{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PSDDRNH4623QBKDWZC7CHIIMTA","short_pith_number":"pith:PSDDRNH4","canonical_record":{"source":{"id":"1901.02599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-09T04:16:20Z","cross_cats_sorted":[],"title_canon_sha256":"d1c77dffd1d54a6fd8b4e562539c11ac671847e8ee71c30ca709e64fd9768c64","abstract_canon_sha256":"8968aed6c4805a53bfcf802e4c2c64174e1ff1ee139f397f9a235fa033619571"},"schema_version":"1.0"},"canonical_sha256":"7c8638b4fcf6b700a876c8be23a10c980fae2c275ef15d3d037593cad0fa9ded","source":{"kind":"arxiv","id":"1901.02599","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02599","created_at":"2026-05-17T23:56:36Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02599v2","created_at":"2026-05-17T23:56:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02599","created_at":"2026-05-17T23:56:36Z"},{"alias_kind":"pith_short_12","alias_value":"PSDDRNH4623Q","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PSDDRNH4623QBKDW","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PSDDRNH4","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PSDDRNH4623QBKDWZC7CHIIMTA","target":"record","payload":{"canonical_record":{"source":{"id":"1901.02599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-09T04:16:20Z","cross_cats_sorted":[],"title_canon_sha256":"d1c77dffd1d54a6fd8b4e562539c11ac671847e8ee71c30ca709e64fd9768c64","abstract_canon_sha256":"8968aed6c4805a53bfcf802e4c2c64174e1ff1ee139f397f9a235fa033619571"},"schema_version":"1.0"},"canonical_sha256":"7c8638b4fcf6b700a876c8be23a10c980fae2c275ef15d3d037593cad0fa9ded","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:36.127407Z","signature_b64":"NMQtb7tPHOU+En9+n9PYkt8ye2KgPra+QXEQgryjhxKSvQ8yOGmXlaqG7nGuhcsE8EqyMPNV7ItBKwp1w+1hAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c8638b4fcf6b700a876c8be23a10c980fae2c275ef15d3d037593cad0fa9ded","last_reissued_at":"2026-05-17T23:56:36.126949Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:36.126949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.02599","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":"2026-05-17T23:56:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"luuKxHhAn2fAz6gkH50mEg1Gup0nH316S3XEggl8Vmfi4ULtRahsLbjvgOrigTFeRtv9Dzd3lYaCmAM3mvXxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:16:06.074177Z"},"content_sha256":"639e2daa1fc5a4a04543ec583370167926cfe6bdac310e1bfd7c475c34278695","schema_version":"1.0","event_id":"sha256:639e2daa1fc5a4a04543ec583370167926cfe6bdac310e1bfd7c475c34278695"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PSDDRNH4623QBKDWZC7CHIIMTA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability and uniqueness of generalized traveling waves of lattice Fisher-KPP equations in heterogeneous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Feng Cao, Wenxian Shen","submitted_at":"2019-01-09T04:16:20Z","abstract_excerpt":"In this paper, we investigate the stability and uniqueness of generalized traveling wave solutions of lattice Fisher-KPP equations with general time and space dependence. We first show the existence, uniqueness, and stability of strictly positive entire solutions of such equations. Next, we show the stability and uniqueness of generalized traveling waves connecting the unique strictly positive entire solution and the trivial solution zero. Applying the general stability and uniqueness theorem, we then prove the existence, stability and uniqueness of periodic traveling wave solutions of lattice"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02599","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":"2026-05-17T23:56:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8+5DyBOkcnUyBLSnoRw8u3c6gKvMjUPJXG1CNC3PGhJsyt+CU8UGvNPVcQI0SUBf2mZeaP41+497vMzCaCdeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:16:06.074887Z"},"content_sha256":"f277ebe09abcf6baabf284e1c978ea80bdcb09434aba2a8c0aba1052749c4cf1","schema_version":"1.0","event_id":"sha256:f277ebe09abcf6baabf284e1c978ea80bdcb09434aba2a8c0aba1052749c4cf1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PSDDRNH4623QBKDWZC7CHIIMTA/bundle.json","state_url":"https://pith