c7bd5154a3079c0e1151724ffd2a8bdef758736d38c","observation_id":"13da9056-a8de-461f-b33d-fdfebf7a36ee","resolution":{"observed_at":"2026-08-06T19:23:31.116913Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:31.420234Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:31.420234Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:7b9d43831972c416d8b18aace69ee8ca14ee912ecf124b5d8d3f094ae05b087e","observation_id":"52d5920e-7564-400f-89a5-ba4c23c1f0cc","resolution":{"observed_at":"2026-08-06T19:23:31.420234Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:31.557274Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:31.557274Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:b85366f2f626e30ba00f84f7f64f30773aedeec56e904ff5f5145a5781ab1664","observation_id":"84da4d13-56ec-4b4f-89d1-16d8e77b99ac","resolution":{"observed_at":"2026-08-06T19:23:31.557274Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.389739Z","title":"Zinn Justin,Path Integrals in Quantum Mechanics, Oxford University Press, 1–334 (2004)","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.389739Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:39b1cc7e9e02b5f85ee53fecada537184bd6cea16ba81c772b678d2ee8724f4e","observation_id":"85cba9ba-1581-40c4-9fab-56da742437ee","resolution":{"observed_at":"2026-08-06T19:23:33.389739Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:31.752136Z","title":"=− 36 ln(Λ/σ4) π + 72c2L π B3 −B 2 + 72c2 2J1[B] ln(Λ/σ4)L2 4π2 + I3(Λ, σ) + I4(Λ, σ) +κ 7S[B], whereκ 7 is a coefficient depending on the parameter Λ","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:31.752136Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:f4f285e7153741edf0788e5f9d9ee99d1e77f4c5718f51ec192b23b125d048d7","observation_id":"18af7eb1-e3f7-4bb8-b69d-4c32aa9b7bab","resolution":{"observed_at":"2026-08-06T19:23:31.752136Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:31.882996Z","title":"Calculations are performed using a shift of variables, and the formulas for the sum of H 3 334 + H4 334 take the form H3 334 + H4 334 =−6 ˆHsc 0 Γ3,r3 −Γ 3,r4 ! s.p","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:31.882996Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:5762f8a276e8835a1fea13b45526ee9ce033ba4c1486967d6baf7c36af6ea041","observation_id":"9219cbd8-761c-4775-832a-b73b340c934d","resolution":{"observed_at":"2026-08-06T19:23:31.882996Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.735709Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.735709Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:0f4d9d7cd8ddddfd3df7992d4573ca12d9c1a195200ce185559a1ba8dacacb59","observation_id":"8beb016e-9311-4146-8581-31dd18bcf3ae","resolution":{"observed_at":"2026-08-06T19:23:33.735709Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.013297Z","title":"Let us consider them separately as well","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.013297Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:92f98eb41d827a3f866ca293e633e9814c330d45a59068836d7677a64810eb5d","observation_id":"b1b15226-25e5-4ccb-ae2a-032989d96876","resolution":{"observed_at":"2026-08-06T19:23:32.013297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.078867Z","title":"Let us consider the last term in more detail","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.078867Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:22c669293af88935758ea707a93a1f5396098b234acd6908e3a2c7710dcb8c26","observation_id":"563c2f26-2869-41d3-ac77-960542f0a9b2","resolution":{"observed_at":"2026-08-06T19:23:32.078867Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.154919Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.154919Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:5cce2d665138af95d4a0bab305dcc3767fac618ae66c665e790f219a0495736c","observation_id":"84a5da96-ffc9-475f-8325-84a00e6566ac","resolution":{"observed_at":"2026-08-06T19:23:32.154919Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.227364Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.227364Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:1eebc69f84a2e4b0549ca085beaebac44b78159dc46dbd2c9641a594bbbfe59d","observation_id":"64be90e9-2894-4560-8660-88af87b216e4","resolution":{"observed_at":"2026-08-06T19:23:32.227364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.317133Z","title":"Part 2Hsc 0 (D1D2)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.317133Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:678baa6f50de3bfab6f0182e614db29097e2e3e4856cf089109a78b84de6c2a1","observation_id":"c46f4197-9158-4643-a111-f707609fd6e6","resolution":{"observed_at":"2026-08-06T19:23:32.317133Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.371485Z","title":"=− 2L π c2B3 −8A 2 + 4A3 + 4A4 + 8A5 + 8A6 −8A 7 −8A 8 , H1,5 44 s.p","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.371485Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:8caaaa9bfbf05d37638cc709718bab7689e5c9be81b4351a49a75be14fa8511b","observation_id":"fd5f4c95-5ca1-402b-a8d0-90cfc644447b","resolution":{"observed_at":"2026-08-06T19:23:32.371485Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.590130Z","title":"6.4.2 Part without loopsH c 2(Γ4) Let us move on to the second part of the decomposition from (6.33)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.590130Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:b92a22bff4855ad5f4343aae888763862a651a26f0c55696e9cfab74dd1e900b","observation_id":"40221356-a0fe-4e64-80cf-40dedf525548","resolution":{"observed_at":"2026-08-06T19:23:32.590130Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.684239Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.684239Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:f8476525968ebed62521b2892f3a82d5ac78ae3a0278acd2f4cbc723d4e64776","observation_id":"561943f3-7959-42f0-8e1e-9ed7fadb017f","resolution":{"observed_at":"2026-08-06T19:23:32.684239Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.755581Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.755581Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:81230544a91a61ff5905355b5607e9c61d57828de8f33bc78a1b6f7470b6b74b","observation_id":"cf5385e6-3bfc-49bd-88e8-fa3196a32023","resolution":{"observed_at":"2026-08-06T19:23:32.755581Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:32.887565Z","title":"This