{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:C35K7FBGNU5Z57KOQ55ZE2QIIF","short_pith_number":"pith:C35K7FBG","canonical_record":{"source":{"id":"1109.1128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-06T09:43:42Z","cross_cats_sorted":[],"title_canon_sha256":"0ad9e79a5c3602c92742e5d500f33b2966a8493fd223ff2514ec2a643749aa91","abstract_canon_sha256":"6da5dbe30ace90d5fd9f7374f957d60d6a6de2f3860617635c4f338b93b6b1a4"},"schema_version":"1.0"},"canonical_sha256":"16faaf94266d3b9efd4e877b926a084160cfaf46e3cea3e3e7fb440ee8cadfae","source":{"kind":"arxiv","id":"1109.1128","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1128","created_at":"2026-05-18T04:14:05Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1128v1","created_at":"2026-05-18T04:14:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1128","created_at":"2026-05-18T04:14:05Z"},{"alias_kind":"pith_short_12","alias_value":"C35K7FBGNU5Z","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C35K7FBGNU5Z57KO","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C35K7FBG","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:C35K7FBGNU5Z57KOQ55ZE2QIIF","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-06T09:43:42Z","cross_cats_sorted":[],"title_canon_sha256":"0ad9e79a5c3602c92742e5d500f33b2966a8493fd223ff2514ec2a643749aa91","abstract_canon_sha256":"6da5dbe30ace90d5fd9f7374f957d60d6a6de2f3860617635c4f338b93b6b1a4"},"schema_version":"1.0"},"canonical_sha256":"16faaf94266d3b9efd4e877b926a084160cfaf46e3cea3e3e7fb440ee8cadfae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:05.332391Z","signature_b64":"COImgKmfiuFgw3nXCbTo0jmzTUbkykAKeiifjQURfIvPDa3apFUtO02+vS42SbJvNlUpL6ZQjO2Vr43hjk2+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16faaf94266d3b9efd4e877b926a084160cfaf46e3cea3e3e7fb440ee8cadfae","last_reissued_at":"2026-05-18T04:14:05.331847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:05.331847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1128","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":"2026-05-18T04:14:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"igQUPqH5di1wRe04MTczpNnwfl5kEEuu9gZ/8tbx2AFb9Is2tQCBxzOP2JyPPqiCQJjiMbwVTyRKCdasrnVyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:37:12.277686Z"},"content_sha256":"a78d63e6f6fa51076226bc205978d452f6a456badbdcebbe2cff7399dc0f3634","schema_version":"1.0","event_id":"sha256:a78d63e6f6fa51076226bc205978d452f6a456badbdcebbe2cff7399dc0f3634"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:C35K7FBGNU5Z57KOQ55ZE2QIIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global dynamics under a weak potential on a sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alessandro Portaluri, Francesco Paparella, Roberto Castelli","submitted_at":"2011-09-06T09:43:42Z","abstract_excerpt":"We give a detailed analytical description of the global dynamics of a point mass moving on a sphere under the action of a logarithmic potential. After performing a McGehee-type blow-up in order to cope with the singularity of the potential, we investigate the rest-points of the flow, the invariant (stable and unstable) manifolds and we give a complete dynamical description of the motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1128","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":"2026-05-18T04:14:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2E/zapXTQ33nZ9zWv+sI75w28REFm2a7yC1r7krTuSYH334wue3GsDjwBxkwRAjMILlWciqUsF4OjqloDoMgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:37:12.278044Z"},"content_sha256":"2d1b9ddc094a246c40c925b98e75442cf81f00324e1cae9a3eb6f4c0d5d287c3","schema_version":"1.0","event_id":"sha256:2d1b9ddc094a246c40c925b98e75442cf81f00324e1cae9a3eb6f4c0d5d287c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C35K7FBGNU5Z57KOQ55ZE2QIIF/bundle.json","state_url":"https://pith.science/pith/C35K7FBGNU5Z57KOQ55ZE2QIIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C35K7FBGNU5Z57KOQ55ZE2QIIF/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":"2026-06-03T17:37:12Z","links":{"resolver":"https://pith.science/pith/C35K7FBGNU5Z57KOQ55ZE2QIIF","bundle":"https://pith.science/pith/C35K7FBGNU5Z57KOQ55ZE2QIIF/bundle.json","state":"https://pith.science/pith/C35K7FBGNU5Z57KOQ55ZE2QIIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C35K7FBGNU5Z57KOQ55ZE2QIIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C35K7FBGNU5Z57KOQ55ZE2QIIF","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":"6da5dbe30ace90d5fd9f7374f957d60d6a6de2f3860617635c4f338b93b6b1a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-06T09:43:42Z","title_canon_sha256":"0ad9e79a5c3602c92742e5d500f33b2966a8493fd223ff2514ec2a643749aa91"},"schema_version":"1.0","source":{"id":"1109.1128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1128","created_at":"2026-05-18T04:14:05Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1128v1","created_at":"2026-05-18T04:14:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1128","created_at":"2026-05-18T04:14:05Z"},{"alias_kind":"pith_short_12","alias_value":"C35K7FBGNU5Z","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C35K7FBGNU5Z57KO","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C35K7FBG","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:2d1b9ddc094a246c40c925b98e75442cf81f00324e1cae9a3eb6f4c0d5d287c3","target":"graph","created_at":"2026-05-18T04:14:05Z","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 give a detailed analytical description of the global dynamics of a point mass moving on a sphere under the action of a logarithmic potential. After performing a McGehee-type blow-up in order to cope with the singularity of the potential, we investigate the rest-points of the flow, the invariant (stable and unstable) manifolds and we give a complete dynamical description of the motion.","authors_text":"Alessandro Portaluri, Francesco Paparella, Roberto Castelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-06T09:43:42Z","title":"Global dynamics under a weak potential on a sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1128","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:a78d63e6f6fa51076226bc205978d452f6a456badbdcebbe2cff7399dc0f3634","target":"record","created_at":"2026-05-18T04:14:05Z","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":"6da5dbe30ace90d5fd9f7374f957d60d6a6de2f3860617635c4f338b93b6b1a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-09-06T09:43:42Z","title_canon_sha256":"0ad9e79a5c3602c92742e5d500f33b2966a8493fd223ff2514ec2a643749aa91"},"schema_version":"1.0","source":{"id":"1109.1128","kind":"arxiv","version":1}},"canonical_sha256":"16faaf94266d3b9efd4e877b926a084160cfaf46e3cea3e3e7fb440ee8cadfae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16faaf94266d3b9efd4e877b926a084160cfaf46e3cea3e3e7fb440ee8cadfae","first_computed_at":"2026-05-18T04:14:05.331847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:05.331847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"COImgKmfiuFgw3nXCbTo0jmzTUbkykAKeiifjQURfIvPDa3apFUtO02+vS42SbJvNlUpL6ZQjO2Vr43hjk2+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:05.332391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a78d63e6f6fa51076226bc205978d452f6a456badbdcebbe2cff7399dc0f3634","sha256:2d1b9ddc094a246c40c925b98e75442cf81f00324e1cae9a3eb6f4c0d5d287c3"],"state_sha256":"bc6fb18019b68738f9df1d6a6037b3f34c7358e47ac049272afd7bd4db0e7a3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"coSdPcJuDmDNvR0o8k8kQ11PdIw8uvZsRTZAxbmX6ir0KVXgZBFR3atdH5NxLJoNRnRz3WYVt2NFxgfGmRyrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:37:12.279993Z","bundle_sha256":"c4c3e24a30a688266286e7ae299f01aa6c1c32d7bfa4793894e4991b6c155475"}}