{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UOWIAHFFC7FE47HMBTHH5UQBP5","short_pith_number":"pith:UOWIAHFF","canonical_record":{"source":{"id":"1501.06480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-01-26T16:53:47Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"3d1cfb79079c3369bf55f6eb5c2766da9846f08d95188be63b57860638eb3046","abstract_canon_sha256":"5353bc33ab077bc2080fccd616b0d2b36c09d0be6595b25892231123a41d4502"},"schema_version":"1.0"},"canonical_sha256":"a3ac801ca517ca4e7cec0cce7ed2017f6cc86cb20ac796e18e650f15695edee3","source":{"kind":"arxiv","id":"1501.06480","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06480","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06480v1","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06480","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"UOWIAHFFC7FE","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UOWIAHFFC7FE47HM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UOWIAHFF","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UOWIAHFFC7FE47HMBTHH5UQBP5","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-01-26T16:53:47Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"3d1cfb79079c3369bf55f6eb5c2766da9846f08d95188be63b57860638eb3046","abstract_canon_sha256":"5353bc33ab077bc2080fccd616b0d2b36c09d0be6595b25892231123a41d4502"},"schema_version":"1.0"},"canonical_sha256":"a3ac801ca517ca4e7cec0cce7ed2017f6cc86cb20ac796e18e650f15695edee3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:41.367244Z","signature_b64":"ZdQei1v7R3yqJJbofelFAqGr/fll8q1BSJV+Vt09HGoxBeIwvG8t/vM170dhQgX9hfTkiuJVSJDVVFlhTUMWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3ac801ca517ca4e7cec0cce7ed2017f6cc86cb20ac796e18e650f15695edee3","last_reissued_at":"2026-05-18T02:28:41.366664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:41.366664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06480","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FGgJFKg8uaBlSOwuisys/8rIllceNsDCj2+Xd3AM1fK1x/jZX7EF9vjrGTAIxs5ze3gpvZXP2BSSZPZ0G5jjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:27:37.144649Z"},"content_sha256":"e44451a2ae5dc28915d41daa8953cbb8fa093afc07ef4929d2384f33f3a2c133","schema_version":"1.0","event_id":"sha256:e44451a2ae5dc28915d41daa8953cbb8fa093afc07ef4929d2384f33f3a2c133"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UOWIAHFFC7FE47HMBTHH5UQBP5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic actions of non-Hamiltonian type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"\\'Alvaro Pelayo","submitted_at":"2015-01-26T16:53:47Z","abstract_excerpt":"Hamiltonian symplectic actions of tori on compact symplectic manifolds have been extensively studied in the past thirty years, and a number of classifications have been achieved, for instance in the case that the acting torus is $n$-dimensional and the symplectic manifold is $2n$-dimensional. In this case the $n$-dimensional orbits are Lagrangian, so it is natural to wonder whether there are interesting classes of symplectic actions with Lagrangian orbits, and that are not Hamiltonian. It turns out that there are many such classes which contain for example the Kodaira variety, and which can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06480","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nkn6NwIXP2s3pTGWbPTWOcsILs7RhiSeQUYMS2nm34CHZE2EgJ0G21Uyq1W+EguP8nbPXkJAlAJ0p02t2DxOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:27:37.145264Z"},"content_sha256":"795e2742e3cc0456c9695060a70d6bf66e15b5eb7aa3f74c7b438e0710268170","schema_version":"1.0","event_id":"sha256:795e2742e3cc0456c9695060a70d6bf66e15b5eb7aa3f74c7b438e0710268170"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOWIAHFFC7FE47HMBTHH5UQBP5/bundle.json","state_url":"https://pith.science/pith/UOWIAHFFC7FE47HMBTHH5UQBP5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOWIAHFFC7FE47HMBTHH5UQBP5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T21:27:37Z","links":{"resolver":"https://pith.science/pith/UOWIAHFFC7FE47HMBTHH5UQBP5","bundle":"https://pith.science/pith/UOWIAHFFC7FE47HMBTHH5UQBP5/bundle.json","state":"https://pith.science/pith/UOWIAHFFC7FE47HMBTHH5UQBP5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOWIAHFFC7FE47HMBTHH5UQBP5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UOWIAHFFC7FE47HMBTHH5UQBP5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5353bc33ab077bc2080fccd616b0d2b36c09d0be6595b25892231123a41d4502","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-01-26T16:53:47Z","title_canon_sha256":"3d1cfb79079c3369bf55f6eb5c2766da9846f08d95188be63b57860638eb3046"},"schema_version":"1.0","source":{"id":"1501.06480","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06480","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06480v1","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06480","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"UOWIAHFFC7FE","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UOWIAHFFC7FE47HM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UOWIAHFF","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:795e2742e3cc0456c9695060a70d6bf66e15b5eb7aa3f74c7b438e0710268170","target":"graph","created_at":"2026-05-18T02:28:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Hamiltonian symplectic actions of tori on compact symplectic manifolds have been extensively studied in the past thirty years, and a number of classifications have been achieved, for instance in the case that the acting torus is $n$-dimensional and the symplectic manifold is $2n$-dimensional. In this case the $n$-dimensional orbits are Lagrangian, so it is natural to wonder whether there are interesting classes of symplectic actions with Lagrangian orbits, and that are not Hamiltonian. It turns out that there are many such classes which contain for example the Kodaira variety, and which can be","authors_text":"\\'Alvaro Pelayo","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-01-26T16:53:47Z","title":"Symplectic actions of non-Hamiltonian type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06480","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e44451a2ae5dc28915d41daa8953cbb8fa093afc07ef4929d2384f33f3a2c133","target":"record","created_at":"2026-05-18T02:28:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5353bc33ab077bc2080fccd616b0d2b36c09d0be6595b25892231123a41d4502","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-01-26T16:53:47Z","title_canon_sha256":"3d1cfb79079c3369bf55f6eb5c2766da9846f08d95188be63b57860638eb3046"},"schema_version":"1.0","source":{"id":"1501.06480","kind":"arxiv","version":1}},"canonical_sha256":"a3ac801ca517ca4e7cec0cce7ed2017f6cc86cb20ac796e18e650f15695edee3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3ac801ca517ca4e7cec0cce7ed2017f6cc86cb20ac796e18e650f15695edee3","first_computed_at":"2026-05-18T02:28:41.366664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:41.366664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZdQei1v7R3yqJJbofelFAqGr/fll8q1BSJV+Vt09HGoxBeIwvG8t/vM170dhQgX9hfTkiuJVSJDVVFlhTUMWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:41.367244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06480","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e44451a2ae5dc28915d41daa8953cbb8fa093afc07ef4929d2384f33f3a2c133","sha256:795e2742e3cc0456c9695060a70d6bf66e15b5eb7aa3f74c7b438e0710268170"],"state_sha256":"3346884e48ad096b43d356ccdf5ec0fc31be8b52b21efba35681a68a47c66ecc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4FKOhYjMRr0tnUoOljBvU/TCRFU9N6CLTcymzn03vb5vSXpyO3hXxdxCRqpTu785Kfh8wKz0XRxJewXkOzfoBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:27:37.148753Z","bundle_sha256":"60a234af708bab7b53f4e7aecc946eea965c2771b6b024970ecbccf2b033a9a3"}}