approach violates locality, but preserves quasi-locality, since averaging occurs over a ”small” neighborhood of the selected point","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:32.887565Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:e62c5e26773868c2ed2884e9474cff32766b6fcd69d75fe87cd83a748e7f0e18","observation_id":"a3539b1f-61f2-43ba-b3f4-e008244d7dcd","resolution":{"observed_at":"2026-08-06T19:23:32.887565Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.001347Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.001347Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:2e30c85da56df14e3e9635592384e54471bc79e82602cd986e35b28901dee59c","observation_id":"6df163b4-2c58-410d-b149-9fa960a9d112","resolution":{"observed_at":"2026-08-06T19:23:33.001347Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.062819Z","title":"Itzykson, J","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.062819Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:6366771a2b478ebf39ffc63b47e903ed03e9f6babc22ca6cd7c1dcb87cf6ad2f","observation_id":"8dc201a9-65cc-464e-9a0b-76968a010fb3","resolution":{"observed_at":"2026-08-06T19:23:33.062819Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.116949Z","title":null,"venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.116949Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:7bd7155b29745dd61949df079ca0ff28f93f42d72e13ed1c79da3ec62a868c94","observation_id":"acd54324-ad29-4e50-89e1-52e3fc02265d","resolution":{"observed_at":"2026-08-06T19:23:33.116949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.188849Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.188849Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:8ae4bbf10f1a4f22a2f0e06f4f5eef2d7a0a5200ddb80dff8bf9475a8fad0f89","observation_id":"c4996127-8301-4129-80b2-174f3b204c25","resolution":{"observed_at":"2026-08-06T19:23:33.188849Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.261764Z","title":"Cartier, C","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.261764Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:e0032a3d679edfcc4210eb02e041228dfe73ad32e1f59db772fa028182f72364","observation_id":"554ce49c-b2d9-47e3-8457-28c36d8f97fa","resolution":{"observed_at":"2026-08-06T19:23:33.261764Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.238692Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.238692Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:4dfef585ec40ffbadd8d094f367debb42b2c2977801f88c1e05206665756b268","observation_id":"53424eb9-84c5-46f6-a7cc-ec2d4d3add1b","resolution":{"observed_at":"2026-08-06T19:23:35.238692Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.526336Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.526336Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:603f7585086f839bc7bbed4ec94e7ff9f617bbd0fcc7d5610782a954ad284888","observation_id":"e9d1193c-b9b4-45b7-9017-8332044a5108","resolution":{"observed_at":"2026-08-06T19:23:33.526336Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.611692Z","title":null,"venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.611692Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:a2ae2c3d25e4d824c8f7d5b630db2b34499282e69c9677b0ab3f79bbb9f84e11","observation_id":"53c3c0db-a7c8-4563-9898-cf5ad4b98285","resolution":{"observed_at":"2026-08-06T19:23:33.611692Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.433247Z","title":null,"venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.433247Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:e10f472e7f6d0927d5ae8fc897f90ab46384b58d8c2b77fa8645c956cf649ab2","observation_id":"c27470ad-419d-4f30-b45e-92eed41110ae","resolution":{"observed_at":"2026-08-06T19:23:35.433247Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0901.2208","last_updated":"2009-01-15T09:49:15Z","snapshot_observed_at":"2026-08-01T15:48:00.918927Z","submitted_at":"2009-01-15T09:49:15Z","title":"Radiative Corrections, Divergences, Regularization, Renormalization, Renormalization Group and All That in Examples in Quantum Field Theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0901.2208","snapshot_observed_at":"2026-08-06T19:23:33.839187Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.839187Z"},"links":{"cited_paper":"/paper/0901.2208","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:b20d4364ddd750985d23c7bda08d4efa7dd3a367be5fe5876aec7a6c811b425e","observation_id":"69485fd5-2497-483d-b477-93c54f8d42b2","resolution":{"observed_at":"2026-08-06T19:23:33.839187Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:33.944817Z","title":"Atiyah,Topological quantum field theories, Publications Math´ ematiques de l’Institut des Hautes Scientifiques68, 175–186 (1988) doi:10.1007/BF02698547","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:33.944817Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:7501b8239ab9029bf4593e0607e761e81ed0718249b66b4b22f8b1fc443c5240","observation_id":"73a359cf-f144-4408-97cd-c852a0423ba7","resolution":{"observed_at":"2026-08-06T19:23:33.944817Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.012658Z","title":"Segal,The definition of conformal field theory, Topology, geometry and quantum field the- ory, London Math","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.012658Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:9fda0df39c45e0dd925184e904fb456be2f5e2f69f9833a63d6427bea0ca6338","observation_id":"5c32cae8-e987-4e15-965a-55c07d9a6b5e","resolution":{"observed_at":"2026-08-06T19:23:34.012658Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.117109Z","title":"Reshetikhin,Lectures on Quantization of Gauge Systems, New Paths Towards