{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GVYK6IMVSKCVEBOXDRSIET26AH","short_pith_number":"pith:GVYK6IMV","canonical_record":{"source":{"id":"1205.0204","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-01T16:13:53Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"13d929e8fd3525b8f0fc6abb34da8436b8f60b6909ffff81373d1b49107d63f9","abstract_canon_sha256":"f319c3965aa8c7f4ef4996f8e2df99f981c010786b69d539afc3cb9a7580c199"},"schema_version":"1.0"},"canonical_sha256":"3570af219592855205d71c64824f5e01fb1bb804791728bca982835e95d4dc68","source":{"kind":"arxiv","id":"1205.0204","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0204","created_at":"2026-05-18T03:33:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0204v7","created_at":"2026-05-18T03:33:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0204","created_at":"2026-05-18T03:33:11Z"},{"alias_kind":"pith_short_12","alias_value":"GVYK6IMVSKCV","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GVYK6IMVSKCVEBOX","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GVYK6IMV","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GVYK6IMVSKCVEBOXDRSIET26AH","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0204","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-01T16:13:53Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"13d929e8fd3525b8f0fc6abb34da8436b8f60b6909ffff81373d1b49107d63f9","abstract_canon_sha256":"f319c3965aa8c7f4ef4996f8e2df99f981c010786b69d539afc3cb9a7580c199"},"schema_version":"1.0"},"canonical_sha256":"3570af219592855205d71c64824f5e01fb1bb804791728bca982835e95d4dc68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:11.846088Z","signature_b64":"c4O3T/Kq+QE2xCiG8hxOyqCY6cndIoJ2i+A6qkkdG749kO/IXlYJMWzKy6zXOLu/wBIOUM3VCdMnSXTPyqeECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3570af219592855205d71c64824f5e01fb1bb804791728bca982835e95d4dc68","last_reissued_at":"2026-05-18T03:33:11.845264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:11.845264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0204","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7cvU5PCsj61K3mwz6N3ZrMU7i9m5HgDgfn0w7ZrVuViZQVr/e424gGSlZU3qlJJbw5fd49f11ICPNtDnA+6KDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T00:21:01.529646Z"},"content_sha256":"deb39778705719d8590edea0b0cee424541d07ef8c8feb02640f41f8dfe76b45","schema_version":"1.0","event_id":"sha256:deb39778705719d8590edea0b0cee424541d07ef8c8feb02640f41f8dfe76b45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GVYK6IMVSKCVEBOXDRSIET26AH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global isochronous potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.DS","authors_text":"Gaetano Zampieri, Gianluca Gorni","submitted_at":"2012-05-01T16:13:53Z","abstract_excerpt":"We present a geometric characterization of the nonlinear smooth functions $V: R\\to R$ for which the origin is a global isochronous center for the scalar equation $\\ddot x=-V'(x)$. We revisit Stillinger and Dorignac isochronous potentials $V$ and show a new simple explicit family. Implicit examples are easily produced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0204","kind":"arxiv","version":7},"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":"2026-05-18T03:33:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n9tlJ0M1QnUgvffTxVvpm/kLizck9mGs6Ce92qp6lHbQn1KULR9gzx28FYt6wTRqaUjTO91EaEe+MrxFB6kQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T00:21:01.530380Z"},"content_sha256":"334c3200ee17bbef92205ccc7a3f4cd5b9bb8bf6ac9223807a02f09e9a74f2e2","schema_version":"1.0","event_id":"sha256:334c3200ee17bbef92205ccc7a3f4cd5b9bb8bf6ac9223807a02f09e9a74f2e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GVYK6IMVSKCVEBOXDRSIET26AH/bundle.json","state_url":"https://pith.science/pith/GVYK6IMVSKCVEBOXDRSIET26AH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GVYK6IMVSKCVEBOXDRSIET26AH/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":"2026-06-07T00:21:01Z","links":{"resolver":"https://pith.science/pith/GVYK6IMVSKCVEBOXDRSIET26AH","bundle":"https://pith.science/pith/GVYK6IMVSKCVEBOXDRSIET26AH/bundle.json","state":"https://pith.science/pith/GVYK6IMVSKCVEBOXDRSIET26AH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GVYK6IMVSKCVEBOXDRSIET26AH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GVYK6IMVSKCVEBOXDRSIET26AH","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":"f319c3965aa8c7f4ef4996f8e2df99f981c010786b69d539afc3cb9a7580c199","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-01T16:13:53Z","title_canon_sha256":"13d929e8fd3525b8f0fc6abb34da8436b8f60b6909ffff81373d1b49107d63f9"},"schema_version":"1.0","source":{"id":"1205.0204","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0204","created_at":"2026-05-18T03:33:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0204v7","created_at":"2026-05-18T03:33:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0204","created_at":"2026-05-18T03:33:11Z"},{"alias_kind":"pith_short_12","alias_value":"GVYK6IMVSKCV","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GVYK6IMVSKCVEBOX","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GVYK6IMV","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:334c3200ee17bbef92205ccc7a3f4cd5b9bb8bf6ac9223807a02f09e9a74f2e2","target":"graph","created_at":"2026-05-18T03:33:11Z","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 present a geometric characterization of the nonlinear smooth functions $V: R\\to R$ for which the origin is a global isochronous center for the scalar equation $\\ddot x=-V'(x)$. We revisit Stillinger and Dorignac isochronous potentials $V$ and show a new simple explicit family. Implicit examples are easily produced.","authors_text":"Gaetano Zampieri, Gianluca Gorni","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-01T16:13:53Z","title":"Global isochronous potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0204","kind":"arxiv","version":7},"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:deb39778705719d8590edea0b0cee424541d07ef8c8feb02640f41f8dfe76b45","target":"record","created_at":"2026-05-18T03:33:11Z","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":"f319c3965aa8c7f4ef4996f8e2df99f981c010786b69d539afc3cb9a7580c199","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-01T16:13:53Z","title_canon_sha256":"13d929e8fd3525b8f0fc6abb34da8436b8f60b6909ffff81373d1b49107d63f9"},"schema_version":"1.0","source":{"id":"1205.0204","kind":"arxiv","version":7}},"canonical_sha256":"3570af219592855205d71c64824f5e01fb1bb804791728bca982835e95d4dc68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3570af219592855205d71c64824f5e01fb1bb804791728bca982835e95d4dc68","first_computed_at":"2026-05-18T03:33:11.845264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:11.845264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c4O3T/Kq+QE2xCiG8hxOyqCY6cndIoJ2i+A6qkkdG749kO/IXlYJMWzKy6zXOLu/wBIOUM3VCdMnSXTPyqeECA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:11.846088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0204","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:deb39778705719d8590edea0b0cee424541d07ef8c8feb02640f41f8dfe76b45","sha256:334c3200ee17bbef92205ccc7a3f4cd5b9bb8bf6ac9223807a02f09e9a74f2e2"],"state_sha256":"f038744100754fcf419414c2012e029bf5dbeb14fc019bb90ce20e37abbf5182"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RWjXX6z4oUDT+qeadsE2MbFIUJ+Wa9eg/ZKK1kFDLVrMnRoQswKRbp64ZE8d+41j20zkO1T4x4Kh3xr0MfJrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T00:21:01.534905Z","bundle_sha256":"12b1ba022111b6ef5de8e69dbcb4b56d8834132525fc2ce75e1b430327171e65"}}