{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:J3H7LMZAOSR7IMTN6INUPYWOEC","short_pith_number":"pith:J3H7LMZA","canonical_record":{"source":{"id":"1304.1596","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-05T01:49:20Z","cross_cats_sorted":[],"title_canon_sha256":"93f7df459c0fd79412117211c13b40e8501fc9dbc65207387d26f0f4a613355c","abstract_canon_sha256":"7fc97850331b4a3421827acaa2b415b246cc9083e70e4ea21a52e65968adf381"},"schema_version":"1.0"},"canonical_sha256":"4ecff5b32074a3f4326df21b47e2ce20bff7ed741a408cdb1dcb6cbd58a437ef","source":{"kind":"arxiv","id":"1304.1596","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1596","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1596v2","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1596","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"J3H7LMZAOSR7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J3H7LMZAOSR7IMTN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J3H7LMZA","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:J3H7LMZAOSR7IMTN6INUPYWOEC","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1596","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-05T01:49:20Z","cross_cats_sorted":[],"title_canon_sha256":"93f7df459c0fd79412117211c13b40e8501fc9dbc65207387d26f0f4a613355c","abstract_canon_sha256":"7fc97850331b4a3421827acaa2b415b246cc9083e70e4ea21a52e65968adf381"},"schema_version":"1.0"},"canonical_sha256":"4ecff5b32074a3f4326df21b47e2ce20bff7ed741a408cdb1dcb6cbd58a437ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:51.344291Z","signature_b64":"z+UKyBl9Hmx5ayyQjIGCKvqS6SUYUbAKt/njTo873f1apGeCfdmRpQFysz4ihYn9tOddjx/ua+zHDp+4vf7mCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ecff5b32074a3f4326df21b47e2ce20bff7ed741a408cdb1dcb6cbd58a437ef","last_reissued_at":"2026-05-18T02:27:51.343629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:51.343629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1596","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":"2026-05-18T02:27:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0mwu00fE1JLxKDOL1xmPXcTutaISQF0h8dnPW8DUJsHqguQvqbFx3PisG9EZIeOw49VexxM37fqGA2NG6KhGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:04:37.257398Z"},"content_sha256":"221e57a4509c99622cdc8028ffcfb0b6cd052606cdff3267a5bb501e5009dbcc","schema_version":"1.0","event_id":"sha256:221e57a4509c99622cdc8028ffcfb0b6cd052606cdff3267a5bb501e5009dbcc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:J3H7LMZAOSR7IMTN6INUPYWOEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Structure of Global Attractors for Dissipative Zakharov Systems with Forcing on the Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jeremy L. Marzuola, Katherine A. Newhall, M. Burak Erdogan, Nikolaos Tzirakis","submitted_at":"2013-04-05T01:49:20Z","abstract_excerpt":"The Zakharov system was originally proposed to study the propagation of Langmuir waves in an ionized plasma. In this paper, motivated by earlier work of the first and third authors, we numerically and analytically investigate the dynamics of the dissipative Zakharov system on the torus in 1 dimension. We find an interesting family of stable periodic orbits and fixed points, and explore bifurcations of those points as we take weaker and weaker dissipation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1596","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":"2026-05-18T02:27:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFRfNXSu8jJIzwnM9mrZb9hWrzUzzyVmcO3/MIV5NltUbb0LwLUY3qIvbAEKBuwAXqa8q/8RrT5LvhDCwNfECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:04:37.257993Z"},"content_sha256":"f71627bdb9b2ef7321edf35d2bc9f7e174dfece71dbb511d826f33908229aaf9","schema_version":"1.0","event_id":"sha256:f71627bdb9b2ef7321edf35d2bc9f7e174dfece71dbb511d826f33908229aaf9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J3H7LMZAOSR7IMTN6INUPYWOEC/bundle.json","state_url":"https://pith.science/pith/J3H7LMZAOSR7IMTN6INUPYWOEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J3H7LMZAOSR7IMTN6INUPYWOEC/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":"2026-05-30T12:04:37Z","links":{"resolver":"https://pith.science/pith/J3H7LMZAOSR7IMTN6INUPYWOEC","bundle":"https://pith.science/pith/J3H7LMZAOSR7IMTN6INUPYWOEC/bundle.json","state":"https://pith.science/pith/J3H7LMZAOSR7IMTN6INUPYWOEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J3H7LMZAOSR7IMTN6INUPYWOEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J3H7LMZAOSR7IMTN6INUPYWOEC","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":"7fc97850331b4a3421827acaa2b415b246cc9083e70e4ea21a52e65968adf381","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-05T01:49:20Z","title_canon_sha256":"93f7df459c0fd79412117211c13b40e8501fc9dbc65207387d26f0f4a613355c"},"schema_version":"1.0","source":{"id":"1304.1596","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1596","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1596v2","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1596","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"J3H7LMZAOSR7","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J3H7LMZAOSR7IMTN","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J3H7LMZA","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:f71627bdb9b2ef7321edf35d2bc9f7e174dfece71dbb511d826f33908229aaf9","target":"graph","created_at":"2026-05-18T02:27:51Z","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":"The Zakharov system was originally proposed to study the propagation of Langmuir waves in an ionized plasma. In this paper, motivated by earlier work of the first and third authors, we numerically and analytically investigate the dynamics of the dissipative Zakharov system on the torus in 1 dimension. We find an interesting family of stable periodic orbits and fixed points, and explore bifurcations of those points as we take weaker and weaker dissipation.","authors_text":"Jeremy L. Marzuola, Katherine A. Newhall, M. Burak Erdogan, Nikolaos Tzirakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-05T01:49:20Z","title":"The Structure of Global Attractors for Dissipative Zakharov Systems with Forcing on the Torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1596","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":"sha256:221e57a4509c99622cdc8028ffcfb0b6cd052606cdff3267a5bb501e5009dbcc","target":"record","created_at":"2026-05-18T02:27:51Z","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":"7fc97850331b4a3421827acaa2b415b246cc9083e70e4ea21a52e65968adf381","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-05T01:49:20Z","title_canon_sha256":"93f7df459c0fd79412117211c13b40e8501fc9dbc65207387d26f0f4a613355c"},"schema_version":"1.0","source":{"id":"1304.1596","kind":"arxiv","version":2}},"canonical_sha256":"4ecff5b32074a3f4326df21b47e2ce20bff7ed741a408cdb1dcb6cbd58a437ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ecff5b32074a3f4326df21b47e2ce20bff7ed741a408cdb1dcb6cbd58a437ef","first_computed_at":"2026-05-18T02:27:51.343629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:51.343629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z+UKyBl9Hmx5ayyQjIGCKvqS6SUYUbAKt/njTo873f1apGeCfdmRpQFysz4ihYn9tOddjx/ua+zHDp+4vf7mCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:51.344291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1596","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:221e57a4509c99622cdc8028ffcfb0b6cd052606cdff3267a5bb501e5009dbcc","sha256:f71627bdb9b2ef7321edf35d2bc9f7e174dfece71dbb511d826f33908229aaf9"],"state_sha256":"2914ff5f63a675d2ddf3e714f1b66145e981ee032d91d6e59094f5e2861a8d38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Ys4iJLMZj0dk9J6GzwCoklzOAbTOeLP7KGLBMGLlIcFCKC5t7DuXU2xUbUAJTaEf1gSCs+dOcRHTKuj6dweAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:04:37.260007Z","bundle_sha256":"f6692ade70270c906b9ed52759baa4a820e00c5b807b5dedd28dea1375267283"}}