Quantum Gravity, Springer Berlin Heidelberg, 125–190 (2010) doi:10.1007/978-3-642-11897-5 3","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.117109Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:ab8b93655d9630510a2a7938124007ca44273b9df833b41f27f885c4a38b6fd0","observation_id":"2ac389f2-c918-4b02-9700-2ad9e29017eb","resolution":{"observed_at":"2026-08-06T19:23:34.117109Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1108.0189","last_updated":"2011-07-31T16:52:20Z","snapshot_observed_at":"2026-08-04T07:54:01.081742Z","submitted_at":"2011-07-31T16:52:20Z","title":"Supersymmetric field theories and generalized cohomology","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1108.0189","snapshot_observed_at":"2026-08-06T19:23:34.210182Z","title":"Stolz, P","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.210182Z"},"links":{"cited_paper":"/paper/1108.0189","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:fa0d37ff9797562bb9e2543a2a1c8523b77621a10d0501b9eeeff28307dd8db4","observation_id":"ccfb8aa3-6595-4019-adb6-cada4f09c196","resolution":{"observed_at":"2026-08-06T19:23:34.210182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.308717Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.308717Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:bf2b3870d93047af5ea0a82b710428823d4ca62913d849831510ad64fbaef2bc","observation_id":"78064628-6baf-4613-a7b8-0def4b943bbb","resolution":{"observed_at":"2026-08-06T19:23:34.308717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.399750Z","title":"Kandel,Functorial quantum field theory in the Riemannian setting, Adv","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.399750Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:586d2d7f9a878c44b0e74ee75251570755760faf2873b7527c02f67c0dc2f228","observation_id":"0df8f23a-81e0-4999-be48-43a865638f51","resolution":{"observed_at":"2026-08-06T19:23:34.399750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.476257Z","title":"Kandel, P","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.476257Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:8fa5f755381f9c81d4505298f17baef61c1a3c935e701a36ae1168aa4a1045bf","observation_id":"8b3e1649-caa3-4f4f-b8b2-cb65bc67bcaa","resolution":{"observed_at":"2026-08-06T19:23:34.476257Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.13857","last_updated":"2024-11-21T05:29:52Z","snapshot_observed_at":"2026-07-06T19:53:34.670694Z","submitted_at":"2024-11-21T05:29:52Z","title":"Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions","version":1},"cited_work":{"arxiv_id":"2411.13857","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.13857","snapshot_observed_at":"2026-08-06T19:23:48.829312Z","title":"Effective actions, cutoff regularization, quasi-locality, and gluing of partition functions","venue":"math-ph","work_id":"c63f32e5-b434-4a44-8dd6-0f6df37fb2e6","year":2024},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.573822Z"},"links":{"cited_paper":"/paper/2411.13857","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:1bb1276537f68981ec192fe560cd151c00ddce2d27242b06d0c64b8c8fdb2afc","observation_id":"43298264-7a4a-4800-8ae0-c16cd1bf0fa7","resolution":{"observed_at":"2026-08-06T19:23:48.911225Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.649601Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.649601Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:733045e6c760e518101ea4357cd73b24f188644baeedab17e4685dd7dfacc9a4","observation_id":"7a98e5e1-099a-4d7c-8c45-0ba19c65862e","resolution":{"observed_at":"2026-08-06T19:23:34.649601Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.724531Z","title":"’t Hooft, M","venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.724531Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:ee59a9542cdad6d081c5aafea70b6c764089accf87c3db091e973aa02b6bb92c","observation_id":"54a69f7e-cbb3-4fdd-b2b8-d693296bf54c","resolution":{"observed_at":"2026-08-06T19:23:34.724531Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.806691Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.806691Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:7a08c6f0f741df999e8f237d8824f0e2d0b26d745794aaec399b92d23ed2fee0","observation_id":"b8f0af0b-70ef-40d9-99b5-469d455915ca","resolution":{"observed_at":"2026-08-06T19:23:34.806691Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.871543Z","title":null,"venue":null,"work_id":null,"year":1972},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.871543Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:273ca49096a85d6c4b74f05b52c81b25dcd0864adcdba8b8ace6ad5fb6d0e261","observation_id":"0b74a757-0532-4649-8400-3e71a26bf9b1","resolution":{"observed_at":"2026-08-06T19:23:34.871543Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:34.965804Z","title":"Bakeyev, A","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:34.965804Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:6b42cce1fcec521eb875e76204d6a3fdc6140c02bccc8469590b3d3fc7c610c5","observation_id":"c97ad389-f115-4ed5-9901-11b7b208d672","resolution":{"observed_at":"2026-08-06T19:23:34.965804Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:31.956139Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:31.956139Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:4a2a9be5d9e9d8e4b0a1df489da825b446b559cf1e9f3309f05be8ce17c0d86c","observation_id":"99a3636f-2e7a-4d17-b895-aed0ed0a7f16","resolution":{"observed_at":"2026-08-06T19:23:31.956139Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.043652Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.043652Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:f80018128b5a31bb9c70c355427e21d6812c2760c43768a31fa74b5fb9cf5cce","observation_id":"02cfa82b-4c67-4f4c-b5e6-7dda1f871320","resolution":{"observed_at":"2026-08-06T19:23:35.043652Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.145789Z","title":"Brizola, O","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.145789Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:94f676c9afcd814089c7415f2a32a28234417dbfa7ec7df584a2ff83d15c4c82","observation_id":"f5dceb4e-f1a4-427d-9c40-15a4da890307","resolution":{"observed_at":"2026-08-06T19:23:35.145789Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.312521Z","title":"Cherchiglia, D","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.312521Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:c2111651b6450579ec7e9d86288d8fcaf561a06546c6a5caaf47c0a58dcba0f4","observation_id":"3d5f8e24-d8da-4dd9-8fb1-f939192fa65b","resolution":{"observed_at":"2026-08-06T19:23:35.312521Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.373312Z","title":null,"venue":null,"work_id":null,"year":1948},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.373312Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:4bf8e8f2ac89971f066db252c97e7b7fe9afc1b3d406c226bffaa704bb5aff4c","observation_id":"c644ead6-ffcf-43a7-947b-516f33a71c2b","resolution":{"observed_at":"2026-08-06T19:23:35.373312Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:53.397434Z","title":"Brezin, J","venue":null,"work_id":"f75d86f5-9022-4fe7-bdfe-59023598775e","year":1976},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.694984Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:a958d3fa408ab3eecd62dc0ef42628f5d7377d4b06bcbb8adfd112c9b4d01a7e","observation_id":"ae454a05-62b5-4dc0-861e-c0666248bbe1","resolution":{"observed_at":"2026-08-06T19:23:53.516244Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.540855Z","title":"Pauli, F","venue":null,"work_id":null,"year":1949},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.540855Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:463ad0f18fd280025d7622a3655ae88d12e3d36b2435dc6630891523765b53ed","observation_id":"0c6cbb8b-45c6-42a1-9dbe-796163f25bd7","resolution":{"observed_at":"2026-08-06T19:23:35.540855Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.642564Z","title":null,"venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.642564Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:cf66cb1c00f81b172f330a02f4604c704bad1e36538c0877e61c55db8177d29e","observation_id":"57bb3d68-93cc-42d6-b27b-54e10a57824f","resolution":{"observed_at":"2026-08-06T19:23:35.642564Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.771716Z","title":"Oleszczuk,A symmetry-preserving cut-off regularization, Z","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.771716Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:72ed15bb0d72e56fc4e3f86f063625b8c876b0098355d028e72250e1daefe827","observation_id":"4d028036-00f6-4488-8ec6-3e0ad3981f3e","resolution":{"observed_at":"2026-08-06T19:23:35.771716Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:35.903264Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:35.903264Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:87c51f36e4b68976c42873504ba7c05a7012abc8ed751906bc26b4fb130b7e5f","observation_id":"a5e1e285-e371-4fca-97db-70d88e4fd643","resolution":{"observed_at":"2026-08-06T19:23:35.903264Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1509.07407","last_updated":"2015-09-24T15:33:58Z","snapshot_observed_at":"2026-07-06T04:30:58.385396Z","submitted_at":"2015-09-24T15:33:58Z","title":"Cutoff Regularization Method in Gauge Theories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1509.07407","snapshot_observed_at":"2026-08-06T19:23:36.029072Z","title":"Cynolter, E","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.029072Z"},"links":{"cited_paper":"/paper/1509.07407","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:3986a3dedb55dbf716a03cc9e70800ae3a8fbb776b5904cc6d6849ce22ca3d0f","observation_id":"290734a2-014c-4da3-b9b8-93d7339b4979","resolution":{"observed_at":"2026-08-06T19:23:36.029072Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:36.124762Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.124762Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:25f6b4c01692232da5321e464dd1b7025a3589e6434a9d4c845c9dd88c77528e","observation_id":"0014fc10-39c5-4c0a-bf4b-41238a1a7d26","resolution":{"observed_at":"2026-08-06T19:23:36.124762Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:36.230724Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.230724Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:474f4421a1d47700b25cb155b0a1e59cc369ee5e17f4b12a980eb0b08d5b1000","observation_id":"964ba3a2-752f-4589-80c5-7b245d5eecf5","resolution":{"observed_at":"2026-08-06T19:23:36.230724Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.04562","last_updated":"2022-03-09T07:49:08Z","snapshot_observed_at":"2026-08-10T11:52:55.699945Z","submitted_at":"2022-03-09T07:49:08Z","title":"Quantum equation of motion and two-loop cutoff renormalization for $\\phi^3$ model","version":1},"cited_work":{"arxiv_id":"2203.04562","doi":null,"metadata_source":"pith","pith_arxiv_id":"2203.04562","snapshot_observed_at":"2026-08-06T19:23:48.590524Z","title":"Quantum equation of motion and two-loop cutoff renormalization for $\\phi^3$ model","venue":"hep-th","work_id":"4d45e01b-5e08-4866-a697-75c06dfe417d","year":2022},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.350941Z"},"links":{"cited_paper":"/paper/2203.04562","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:af0eacaf0116f4022c745d6f6a99c3f9ab93c3c38c299ac399b39bd7b4064791","observation_id":"3d549c24-c7a5-45f4-80cc-28c6fbd4824f","resolution":{"observed_at":"2026-08-06T19:23:48.676780Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2004.05999","last_updated":"2020-04-20T06:33:03Z","snapshot_observed_at":"2026-08-10T00:36:00.421938Z","submitted_at":"2020-04-13T15:17:52Z","title":"Two-Loop Cutoff Renormalization of 4-D Yang-Mills Effective Action","version":2},"cited_work":{"arxiv_id":"2004.05999","doi":null,"metadata_source":"pith","pith_arxiv_id":"2004.05999","snapshot_observed_at":"2026-08-06T19:23:48.401543Z","title":"Two-Loop Cutoff Renormalization of 4-D Yang-Mills Effective