{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:BFFPMXZSG5RRNDEAR4AXMXOU4Z","short_pith_number":"pith:BFFPMXZS","canonical_record":{"source":{"id":"1104.0348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-04-03T03:22:37Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"f4fc008c706d619ce8ba77c400b1e460f2ab0b7df16954bc62360e2f3a98723a","abstract_canon_sha256":"e874292bcb6497783b486f047fb9e386ee3866857763d1260dd314c999964d54"},"schema_version":"1.0"},"canonical_sha256":"094af65f323763168c808f01765dd4e65f4393c3dea28c65484144b73c762ac3","source":{"kind":"arxiv","id":"1104.0348","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0348","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0348v2","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0348","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"BFFPMXZSG5RR","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BFFPMXZSG5RRNDEA","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BFFPMXZS","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:BFFPMXZSG5RRNDEAR4AXMXOU4Z","target":"record","payload":{"canonical_record":{"source":{"id":"1104.0348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-04-03T03:22:37Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"f4fc008c706d619ce8ba77c400b1e460f2ab0b7df16954bc62360e2f3a98723a","abstract_canon_sha256":"e874292bcb6497783b486f047fb9e386ee3866857763d1260dd314c999964d54"},"schema_version":"1.0"},"canonical_sha256":"094af65f323763168c808f01765dd4e65f4393c3dea28c65484144b73c762ac3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:41.702471Z","signature_b64":"jOCpBTTEyx45+vDe0odOIPLMdWvcfcquBo41e5MzvFfKTmEaW0UVEr5UAcBgvNBRUBSbcrba1DklMg5kFGB+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"094af65f323763168c808f01765dd4e65f4393c3dea28c65484144b73c762ac3","last_reissued_at":"2026-05-18T04:11:41.701989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:41.701989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.0348","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LJNMQssftmcw/5ayK11Kvj197UJTQ2PIF6ISOs7HkjJbn6U5/jQ3mnqdm93cna3Xi31NQ0NQ6kQX/fxRxB7KDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:08:31.106019Z"},"content_sha256":"5fda1981022b96f464e7a7117252b8cefab0fe74f26db2ffdbb8a216e299f8a9","schema_version":"1.0","event_id":"sha256:5fda1981022b96f464e7a7117252b8cefab0fe74f26db2ffdbb8a216e299f8a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:BFFPMXZSG5RRNDEAR4AXMXOU4Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"RAAGs in Ham","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.SG","authors_text":"Michael Kapovich","submitted_at":"2011-04-03T03:22:37Z","abstract_excerpt":"We prove that every RAAG (a Right-Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of the 2-sphere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0348","kind":"arxiv","version":2},"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":"2026-05-18T04:11:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vAXGHZJny0fXBNfnkqg9pR8I9iXvZUzF0Fu4StaW3jT7Ry5b8i0AcH/GVpsf9DSj0CeakE/xxvds+hCaWf/xDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:08:31.106379Z"},"content_sha256":"1bbaac6847820f20ae0ff02b6bbd99e73f33b446914f9768a6df8ca4b5631852","schema_version":"1.0","event_id":"sha256:1bbaac6847820f20ae0ff02b6bbd99e73f33b446914f9768a6df8ca4b5631852"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFFPMXZSG5RRNDEAR4AXMXOU4Z/bundle.json","state_url":"https://pith.science/pith/BFFPMXZSG5RRNDEAR4AXMXOU4Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFFPMXZSG5RRNDEAR4AXMXOU4Z/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":"2026-06-21T23:08:31Z","links":{"resolver":"https://pith.science/pith/BFFPMXZSG5RRNDEAR4AXMXOU4Z","bundle":"https://pith.science/pith/BFFPMXZSG5RRNDEAR4AXMXOU4Z/bundle.json","state":"https://pith.science/pith/BFFPMXZSG5RRNDEAR4AXMXOU4Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFFPMXZSG5RRNDEAR4AXMXOU4Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BFFPMXZSG5RRNDEAR4AXMXOU4Z","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":"e874292bcb6497783b486f047fb9e386ee3866857763d1260dd314c999964d54","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-04-03T03:22:37Z","title_canon_sha256":"f4fc008c706d619ce8ba77c400b1e460f2ab0b7df16954bc62360e2f3a98723a"},"schema_version":"1.0","source":{"id":"1104.0348","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0348","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0348v2","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0348","created_at":"2026-05-18T04:11:41Z"},{"alias_kind":"pith_short_12","alias_value":"BFFPMXZSG5RR","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BFFPMXZSG5RRNDEA","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BFFPMXZS","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:1bbaac6847820f20ae0ff02b6bbd99e73f33b446914f9768a6df8ca4b5631852","target":"graph","created_at":"2026-05-18T04:11:41Z","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":"We prove that every RAAG (a Right-Angled Artin Group) embeds in the group of Hamiltonian symplectomorphisms of the 2-sphere.","authors_text":"Michael Kapovich","cross_cats":["math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-04-03T03:22:37Z","title":"RAAGs in Ham"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0348","kind":"arxiv","version":2},"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":"sha256:5fda1981022b96f464e7a7117252b8cefab0fe74f26db2ffdbb8a216e299f8a9","target":"record","created_at":"2026-05-18T04:11:41Z","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":"e874292bcb6497783b486f047fb9e386ee3866857763d1260dd314c999964d54","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-04-03T03:22:37Z","title_canon_sha256":"f4fc008c706d619ce8ba77c400b1e460f2ab0b7df16954bc62360e2f3a98723a"},"schema_version":"1.0","source":{"id":"1104.0348","kind":"arxiv","version":2}},"canonical_sha256":"094af65f323763168c808f01765dd4e65f4393c3dea28c65484144b73c762ac3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"094af65f323763168c808f01765dd4e65f4393c3dea28c65484144b73c762ac3","first_computed_at":"2026-05-18T04:11:41.701989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:41.701989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jOCpBTTEyx45+vDe0odOIPLMdWvcfcquBo41e5MzvFfKTmEaW0UVEr5UAcBgvNBRUBSbcrba1DklMg5kFGB+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:41.702471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0348","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fda1981022b96f464e7a7117252b8cefab0fe74f26db2ffdbb8a216e299f8a9","sha256:1bbaac6847820f20ae0ff02b6bbd99e73f33b446914f9768a6df8ca4b5631852"],"state_sha256":"22f65be1ebad8b9859fe17b19cdf4b82c4bed877b7fbc8846f0e0665b601b89d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"krrqASQK4plqWugNLwo9h4Mg2HAIrJe5XxTQaS62BvlkUFEUcHOHGnsTf7M3t4/ulL9Q4SQm68jPFQNwjJJ4Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:08:31.108340Z","bundle_sha256":"90c6f8d96b21b82757dc505b92a942bfdd3db3b66ff33382b601ad5ed268cbdf"}}