{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:26DEJEIWRMVJZSKL7CVJIFFTTY","short_pith_number":"pith:26DEJEIW","canonical_record":{"source":{"id":"math/0404539","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2004-04-29T19:52:26Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"67707977d3b7cc34db730fe65c0b8ddacbd214cd28d9ccf91d20b10f9ad316ca","abstract_canon_sha256":"76f927f0b24435a51def5339fcb2bb42b4ece90844ffaa91d9d6bb0cb30c77d6"},"schema_version":"1.0"},"canonical_sha256":"d7864491168b2a9cc94bf8aa9414b39e029effaa7b2b95e64f444aa2f60f90a6","source":{"kind":"arxiv","id":"math/0404539","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404539","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404539v3","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404539","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"26DEJEIWRMVJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"26DEJEIWRMVJZSKL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"26DEJEIW","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:26DEJEIWRMVJZSKL7CVJIFFTTY","target":"record","payload":{"canonical_record":{"source":{"id":"math/0404539","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.SG","submitted_at":"2004-04-29T19:52:26Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"67707977d3b7cc34db730fe65c0b8ddacbd214cd28d9ccf91d20b10f9ad316ca","abstract_canon_sha256":"76f927f0b24435a51def5339fcb2bb42b4ece90844ffaa91d9d6bb0cb30c77d6"},"schema_version":"1.0"},"canonical_sha256":"d7864491168b2a9cc94bf8aa9414b39e029effaa7b2b95e64f444aa2f60f90a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:00.098488Z","signature_b64":"gVYb+cUO6q31ZriVnjUJH7qsmgHUw8j7fIowJ7Bu4v3/W2IELDve/XzRCrAx0SqnjYGcXpOx8C1b/dWh2euMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7864491168b2a9cc94bf8aa9414b39e029effaa7b2b95e64f444aa2f60f90a6","last_reissued_at":"2026-05-18T02:38:00.098084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:00.098084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0404539","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YQO0NDjVZkmegwD91VH2updkw5QOrh6IjgmntYL0l0RqusbKMpmpBFomduE+DbcVbLZiCbZ4fzjYZMiva4q8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:33:52.048082Z"},"content_sha256":"6500d7401a384f5986011109b6faf0c6b6ed778aa1b2e62cd15f1c680b5998d7","schema_version":"1.0","event_id":"sha256:6500d7401a384f5986011109b6faf0c6b6ed778aa1b2e62cd15f1c680b5998d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:26DEJEIWRMVJZSKL7CVJIFFTTY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy properties of Hamiltonian group actions","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Dusa McDuff, Jarek Kedra","submitted_at":"2004-04-29T19:52:26Z","abstract_excerpt":"Consider a Hamiltonian action of a compact Lie group H on a compact symplectic manifold (M,w) and let G be a subgroup of the diffeomorphism group Diff(M). We develop techniques to decide when the maps on rational homotopy and rational homology induced by the classifying map BH --> BG are injective. For example, we extend Reznikov's result for complex projective space CP^n to show that both in this case and the case of generalized flag manifolds the natural map H_*(BSU(n+1)) --> H_*(BG) is injective, where G denotes the group of all diffeomorphisms that act trivially on cohomology. We also show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404539","kind":"arxiv","version":3},"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":"2026-05-18T02:38:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5q3N3PWgdXXyXlsVt77CDvGcaz0YkoN2LfYFVkLSHZQiqtBf45stJrBmDs2r3aAWz/cVB7PVsbrGym0+nlz6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:33:52.048519Z"},"content_sha256":"f15ce98ccddcd192d20934bba410a0fbaabf223dabacf0931d475d369678a0cf","schema_version":"1.0","event_id":"sha256:f15ce98ccddcd192d20934bba410a0fbaabf223dabacf0931d475d369678a0cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/26DEJEIWRMVJZSKL7CVJIFFTTY/bundle.json","state_url":"https://pith.science/pith/26DEJEIWRMVJZSKL7CVJIFFTTY