Action","venue":"hep-th","work_id":"b8595ec5-20f4-435a-b2f3-33d04f72551f","year":2020},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.476270Z"},"links":{"cited_paper":"/paper/2004.05999","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:bb94dc5b88f12422bb53be63159b70a106715e6cdb49eb51928ca1bd6b79f9f2","observation_id":"f29259bc-2d52-41fa-a61f-e3db0b1e3dfc","resolution":{"observed_at":"2026-08-06T19:23:48.485585Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2203.07131","last_updated":"2022-03-14T14:26:20Z","snapshot_observed_at":"2026-08-10T03:39:15.929390Z","submitted_at":"2022-03-14T14:26:20Z","title":"Formula for two-loop divergent part of 4-D Yang-Mills effective action","version":1},"cited_work":{"arxiv_id":"2203.07131","doi":null,"metadata_source":"pith","pith_arxiv_id":"2203.07131","snapshot_observed_at":"2026-08-06T19:23:48.187253Z","title":"Formula for two-loop divergent part of 4-D Yang-Mills effective action","venue":"hep-th","work_id":"0c2891ee-d6b3-42d9-91de-7e57b922625c","year":2022},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.604791Z"},"links":{"cited_paper":"/paper/2203.07131","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:7fae9707114216803734a23c8c26736b21408601d393c6c58053076cb3c663d5","observation_id":"8396f5c6-da1a-481d-bb28-30f8e5f77eff","resolution":{"observed_at":"2026-08-06T19:23:48.282230Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.02374","last_updated":"2023-04-05T11:28:52Z","snapshot_observed_at":"2026-07-06T15:12:26.487146Z","submitted_at":"2023-04-05T11:28:52Z","title":"On Two-Loop Effective Action of 2D Sigma Model","version":1},"cited_work":{"arxiv_id":"2304.02374","doi":null,"metadata_source":"pith","pith_arxiv_id":"2304.02374","snapshot_observed_at":"2026-08-06T19:23:48.043489Z","title":"On Two-Loop Effective Action of 2D Sigma Model","venue":"hep-th","work_id":"068dac46-eb05-431b-a835-8b242780843e","year":2023},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.738128Z"},"links":{"cited_paper":"/paper/2304.02374","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:bc4d6639f7b0e116042d0eeb182ff09286057d869f677dee7647872bb357eae8","observation_id":"86a45136-4366-4547-b139-9acf36688289","resolution":{"observed_at":"2026-08-06T19:23:48.110691Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:36.814429Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.814429Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:d73ab16412541e634d19c807cada29eb41fde5693a1dd35277809b70588ad01a","observation_id":"48e73167-7afd-4c8a-b90f-6c286fdcc4e7","resolution":{"observed_at":"2026-08-06T19:23:36.814429Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2024.11664","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:47.841168Z","title":null,"venue":null,"work_id":"4a904254-1d7f-4a32-abd6-ef0c2a006993","year":2024},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:36.915629Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:d6a0162e4e1f07c45a049d62b806444c6f44c24642353c86828127c049f29078","observation_id":"554458ec-6812-4bf9-b16d-3d2fff89a5bc","resolution":{"observed_at":"2026-08-06T19:23:47.919651Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.07513","last_updated":"2024-04-11T07:09:56Z","snapshot_observed_at":"2026-08-09T03:54:36.476004Z","submitted_at":"2024-04-11T07:09:56Z","title":"Three-loop renormalization of the quantum action for a five-dimensional scalar cubic model with the usage of the background field method and a cutoff regularization","version":1},"cited_work":{"arxiv_id":"2404.07513","doi":null,"metadata_source":"pith","pith_arxiv_id":"2404.07513","snapshot_observed_at":"2026-08-06T19:23:47.577463Z","title":"Three-loop renormalization of the quantum action for a five-dimensional scalar cubic model with the usage of the background field method and a cutoff regularization","venue":"hep-th","work_id":"d01f6224-8b68-432e-92e9-aa99dfca1c41","year":2024},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.039138Z"},"links":{"cited_paper":"/paper/2404.07513","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:babcc2b122df46d9d442c5625cd57ddcb2b2f20167db126e55e5e120af53e43c","observation_id":"3fd4ec0a-b7df-4a0f-adf4-575e441ed8c9","resolution":{"observed_at":"2026-08-06T19:23:47.632538Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:37.175422Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.175422Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:6f50fe5195ce674eb0b4361043da8dbe0acd19462c11dda845a4dcb866610a09","observation_id":"39a51bba-88f0-478d-ae3b-ea6f2c467354","resolution":{"observed_at":"2026-08-06T19:23:37.175422Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.07688","last_updated":"2025-04-10T12:16:46Z","snapshot_observed_at":"2026-08-07T16:06:52.995966Z","submitted_at":"2025-04-10T12:16:46Z","title":"Four-loop renormalization with a cutoff in a sextic model","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.07688","snapshot_observed_at":"2026-08-06T19:23:37.250066Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.250066Z"},"links":{"cited_paper":"/paper/2504.07688","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:c84268dc85f31b64aa7f72de41a0abfbc304d657e7497b449b56ea2a04f52fcf","observation_id":"2c00e306-33aa-44fc-a73c-7566845bc456","resolution":{"observed_at":"2026-08-06T19:23:37.250066Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:37.384642Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.384642Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:0e8369b61a5bce625cf18dbbda8e78575303d7fc1d3563ef1a7fccb29e25f4d8","observation_id":"968352b3-2eb4-46b2-8683-07e989c1d110","resolution":{"observed_at":"2026-08-06T19:23:37.384642Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:37.491416Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.491416Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:148f414fca557f5dea273811098d87bcd8dfffffd81afd2ba1c1dc304efe2d89","observation_id":"e186239c-4137-4a80-8ed2-7e10937d9f3e","resolution":{"observed_at":"2026-08-06T19:23:37.491416Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:53.622480Z","title":"Brezin, J","venue":null,"work_id":"d8919f54-7ee0-4f52-ad3a-d38067c642ec","year":1976},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.603766Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:def8a54dcdb4843aa61fec3caad23bd0e7f2f5d67bbcc16c554dada955968232","observation_id":"252d53b4-d2f7-4da9-a120-0e45a075814a","resolution":{"observed_at":"2026-08-06T19:23:53.726202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:40.223908Z","title":"Nguyen,Quantization