{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GJZDUY2FFL5GAT3BG3RDBWXOLN","short_pith_number":"pith:GJZDUY2F","canonical_record":{"source":{"id":"2607.12940","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2026-07-14T16:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"533bfbdd8262428cddc23260c3c7ebd043fc5adb37d7c615f772060a572ed252","abstract_canon_sha256":"b0c8fc367443378dd316abe5024d7d5d6950d016b63caa8bfe7710e9b928e1fe"},"schema_version":"1.0"},"canonical_sha256":"32723a63452afa604f6136e230daee5b6974933a66386472dd82c748d9187e69","source":{"kind":"arxiv","id":"2607.12940","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.12940","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"2607.12940v1","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12940","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"GJZDUY2FFL5G","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_16","alias_value":"GJZDUY2FFL5GAT3B","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_8","alias_value":"GJZDUY2F","created_at":"2026-07-15T01:22:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GJZDUY2FFL5GAT3BG3RDBWXOLN","target":"record","payload":{"canonical_record":{"source":{"id":"2607.12940","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2026-07-14T16:14:57Z","cross_cats_sorted":[],"title_canon_sha256":"533bfbdd8262428cddc23260c3c7ebd043fc5adb37d7c615f772060a572ed252","abstract_canon_sha256":"b0c8fc367443378dd316abe5024d7d5d6950d016b63caa8bfe7710e9b928e1fe"},"schema_version":"1.0"},"canonical_sha256":"32723a63452afa604f6136e230daee5b6974933a66386472dd82c748d9187e69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:22:26.469168Z","signature_b64":"PkuzRJlCikCs7c/z0Iah0BqtHkpOuqQBCXLiyhrD+NnNTKaduy8gejH0LHgptJwnFdOjZNZObO8jz3yDOGWMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32723a63452afa604f6136e230daee5b6974933a66386472dd82c748d9187e69","last_reissued_at":"2026-07-15T01:22:26.468348Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:22:26.468348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.12940","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":"2026-07-15T01:22:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ti0wXH4Xq+1yM0Uif89O8ljpPfvcHlZKc/N5gTgQJXydYJ+8EkfxTlgsKMZzeK8ZdmzEcvClbK/draxGONIhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T09:08:36.069627Z"},"content_sha256":"0663d58fcc8ba9af2a8aa274fdb0a8ad25cc70b40de5a372910608ef4e722233","schema_version":"1.0","event_id":"sha256:0663d58fcc8ba9af2a8aa274fdb0a8ad25cc70b40de5a372910608ef4e722233"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GJZDUY2FFL5GAT3BG3RDBWXOLN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The symplectic Hadamard question","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dan Cristofaro-Gardiner","submitted_at":"2026-07-14T16:14:57Z","abstract_excerpt":"We show that a simply connected symplectic manifold admitting a complete nonpositively curved compatible metric is symplectomorphic to R^{2n} with its standard symplectic form. This answers the \"symplectic Hadamard question\" of McDuff-Salamon in the affirmative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12940","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.12940/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-15T01:22:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w66eHgUy4IQfn02Zh9MFbM11a20wUNmdiMLIEiwPw8uCpllbkJQjxsyO7kKwxE8eFPANTmW4CIIpB2QC9RpbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-01T09:08:36.069964Z"},"content_sha256":"467f7caa4a580956f610f25cf44f65053658029fcc64bfac7f927e14000590c5","schema_version":"1.0","event_id":"sha256:467f7caa4a580956f610f25cf44f65053658029fcc64bfac7f927e14000590c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJZDUY2FFL5GAT3BG3RDBWXOLN/bundle.json","state_url":"https://pith.science/pith/GJZDUY2FFL5GAT3BG3RDBWXOLN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJZDUY2FFL5GAT3BG3RDBWXOLN/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":"2026-08-01T09:08:36Z","links":{"resolver":"https://pith.science/pith/GJZDUY2FFL5GAT3BG3RDBWXOLN","bundle":"https://pith.science/pith/GJZDUY2FFL5GAT3BG3RDBWXOLN/bundle.json","state":"https://pith.science/pith/GJZDUY2FFL5GAT3BG3RDBWXOLN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJZDUY2FFL5GAT3BG3RDBWXOLN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GJZDUY2FFL5GAT3BG3RDBWXOLN","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":"b0c8fc367443378dd316abe5024d7d5d6950d016b63caa8bfe7710e9b928e1fe","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2026-07-14T16:14:57Z","title_canon_sha256":"533bfbdd8262428cddc23260c3c7ebd043fc5adb37d7c615f772060a572ed252"},"schema_version":"1.0","source":{"id":"2607.12940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.12940","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"2607.12940v1","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12940","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"GJZDUY2FFL5G","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_16","alias_value":"GJZDUY2FFL5GAT3B","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_8","alias_value":"GJZDUY2F","created_at":"2026-07-15T01:22:26Z"}],"graph_snapshots":[{"event_id":"sha256:467f7caa4a580956f610f25cf44f65053658029fcc64bfac7f927e14000590c5","target":"graph","created_at":"2026-07-15T01:22:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.12940/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that a simply connected symplectic manifold admitting a complete nonpositively curved compatible metric is symplectomorphic to R^{2n} with its standard symplectic form. This answers the \"symplectic Hadamard question\" of McDuff-Salamon in the affirmative.","authors_text":"Dan Cristofaro-Gardiner","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2026-07-14T16:14:57Z","title":"The symplectic Hadamard question"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12940","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":"sha256:0663d58fcc8ba9af2a8aa274fdb0a8ad25cc70b40de5a372910608ef4e722233","target":"record","created_at":"2026-07-15T01:22:26Z","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":"b0c8fc367443378dd316abe5024d7d5d6950d016b63caa8bfe7710e9b928e1fe","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2026-07-14T16:14:57Z","title_canon_sha256":"533bfbdd8262428cddc23260c3c7ebd043fc5adb37d7c615f772060a572ed252"},"schema_version":"1.0","source":{"id":"2607.12940","kind":"arxiv","version":1}},"canonical_sha256":"32723a63452afa604f6136e230daee5b6974933a66386472dd82c748d9187e69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32723a63452afa604f6136e230daee5b6974933a66386472dd82c748d9187e69","first_computed_at":"2026-07-15T01:22:26.468348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-15T01:22:26.468348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PkuzRJlCikCs7c/z0Iah0BqtHkpOuqQBCXLiyhrD+NnNTKaduy8gejH0LHgptJwnFdOjZNZObO8jz3yDOGWMAA==","signature_status":"signed_v1","signed_at":"2026-07-15T01:22:26.469168Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.12940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0663d58fcc8ba9af2a8aa274fdb0a8ad25cc70b40de5a372910608ef4e722233","sha256:467f7caa4a580956f610f25cf44f65053658029fcc64bfac7f927e14000590c5"],"state_sha256":"ed0df02ed176d00929a91eacbd0e9ded4122cbf38a216396f8c48ced19d5650c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vQ6+qnQLf3MGxptyzJ2uZ0fEjLu2MunFhYrcwPDRoozLlr8bTVg9mmnjo+LEHqHwBC3TX09dCjwCGSZT7RFQCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-01T09:08:36.073267Z","bundle_sha256":"9d0f413452a5bda84faad02d4adc0dffda6876f59fa17357e8d4d1f27930dffb"}}