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/26DEJEIWRMVJZSKL7CVJIFFTTY/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":"2026-06-07T18:33:52Z","links":{"resolver":"https://pith.science/pith/26DEJEIWRMVJZSKL7CVJIFFTTY","bundle":"https://pith.science/pith/26DEJEIWRMVJZSKL7CVJIFFTTY/bundle.json","state":"https://pith.science/pith/26DEJEIWRMVJZSKL7CVJIFFTTY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/26DEJEIWRMVJZSKL7CVJIFFTTY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:26DEJEIWRMVJZSKL7CVJIFFTTY","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":"76f927f0b24435a51def5339fcb2bb42b4ece90844ffaa91d9d6bb0cb30c77d6","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.SG","submitted_at":"2004-04-29T19:52:26Z","title_canon_sha256":"67707977d3b7cc34db730fe65c0b8ddacbd214cd28d9ccf91d20b10f9ad316ca"},"schema_version":"1.0","source":{"id":"math/0404539","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0404539","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0404539v3","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0404539","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"26DEJEIWRMVJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"26DEJEIWRMVJZSKL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"26DEJEIW","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:f15ce98ccddcd192d20934bba410a0fbaabf223dabacf0931d475d369678a0cf","target":"graph","created_at":"2026-05-18T02:38:00Z","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":"Consider a Hamiltonian action of a compact Lie group H on a compact symplectic manifold (M,w) and let G be a subgroup of the diffeomorphism group Diff(M). We develop techniques to decide when the maps on rational homotopy and rational homology induced by the classifying map BH --> BG are injective. For example, we extend Reznikov's result for complex projective space CP^n to show that both in this case and the case of generalized flag manifolds the natural map H_*(BSU(n+1)) --> H_*(BG) is injective, where G denotes the group of all diffeomorphisms that act trivially on cohomology. We also show","authors_text":"Dusa McDuff, Jarek Kedra","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2004-04-29T19:52:26Z","title":"Homotopy properties of Hamiltonian group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0404539","kind":"arxiv","version":3},"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":"sha256:6500d7401a384f5986011109b6faf0c6b6ed778aa1b2e62cd15f1c680b5998d7","target":"record","created_at":"2026-05-18T02:38:00Z","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":"76f927f0b24435a51def5339fcb2bb42b4ece90844ffaa91d9d6bb0cb30c77d6","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.SG","submitted_at":"2004-04-29T19:52:26Z","title_canon_sha256":"67707977d3b7cc34db730fe65c0b8ddacbd214cd28d9ccf91d20b10f9ad316ca"},"schema_version":"1.0","source":{"id":"math/0404539","kind":"arxiv","version":3}},"canonical_sha256":"d7864491168b2a9cc94bf8aa9414b39e029effaa7b2b95e64f444aa2f60f90a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7864491168b2a9cc94bf8aa9414b39e029effaa7b2b95e64f444aa2f60f90a6","first_computed_at":"2026-05-18T02:38:00.098084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:00.098084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVYb+cUO6q31ZriVnjUJH7qsmgHUw8j7fIowJ7Bu4v3/W2IELDve/XzRCrAx0SqnjYGcXpOx8C1b/dWh2euMAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:00.098488Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0404539","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6500d7401a384f5986011109b6faf0c6b6ed778aa1b2e62cd15f1c680b5998d7","sha256:f15ce98ccddcd192d20934bba410a0fbaabf223dabacf0931d475d369678a0cf"],"state_sha256":"f2d9be4319e2cbe6f5afa903579d0218db4659b2a5cc8a6d73fb221d611b4db9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lMS5S5KMYVxFTnocewpmtzgYF0kR8QISDjhm1LzBJ4pT4L3Iw4HL2HKgBwFWdcDzcIjtGV7R+ICEJQtbSs9FBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:33:52.051827Z","bundle_sha256":"490742c800b61ad66854fb8e13fd0600deff9568472f092f6d648b77c5e3954a"}}