of the nonlinear sigma model revisited, J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:40.223908Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:d645c37c322e490368220a27052b6934774d5320e9b56f28fefe1f51fbd9eeac","observation_id":"97cf05c0-4d5f-4e81-b382-2d1dbb0d6b3a","resolution":{"observed_at":"2026-08-06T19:23:40.223908Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:53.189496Z","title":"Brezin, J","venue":null,"work_id":"b5118f1a-57d4-4684-9846-ff9d6d1a96a0","year":1976},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.827807Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:b8ac41cecf8a8e96bdeb2ad3afaaa38e100060c4c33ee4a30e18edb676a6b2fc","observation_id":"601cc31d-0320-4af3-9d5d-51459eac78b6","resolution":{"observed_at":"2026-08-06T19:23:53.287503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:52.943782Z","title":"Hikami, E","venue":null,"work_id":"ab9420f8-3b2b-4401-b7d0-61bfed2dd24e","year":1978},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:37.939697Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:52d1abd8c2699e9d5d7894ee134116e02495df4970f29ca1a0cf219f528460fa","observation_id":"0ef176c2-caaa-413e-aee3-dd32678db484","resolution":{"observed_at":"2026-08-06T19:23:53.066905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:52.756117Z","title":"Friedan,Nonlinear models in2 +εdimensions, Ann","venue":null,"work_id":"764b3851-352f-4708-b57e-745972333a80","year":1985},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:38.023807Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:96b552f6e53f3214a78738f5e5252fb8f7e8da5907e09d64e5e7a52d863e6325","observation_id":"b9dc51ac-6c72-416b-b0cf-fe782ead00dd","resolution":{"observed_at":"2026-08-06T19:23:52.819336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:52.522531Z","title":null,"venue":null,"work_id":"02c03b76-c632-4f5c-8abc-c05598e6fb24","year":1987},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:38.159283Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:ff0c806bb22218eaa2a85b5a42da1f8a3abbbe40b5bdcff8bce7cdda177f9308","observation_id":"ae50b954-f37f-41cf-a318-35346a62ebd3","resolution":{"observed_at":"2026-08-06T19:23:52.612404Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:38.300805Z","title":"Bakas,Renormalization group equations and geometric flows, (2007) doi:10.48550/arXiv.hep- th/0702034","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:38.300805Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:2da0969ca082e70e5c5663ebcc53819eacf89a92f395281f97fb7b0245c46f67","observation_id":"911eb2b8-ab90-4e46-b392-462fe911560c","resolution":{"observed_at":"2026-08-06T19:23:38.300805Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1007.0355","last_updated":"2010-07-02T12:39:26Z","snapshot_observed_at":"2026-07-06T02:12:33.738387Z","submitted_at":"2010-07-02T12:39:26Z","title":"Non-Linear Sigma Model and asymptotic freedom at the Lifshitz point","version":1},"cited_work":{"arxiv_id":"1007.0355","doi":"10.48550/arxiv.1007.0355","metadata_source":"pith","pith_arxiv_id":"1007.0355","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Non-Linear Sigma Model and asymptotic freedom at the Lifshitz point","venue":"hep-th","work_id":"bb6d5887-2471-436e-a710-0c8c11869389","year":2010},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:38.451730Z"},"links":{"cited_paper":"/paper/1007.0355","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:929bfd6a0b3dd4d7a24a9fea997f388089062e8812e472eecbc04ad155189c7e","observation_id":"008f2ae6-05c5-4b77-8b1b-c420e6c8ad75","resolution":{"observed_at":"2026-08-06T19:23:46.483200Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00032-010-0110-y","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Carfora,Renormalization Group and the Ricci Flow, Milan Journal of Mathematics,78(1), 319– 353 (2010) doi:10.1007/s00032-010-0110-y","venue":"Milan Journal of Mathematics","work_id":"2acf8d01-88eb-40fe-a657-da6940de6d90","year":2010},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:38.607638Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:51cfa37f5ab0e37d26d5803edfc94c4e5d8b8f48646a07b1ae5044a391a840cf","observation_id":"ad691dd8-1d65-4bb9-8676-39585cde2a75","resolution":{"observed_at":"2026-08-06T19:23:46.284682Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevd.104.105003","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Physical review. D/Physical review. D.","work_id":"ef864b29-7a99-4c80-9b3f-a070b389efa9","year":2021},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:38.705222Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:e4a767007cfd2b820ce9e287c4f237c8e307f140a2dba717d1319ebcb2e17228","observation_id":"a786d6a7-8bc1-4e7b-86b8-ae90e1d6ef12","resolution":{"observed_at":"2026-08-06T19:23:46.077801Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/jhep03(2023)003","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Levine,Universal 1-loop divergences for integrable sigma models, J","venue":"Journal of High Energy Physics","work_id":"90f1e3dc-b66d-450c-ab44-c5d9c13a1d87","year":2023},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:38.836672Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:c2d79e7ad84f0d0f1741a10b1e84a34ea8ca53c2eaf64e08b73bc5a37abacf71","observation_id":"c3133071-4060-4bc3-a8b8-0e73560d6f06","resolution":{"observed_at":"2026-08-06T19:23:45.903813Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2209.01783","last_updated":"2022-09-05T06:40:32Z","snapshot_observed_at":"2026-07-06T13:48:46.364019Z","submitted_at":"2022-09-05T06:40:32Z","title":"Explicit