{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6CVZ5FPSBMZ735JWXJCJKS3IWP","short_pith_number":"pith:6CVZ5FPS","canonical_record":{"source":{"id":"1507.05842","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-07-21T14:14:46Z","cross_cats_sorted":["math.AG","math.AT"],"title_canon_sha256":"15f4e3960f55a0af03a613e1eee82a5e86da8f1ebaf22a81e148b5fe23b1ae62","abstract_canon_sha256":"7c25d3762bd9c5bedaaee47334a816e2e6feedabc31f826d51786873f509b072"},"schema_version":"1.0"},"canonical_sha256":"f0ab9e95f20b33fdf536ba44954b68b3e53a9da9d92ee59ac0a26693b1bcb781","source":{"kind":"arxiv","id":"1507.05842","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05842","created_at":"2026-05-18T00:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05842v3","created_at":"2026-05-18T00:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05842","created_at":"2026-05-18T00:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"6CVZ5FPSBMZ7","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6CVZ5FPSBMZ735JW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6CVZ5FPS","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6CVZ5FPSBMZ735JWXJCJKS3IWP","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05842","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-07-21T14:14:46Z","cross_cats_sorted":["math.AG","math.AT"],"title_canon_sha256":"15f4e3960f55a0af03a613e1eee82a5e86da8f1ebaf22a81e148b5fe23b1ae62","abstract_canon_sha256":"7c25d3762bd9c5bedaaee47334a816e2e6feedabc31f826d51786873f509b072"},"schema_version":"1.0"},"canonical_sha256":"f0ab9e95f20b33fdf536ba44954b68b3e53a9da9d92ee59ac0a26693b1bcb781","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:56.279241Z","signature_b64":"YQFGVWhhvPDuWYjORZerHPLCi4eVSwtCfzfm9TfLBpR6XlTy2jZY39IN1eEUFG56LxE+h5XJ6nghHehhnKzeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0ab9e95f20b33fdf536ba44954b68b3e53a9da9d92ee59ac0a26693b1bcb781","last_reissued_at":"2026-05-18T00:07:56.278621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:56.278621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05842","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":"2026-05-18T00:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z79dIWYa1dl15b1aByxhkOe7XpJW3Bw5zUbrefLhY7BxM/MKAKvaU1FDmRqj6SY1kRBz/v+3OOim+ZgADVA+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:19:38.005699Z"},"content_sha256":"b131bff524b18622bfb86bd783508536f2abc93bafbb288ee0fed4b633f425b6","schema_version":"1.0","event_id":"sha256:b131bff524b18622bfb86bd783508536f2abc93bafbb288ee0fed4b633f425b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6CVZ5FPSBMZ735JWXJCJKS3IWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generating the Fukaya categories of Hamiltonian G-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.SG","authors_text":"Jonathan David Evans, Yanki Lekili","submitted_at":"2015-07-21T14:14:46Z","abstract_excerpt":"Let $G$ be a compact Lie group and $\\mathbf{k}$ be a field of characteristic $p \\geq 0$ such that $H^* (G)$ does not have $p$-torsion. We show that a free Lagrangian orbit of a Hamiltonian $G$-action on a compact, monotone, symplectic manifold $X$ split-generates an idempotent summand of the monotone Fukaya category $\\mathcal{F}(X; \\mathbf{k})$ if and only if it represents a non-zero object of that summand (slightly more general results are also provided). Our result is based on: an explicit understanding of the wrapped Fukaya category $\\mathcal{W}(T^*G; \\mathbf{k})$ through Koszul twisted com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05842","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":"2026-05-18T00:07:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iM6LobctWuraJFAIHaLgKhxbjQ1sT7OqVJEUx6D7OTBF/qtldZLvkdKtIFs4WOka61ptI17Se3kyJYu9QCWqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:19:38.006040Z"},"content_sha256":"7f0bc8eb3b82dddabbbde5535aa3da13c105462f704a8bf31dee64e97804d81b","schema_version":"1.0","event_id":"sha256:7f0bc8eb3b82dddabbbde5535aa3da13c105462f704a8bf31dee64e97804d81b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CVZ5FPSBMZ735JWXJCJKS3IWP/bundle.json","state_url":"https://pith.science/pith/6CVZ5FPSBMZ735JWXJCJKS3IWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CVZ5FPSBMZ735JWXJCJKS3IWP/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":"2026-06-25T06:19:38Z","links":{"resolver":"https://pith.science/pith/6CVZ5FPSBMZ735JWXJCJKS3IWP","bundle":"https://pith.science/pith/6CVZ5FPSBMZ735JWXJCJKS3IWP/bundle.json","state":"https://pith.science/pith/6CVZ5FPSBMZ735JWXJCJKS3IWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CVZ5FPSBMZ735JWXJCJKS3IWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6CVZ5FPSBMZ735JWXJCJKS3IWP","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":"7c25d3762bd9c5bedaaee47334a816e2e6feedabc31f826d51786873f509b072","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-07-21T14:14:46Z","title_canon_sha256":"15f4e3960f55a0af03a613e1eee82a5e86da8f1ebaf22a81e148b5fe23b1ae62"},"schema_version":"1.0","source":{"id":"1507.05842","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05842","created_at":"2026-05-18T00:07:56Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05842v3","created_at":"2026-05-18T00:07:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05842","created_at":"2026-05-18T00:07:56Z"},{"alias_kind":"pith_short_12","alias_value":"6CVZ5FPSBMZ7","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6CVZ5FPSBMZ735JW","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6CVZ5FPS","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:7f0bc8eb3b82dddabbbde5535aa3da13c105462f704a8bf31dee64e97804d81b","target":"graph","created_at":"2026-05-18T00:07:56Z","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":"Let $G$ be a compact Lie group and $\\mathbf{k}$ be a field of characteristic $p \\geq 0$ such that $H^* (G)$ does not have $p$-torsion. We show that a free Lagrangian orbit of a Hamiltonian $G$-action on a compact, monotone, symplectic manifold $X$ split-generates an idempotent summand of the monotone Fukaya category $\\mathcal{F}(X; \\mathbf{k})$ if and only if it represents a non-zero object of that summand (slightly more general results are also provided). Our result is based on: an explicit understanding of the wrapped Fukaya category $\\mathcal{W}(T^*G; \\mathbf{k})$ through Koszul twisted com","authors_text":"Jonathan David Evans, Yanki Lekili","cross_cats":["math.AG","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-07-21T14:14:46Z","title":"Generating the Fukaya categories of Hamiltonian G-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05842","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:b131bff524b18622bfb86bd783508536f2abc93bafbb288ee0fed4b633f425b6","target":"record","created_at":"2026-05-18T00:07:56Z","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":"7c25d3762bd9c5bedaaee47334a816e2e6feedabc31f826d51786873f509b072","cross_cats_sorted":["math.AG","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-07-21T14:14:46Z","title_canon_sha256":"15f4e3960f55a0af03a613e1eee82a5e86da8f1ebaf22a81e148b5fe23b1ae62"},"schema_version":"1.0","source":{"id":"1507.05842","kind":"arxiv","version":3}},"canonical_sha256":"f0ab9e95f20b33fdf536ba44954b68b3e53a9da9d92ee59ac0a26693b1bcb781","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0ab9e95f20b33fdf536ba44954b68b3e53a9da9d92ee59ac0a26693b1bcb781","first_computed_at":"2026-05-18T00:07:56.278621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:56.278621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YQFGVWhhvPDuWYjORZerHPLCi4eVSwtCfzfm9TfLBpR6XlTy2jZY39IN1eEUFG56LxE+h5XJ6nghHehhnKzeAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:56.279241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05842","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b131bff524b18622bfb86bd783508536f2abc93bafbb288ee0fed4b633f425b6","sha256:7f0bc8eb3b82dddabbbde5535aa3da13c105462f704a8bf31dee64e97804d81b"],"state_sha256":"48086ed0c0d937826019e8cb907f2f4acb5b6b22011e5b6b94b03f5cc68ef678"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NcegTLxpk/Azr6R0JLiP966o8tYGbxkGkERKiIDWUBdO6EPuxP9SZi5Y3hTJ0UN01dHyj4yn4kVHhYUnwRM1Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:19:38.009229Z","bundle_sha256":"dbf50fa420ffd6cead332289dfc5778b1f35bc75fe19f7a68896a0cb9ce1e41d"}}