{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SGZ4SIKV2DSTMHBHGGENABLMDR","short_pith_number":"pith:SGZ4SIKV","canonical_record":{"source":{"id":"1712.08007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-20T16:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"403927d4d2cabd4fd7ee29c0fe67de401372ac479d15b41c4e642c582e7ffb84","abstract_canon_sha256":"3cdc526ccdcff5ef0562b090c8ccd039a522880ac60b361a78b1056c857f3185"},"schema_version":"1.0"},"canonical_sha256":"91b3c92155d0e5361c273188d0056c1c6bbccdce0303385a9144489fbcf14818","source":{"kind":"arxiv","id":"1712.08007","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08007","created_at":"2026-05-18T00:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08007v1","created_at":"2026-05-18T00:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08007","created_at":"2026-05-18T00:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"SGZ4SIKV2DST","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SGZ4SIKV2DSTMHBH","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SGZ4SIKV","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SGZ4SIKV2DSTMHBHGGENABLMDR","target":"record","payload":{"canonical_record":{"source":{"id":"1712.08007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-20T16:02:32Z","cross_cats_sorted":[],"title_canon_sha256":"403927d4d2cabd4fd7ee29c0fe67de401372ac479d15b41c4e642c582e7ffb84","abstract_canon_sha256":"3cdc526ccdcff5ef0562b090c8ccd039a522880ac60b361a78b1056c857f3185"},"schema_version":"1.0"},"canonical_sha256":"91b3c92155d0e5361c273188d0056c1c6bbccdce0303385a9144489fbcf14818","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:29.128273Z","signature_b64":"5gl93T3lMsx7wPeNyLNzlzIoNRqa/PKcPDU/TiRAsjh/cKLfHCzgzapd64Of68DM5Umes5Xcklq0Od4JuvASBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91b3c92155d0e5361c273188d0056c1c6bbccdce0303385a9144489fbcf14818","last_reissued_at":"2026-05-18T00:27:29.127563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:29.127563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.08007","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":"2026-05-18T00:27:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/BQWSMFaPwYNhCXv81ObxdhfY5rzYP3X2ulVVfxS1zBIEUOEwj1LaCHqCpEWDkWAGCGDclCj1wUxbZyoP/xCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:33:37.510439Z"},"content_sha256":"6013420926b53e99883d7dcfd9840ce43e0ab63f5831b29b2d3b27520ac2b293","schema_version":"1.0","event_id":"sha256:6013420926b53e99883d7dcfd9840ce43e0ab63f5831b29b2d3b27520ac2b293"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SGZ4SIKV2DSTMHBHGGENABLMDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation Dynamics for a Spatially Periodic Integrodifference Competition Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ruiwen Wu, Xiao-Qiang Zhao","submitted_at":"2017-12-20T16:02:32Z","abstract_excerpt":"In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means different species may have different spreading speeds. We show that the model system admits a single spreading speed, and it coincides with the minimal wave speed of the spatially periodic traveling waves. A set of sufficient conditions for linear determinacy of the spreading speed is also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08007","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":"2026-05-18T00:27:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0VkSUcS8GcjPApD+lgRBKkviuUGjxI2WSyjhdPqfvUz5XWzdVv8cFFh+q7qJP6eertE/pSPGJajiZ6NwsZ+xBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:33:37.511084Z"},"content_sha256":"29b9a21ffeb45e53509a3a81c28ed614a7c772edf5f45840e625ee767381eb0f","schema_version":"1.0","event_id":"sha256:29b9a21ffeb45e53509a3a81c28ed614a7c772edf5f45840e625ee767381eb0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGZ4SIKV2DSTMHBHGGENABLMDR/bundle.json","state_url":"https://pith.science/pith/SGZ4SIKV2DSTMHBHGGENABLMDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGZ4SIKV2DSTMHBHGGENABLMDR/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":"2026-05-30T07:33:37Z","links":{"resolver":"https://pith.science/pith/SGZ4SIKV2DSTMHBHGGENABLMDR","bundle":"https://pith.science/pith/SGZ4SIKV2DSTMHBHGGENABLMDR/bundle.json","state":"https://pith.science/pith/SGZ4SIKV2DSTMHBHGGENABLMDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGZ4SIKV2DSTMHBHGGENABLMDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SGZ4SIKV2DSTMHBHGGENABLMDR","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":"3cdc526ccdcff5ef0562b090c8ccd039a522880ac60b361a78b1056c857f3185","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-20T16:02:32Z","title_canon_sha256":"403927d4d2cabd4fd7ee29c0fe67de401372ac479d15b41c4e642c582e7ffb84"},"schema_version":"1.0","source":{"id":"1712.08007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08007","created_at":"2026-05-18T00:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08007v1","created_at":"2026-05-18T00:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08007","created_at":"2026-05-18T00:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"SGZ4SIKV2DST","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SGZ4SIKV2DSTMHBH","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SGZ4SIKV","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:29b9a21ffeb45e53509a3a81c28ed614a7c772edf5f45840e625ee767381eb0f","target":"graph","created_at":"2026-05-18T00:27:29Z","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":"In this paper, we study the propagation dynamics for a class of integrodifference competition models in a periodic habitat. An interesting feature of such a system is that multiple spreading speeds can be observed, which biologically means different species may have different spreading speeds. We show that the model system admits a single spreading speed, and it coincides with the minimal wave speed of the spatially periodic traveling waves. A set of sufficient conditions for linear determinacy of the spreading speed is also given.","authors_text":"Ruiwen Wu, Xiao-Qiang Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-20T16:02:32Z","title":"Propagation Dynamics for a Spatially Periodic Integrodifference Competition Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08007","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":"sha256:6013420926b53e99883d7dcfd9840ce43e0ab63f5831b29b2d3b27520ac2b293","target":"record","created_at":"2026-05-18T00:27:29Z","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":"3cdc526ccdcff5ef0562b090c8ccd039a522880ac60b361a78b1056c857f3185","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-20T16:02:32Z","title_canon_sha256":"403927d4d2cabd4fd7ee29c0fe67de401372ac479d15b41c4e642c582e7ffb84"},"schema_version":"1.0","source":{"id":"1712.08007","kind":"arxiv","version":1}},"canonical_sha256":"91b3c92155d0e5361c273188d0056c1c6bbccdce0303385a9144489fbcf14818","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91b3c92155d0e5361c273188d0056c1c6bbccdce0303385a9144489fbcf14818","first_computed_at":"2026-05-18T00:27:29.127563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:29.127563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5gl93T3lMsx7wPeNyLNzlzIoNRqa/PKcPDU/TiRAsjh/cKLfHCzgzapd64Of68DM5Umes5Xcklq0Od4JuvASBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:29.128273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6013420926b53e99883d7dcfd9840ce43e0ab63f5831b29b2d3b27520ac2b293","sha256:29b9a21ffeb45e53509a3a81c28ed614a7c772edf5f45840e625ee767381eb0f"],"state_sha256":"7e7de954a99269057db95823be7bace97e05e5ffbb72aea8c7335af523ddc388"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GMR3C8TYHfhEKXAeaUBt50hwb7X41xWv4WYJlki4GDSZ3ulvAxxpBryoNgpPDTBWfq/pBmvXhbOmhVWjh6cPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:33:37.513920Z","bundle_sha256":"cf41119a576fb4ae5d5ba3561db1db7259c4c3207f9dc79f400dab34339c3472"}}