Cutoff Regularization in Coordinate Representation","version":1},"cited_work":{"arxiv_id":"2209.01783","doi":null,"metadata_source":"pith","pith_arxiv_id":"2209.01783","snapshot_observed_at":"2026-08-06T19:23:47.371824Z","title":"Explicit Cutoff Regularization in Coordinate Representation","venue":"hep-th","work_id":"a5410a39-af8c-40db-97ce-d29c97b3445d","year":2022},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:38.947444Z"},"links":{"cited_paper":"/paper/2209.01783","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:05d0e2bd01a9d56b0512baf077ed1d9a1180000a64df9494f4abee15792aafcf","observation_id":"eddc5290-551b-425d-a675-5d5457778c10","resolution":{"observed_at":"2026-08-06T19:23:47.440846Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.09218","last_updated":"2024-03-14T09:33:37Z","snapshot_observed_at":"2026-08-02T06:47:43.227545Z","submitted_at":"2024-03-14T09:33:37Z","title":"On a criterion for a cutoff regularization in the coordinate representation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.09218","snapshot_observed_at":"2026-08-06T19:23:39.098743Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:39.098743Z"},"links":{"cited_paper":"/paper/2403.09218","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:fb4a433be53eb790dea9c57726f7a4f2d1ebba120b9a3c51836d7df22dc5e495","observation_id":"e7fe2ba6-abdf-4325-84fe-7e0199836133","resolution":{"observed_at":"2026-08-06T19:23:39.098743Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:39.214601Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:39.214601Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:a1d053710a02d1ad7a698d12977a175cc9353ebc8631d46e9c9d2c005c133bdf","observation_id":"0abbe150-2f03-454c-a720-9b9ea24cb8f0","resolution":{"observed_at":"2026-08-06T19:23:39.214601Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:52.295279Z","title":null,"venue":null,"work_id":"374c9813-c913-4438-869a-9fd0186be266","year":1986},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:39.328302Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:79f6c50dce17e2df5d51a110bf79ffe462455a07fc545416ce845fbea88fe000","observation_id":"8cdb129f-6847-4de3-b974-92a79fa07bd9","resolution":{"observed_at":"2026-08-06T19:23:52.398023Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:52.102529Z","title":null,"venue":null,"work_id":"ec1c1bc5-59cd-43da-919f-fb0abb1ebe48","year":1986},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:39.452537Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:c0599f70254b8d818ac89fe6abd41293579d60fae92c992b5afbfa6e3e900e91","observation_id":"a890cbf5-c3bf-4cbc-b125-c2b715daa53d","resolution":{"observed_at":"2026-08-06T19:23:52.195739Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:39.579892Z","title":null,"venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:39.579892Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:31dbf851220cde461fce16f3d823fa0be79c917b48420e625ee2df5aef8ecb21","observation_id":"cc50f63a-3dc5-411f-93d7-b140c3c8053d","resolution":{"observed_at":"2026-08-06T19:23:39.579892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0003-4916(79)90361-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Annals of Physics","work_id":"3b8058b6-c6cd-4f6c-95b2-176e50b2d1ad","year":1979},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:39.668715Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:55d56faec6c944cf68bef2b4a4b700052bbf68f2d07c55b3d5a880ab2865aa46","observation_id":"ff7e0e99-5e35-4ce5-bfbf-991211f1fa4e","resolution":{"observed_at":"2026-08-06T19:23:45.660959Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:51.841829Z","title":null,"venue":null,"work_id":"9adcd86e-be37-4c0b-a9f2-170d3cc917b6","year":1982},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:39.776291Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:fd7edc83d8a399c57038b4cb91d19542cb474ca432872742f19ad0ef27a213f7","observation_id":"536bea3b-e9e9-4f9f-b5da-6c7a4bcb9b62","resolution":{"observed_at":"2026-08-06T19:23:51.964168Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:39.906576Z","title":"D Faddeev, N","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:39.906576Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:a8c49acb44404f919ba35d0c6c8e3e8ffcec022c0edcee27f29ae9ea5c45b55e","observation_id":"0353cf8f-050f-4fb6-814e-5d036f698cd1","resolution":{"observed_at":"2026-08-06T19:23:39.906576Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:40.071343Z","title":"Arutyunov, S","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:40.071343Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:3f8509cfee8514e6b3c1d92cb99cccf2e01bce84534ffeed9d655b82a715ba53","observation_id":"93aceb53-9bae-4b3a-a664-70a7afd542ab","resolution":{"observed_at":"2026-08-06T19:23:40.071343Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:50.262736Z","title":null,"venue":null,"work_id":"f8d0d52e-5083-41db-8fd6-fef8ae9c048b","year":1998},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:42.696268Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:d6efc5f9e618f353e43f59081e3df6a0986dede74aeba4182e3bfcb954254a31","observation_id":"a27aeb69-babc-49c3-8d9c-5ca1c5e08222","resolution":{"observed_at":"2026-08-06T19:23:50.350965Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:40.343787Z","title":"Evslin, B","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:40.343787Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:67d304dec07d483a54894deab7c94a671a251dd41d2fc681ff901040b8cfe5a8","observation_id":"53faef5d-07ba-46bd-be88-84c056fc2211","resolution":{"observed_at":"2026-08-06T19:23:40.343787Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevlett.121.227201","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Physical Review