.science/pith/PSDDRNH4623QBKDWZC7CHIIMTA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PSDDRNH4623QBKDWZC7CHIIMTA/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":"2026-06-01T02:16:06Z","links":{"resolver":"https://pith.science/pith/PSDDRNH4623QBKDWZC7CHIIMTA","bundle":"https://pith.science/pith/PSDDRNH4623QBKDWZC7CHIIMTA/bundle.json","state":"https://pith.science/pith/PSDDRNH4623QBKDWZC7CHIIMTA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PSDDRNH4623QBKDWZC7CHIIMTA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PSDDRNH4623QBKDWZC7CHIIMTA","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":"8968aed6c4805a53bfcf802e4c2c64174e1ff1ee139f397f9a235fa033619571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-09T04:16:20Z","title_canon_sha256":"d1c77dffd1d54a6fd8b4e562539c11ac671847e8ee71c30ca709e64fd9768c64"},"schema_version":"1.0","source":{"id":"1901.02599","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02599","created_at":"2026-05-17T23:56:36Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02599v2","created_at":"2026-05-17T23:56:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02599","created_at":"2026-05-17T23:56:36Z"},{"alias_kind":"pith_short_12","alias_value":"PSDDRNH4623Q","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PSDDRNH4623QBKDW","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PSDDRNH4","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:f277ebe09abcf6baabf284e1c978ea80bdcb09434aba2a8c0aba1052749c4cf1","target":"graph","created_at":"2026-05-17T23:56:36Z","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 investigate the stability and uniqueness of generalized traveling wave solutions of lattice Fisher-KPP equations with general time and space dependence. We first show the existence, uniqueness, and stability of strictly positive entire solutions of such equations. Next, we show the stability and uniqueness of generalized traveling waves connecting the unique strictly positive entire solution and the trivial solution zero. Applying the general stability and uniqueness theorem, we then prove the existence, stability and uniqueness of periodic traveling wave solutions of lattice","authors_text":"Feng Cao, Wenxian Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-09T04:16:20Z","title":"Stability and uniqueness of generalized traveling waves of lattice Fisher-KPP equations in heterogeneous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02599","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":"sha256:639e2daa1fc5a4a04543ec583370167926cfe6bdac310e1bfd7c475c34278695","target":"record","created_at":"2026-05-17T23:56:36Z","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":"8968aed6c4805a53bfcf802e4c2c64174e1ff1ee139f397f9a235fa033619571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-01-09T04:16:20Z","title_canon_sha256":"d1c77dffd1d54a6fd8b4e562539c11ac671847e8ee71c30ca709e64fd9768c64"},"schema_version":"1.0","source":{"id":"1901.02599","kind":"arxiv","version":2}},"canonical_sha256":"7c8638b4fcf6b700a876c8be23a10c980fae2c275ef15d3d037593cad0fa9ded","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c8638b4fcf6b700a876c8be23a10c980fae2c275ef15d3d037593cad0fa9ded","first_computed_at":"2026-05-17T23:56:36.126949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:36.126949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NMQtb7tPHOU+En9+n9PYkt8ye2KgPra+QXEQgryjhxKSvQ8yOGmXlaqG7nGuhcsE8EqyMPNV7ItBKwp1w+1hAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:36.127407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.02599","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:639e2daa1fc5a4a04543ec583370167926cfe6bdac310e1bfd7c475c34278695","sha256:f277ebe09abcf6baabf284e1c978ea80bdcb09434aba2a8c0aba1052749c4cf1"],"state_sha256":"c72bb18c94bb95a78db9eb2d65dd890398a27b2e93abe94620ec1a9d8e3c5f30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1sINA8O9/2CmgcLTXEhH0FCwn73Ujy9/fHdxv2kgNKGzp9Od0BgfUb8awPvqiuXVzEWgbmQ4eAwDQSPtwOyDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:16:06.078783Z","bundle_sha256":"4c7196fb2df440d57a6369468b89be94bf850dd1b575da5e7a6ef4b657347f91"}}