{"as_of":"2026-08-12T05:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:28a1e335e1791d1ee27dbbd7c72e666f73c79a0b711fb609f81edfb680b7b195","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T18:33:22.621166Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-27T21:21:09.871182Z","state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2606.02150/citation-record","integrity":"/paper/2606.02150/integrity","json":"/paper/2606.02150/citation-record.json","paper":"/paper/2606.02150"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:1747b57d7bec966e231eb808fa08a11fec3cf05df949ec00fc73d44ace6c603b","observation_id":"6f6c6961-cdb5-44d2-89af-e3ce530ae5c4","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"Electron","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:329ca51cdde71199a5340829a0c510183d2e350fee9b7075918e83507f24909d","observation_id":"9524d0e8-3ffa-488e-94e4-ca6151387be2","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"A., Perween, A.,A Comprehensive Review of Golden Riemannian Mani- folds, Axioms 13(10), (2024), 724","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:09a0aea612f7cc31e660ad8cf32e9ae605b496a617abad815fa5af5ae59c8e8e","observation_id":"51d08084-3d82-43a0-ad54-2e91e6dd66e3","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"et al.,Quantum criticality in an Ising chain: experimental evidence for emergentE 8 sym- metry, ScienceVol 327, Issue 5962 (2010), 177-180","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:9aefdab159668767df4607b1e8ed5004363967611b3bdd6c98eb85fe362c5448","observation_id":"0d0ddc2c-c7e6-434e-a62e-ef473dd4d48c","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"E.,Golden differential geometry, Chaos Solitons Fractals 38 (2008), 1229–1238","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:c9a96cf9940d9ec55dd89f3adb86feec64cbdef8d15058df653f2e6f50cde44e","observation_id":"d4d136b2-4abc-4efa-ab09-2ebdc295b7a4","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"and Moody, R","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:7e3c96db5c17d0ddcef9d63bb3c7f6134cde411ea1370a5cd62d8d0f3ecba4ea","observation_id":"dbc704f8-6c64-49eb-86fd-406493365d4c","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:6ecc4da09074ca1a64f5db1684d249c7d9e8e571acf302bb7990b38f3420da2d","observation_id":"4556572b-24a3-4210-8249-e99839b31493","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:a85b28a9bb380e2b661516f9c969780468133acbb5506c323ace6dbf3b012964","observation_id":"055cb9cc-b340-45fd-81f3-95268eb3239e","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"I., Yano, K.,Polynomial structures on manifolds, Kodai Math","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:ffdc8f904316675d092416e283e84b095710451e302478cbdcd01d77ffcbf9aa","observation_id":"03608c09-b777-4901-bce1-8d41931dce5b","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"E., Cr˘ a¸ smareanu, M.,On some invariant submanifolds in a Riemannian manifold with golden structure, An","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:2dc7c70a4ff7dd9b063ccb8cd9409020fe267be09a428f3e78258e53f7551a5f","observation_id":"c7484bf1-d693-4b02-ad03-aeee8c285e80","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:6b984345e3c5570e6a4049926126983c2ec22d80536544cd169c92e7ba0e2f22","observation_id":"a21e5360-93ab-45a6-bb9b-73a45161fae7","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:0db4f5f8e3f1f4bfc10dcc0689220728b1830eafb17dfb296b8e76955375a33f","observation_id":"95de9233-e572-4db6-af09-d48a4e6b481f","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:94c4a3ca77bad924cac577e805b445c0a5bbf0b6b86340b93b65d94b315a07fb","observation_id":"428b541f-5346-4fce-830b-7d119c0aa1b5","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:8f29970d7ef32f3d69deea4b2c817588705e704360589a663f5f6679e21f3c93","observation_id":"9279dabf-7ea6-4f0f-9543-c23117c2c668","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:9489270394258757ed82486a2a464cfd40facf0e934995791ccceaf93ff4c4fa","observation_id":"f5e39701-27be-40c8-b826-1c983854f4cd","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:d66de29708991612dcb16a8588de2249a72b0aed2efee3f7a32697d6a1fa0dfc","observation_id":"015d0a08-c572-46b1-955e-d40f95ba540c","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"W.,On characterization of the onset to chaos, Chaos Solitons Fractals 8(10) (1997), 1631–1643","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:ad5ed2147697d3258ce04902ba219fb34618b2f0dbe7d72bd231deca4630ff55","observation_id":"b536accb-2eca-4cf9-9bc4-3e6d58c070d8","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"W.,The Metallic Means family and multifractal spectra, Nonlinear Analysis 36 (1999), 721–745","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:d4c5eaa5e2a52fb0ca160ea6f949e6152e3baeda5b92e040ab74382f86d30fbf","observation_id":"d827034c-3d3b-4363-ad5a-d9b41f1efa34","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"W.,The metallic means family and renormalization group techniques, Proc","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:1dc6042848deb66d1a4a0f5cd95bc9e9dd88ef8eb13a7781ee69fcbb1667b053","observation_id":"d0af410c-b245-40c6-8ed9-f23b23b423d1","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"P.,The generalized golden proportions, a new theory of real numbers, and ternary mirror- symmetrical arithmetic, Chaos Solitons Fractals 33(2) (2007), 315–334","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:babc1499ddd133d07bd16ec7c25f57cd56f919cbab93bfc11996b0f5c8a1121e","observation_id":"e262c27f-06ad-46cc-8d0a-1a0d0b05a361","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:e0ee661f5cea08b0ee42cc2af1df6ebb2723580c30fa8db11adc507785de8a9c","observation_id":"413f6280-5cab-49e7-81ed-aaab1fa0b53c","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"and Zlatanovi´ c, M.,Uniqueness of the Canonical Reciprocal Cost, Mathematics14(2026),","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:f21357b4c36c6a2523db93eb17b912bade8bb29a236ea394b691ff62355e1355","observation_id":"a5a74c34-f544-4f6a-8837-0d2986e9d639","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":"and Zlatanovi´ c, M., Allahyarov, E.,The D’Alembert Inevitability Theorem, Mathematics 14(2026), 1386","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:97166ea5599126df292d483d2a30433a654c1ba5462430bd70241da29c1da903","observation_id":"c4a79cfb-95d9-4a23-a67b-adee4baa246f","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:6404111e5441df3a7b813252f5e46fcf2d6b39aa5fc13542a9cbc0f91cc47e17","observation_id":"c2e60265-8b9a-4a19-8f86-328245a8611b","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:de881eaabfa5a324980df504a92888efce5daaad02adf69f1a938a0e10b247f5","observation_id":"25302199-2819-4cbe-8657-4c0e19353762","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","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":"2026-07-14T18:33:22.621166Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-14T18:33:22.621166Z"},"links":{"citing_paper":"/paper/2606.02150"},"observation_digest":"sha256:933517058fa1bf7c9c0d968ee230493f69773c6c3d6656339c782db1afd6dc1b","observation_id":"a133f204-30a4-4dc4-8902-811d1a3f1e00","resolution":{"observed_at":"2026-07-14T18:33:22.621166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.02150","last_updated":"2026-07-13T17:40:38Z","latest_version":2,"primary_category":"math.DG","snapshot_observed_at":"2026-07-16T23:19:36.582612Z","submitted_at":"2026-06-01T12:17:08Z","title":"Golden and Metallic Structures on Hessian Manifolds"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":26,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":26},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2606.02150."}