Letters","work_id":"15c55e20-b785-4bd0-938a-a304611fc7fe","year":2018},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:40.447081Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:e28a2b0036ceefb27e0333c0b7c4432069cbed5b8fe11efbb6beb616649da542","observation_id":"5a6958f8-e7d4-4003-8291-fb9b9f97427e","resolution":{"observed_at":"2026-08-06T19:23:45.370753Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1140/epjc/s10052-019-6623-9","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Kluson,Nonrelativistic String Theory Sigma Model and Its Canonical Formulation, Eur","venue":"The European Physical Journal C","work_id":"d0b64e99-1474-49b6-bb94-a9cb53c5c17f","year":2019},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:40.567655Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:8cd2134c2e386c9317dd5e3a77057b05d2c3707381cd849fc655e9ffb5fd6a0a","observation_id":"328712e1-8cd9-45f5-9d79-817bd60c4f0c","resolution":{"observed_at":"2026-08-06T19:23:45.109863Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:40.661801Z","title":"Bascone, F","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:40.661801Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:7eb4e5991055832d1a3591fd6873db6531d60e3da9499901ec84669a1487c37a","observation_id":"1d64dd75-4d96-4120-b7e7-8bea70f6c432","resolution":{"observed_at":"2026-08-06T19:23:40.661801Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:40.808031Z","title":"Hoare,Integrable deformations of sigma models, J","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:40.808031Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:255406c14fe51a987458b44c18621fb98a023a12504cdf9406f5a0225a7575f7","observation_id":"af34ebdb-0c81-4b9e-8a78-ece9229b59ed","resolution":{"observed_at":"2026-08-06T19:23:40.808031Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2022.83227","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:47.186273Z","title":"Oling, Z","venue":null,"work_id":"37542804-47cd-4eac-9479-11b64dbfd778","year":2022},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:40.938339Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:4915b84bc895277e879d299b557c9dd56f1e104c2b4475a0d73c0b737ab51843","observation_id":"1b7b0c19-dccc-4a1f-b4c4-ccef25fbc2af","resolution":{"observed_at":"2026-08-06T19:23:47.258599Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02605","last_updated":"2026-04-21T08:58:10Z","snapshot_observed_at":"2026-07-06T21:51:42.968922Z","submitted_at":"2025-07-03T13:27:25Z","title":"Trans-series from condensates in the non-linear sigma model","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02605","snapshot_observed_at":"2026-08-06T19:23:41.030948Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:41.030948Z"},"links":{"cited_paper":"/paper/2507.02605","citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:a1ddd1b657f2e725b3f20512cbe4c57f0873575addb19fae74b66000cd731644","observation_id":"8a872532-0013-4356-a561-598546def22e","resolution":{"observed_at":"2026-08-06T19:23:41.030948Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:51.601932Z","title":null,"venue":null,"work_id":"e57968a7-d0be-472a-bb10-30d84356555a","year":2016},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:41.204076Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:695cab22333a63abed742ac1f9a2af7579ce17dbc1e5fec217bb467dec6fa943","observation_id":"646e3fc8-d157-436b-b048-441178bd7b8e","resolution":{"observed_at":"2026-08-06T19:23:51.707010Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:41.304357Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:41.304357Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:d6b9f31dfede810aff2ca623df7afebbaa4a3777a31a7cfb8ac420dc7cdb9dfc","observation_id":"2e468b3e-72a3-4ab9-aed2-aaf8d9dc61ef","resolution":{"observed_at":"2026-08-06T19:23:41.304357Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:51.399430Z","title":"Nakahara,Geometry, topology and physics, Second Edition, CRC Press, 1–573 (2003)","venue":null,"work_id":"ecd9a227-8131-425d-83b9-382ec7d03d82","year":2003},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:41.425156Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:dae28dea309cd164f83dc1222696b38504d4f4ff1a0918f578cff544b5f65acd","observation_id":"3ff49fd3-e1c4-4ec4-a33d-50ff485ebaa8","resolution":{"observed_at":"2026-08-06T19:23:51.483742Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:51.214273Z","title":null,"venue":null,"work_id":"8f942996-94e1-4e2c-abf3-a8c045cf7301","year":1967},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:41.555132Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:a02556536445adbd5557b0801b5842cc6d99a6269f0e8bb2db40fe5df68aefed","observation_id":"19fb37a0-b3d1-448f-a5cb-4b4b894cb0ae","resolution":{"observed_at":"2026-08-06T19:23:51.303640Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:23:51.024869Z","title":null,"venue":null,"work_id":"adb2297c-242e-48fe-97e8-087333a38c2a","year":1967},"citing_paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model","version":1},"reference_index":101,"source":"pdf_text","source_observed_at":"2026-08-06T19:23:41.679241Z"},"links":{"citing_paper":"/paper/2507.05923"},"observation_digest":"sha256:9737d74c93007ccb446e80cfaca0e3f8dd47d1d09cfa76ac4cc9c244be2b2b23","observation_id":"84f67887-555d-4357-bc96-11121c58134e","resolution":{"observed_at":"2026-08-06T19:23:51.105603Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.05923","last_updated":"2025-07-08T12:11:02Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-07T23:02:41.624275Z","submitted_at":"2025-07-08T12:11:02Z","title":"Three-loop singularity structure for a non-linear sigma model"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":3,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":75,"verified_exact":14,"verified_fuzzy":6},"total_outbound_references":121},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 100 of 121 outbound references and 1 inbound Pith citation observation for arXiv:2507.05923."}