{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HNTJTXEWRVBSUEGYAFMT2YZDBD","short_pith_number":"pith:HNTJTXEW","canonical_record":{"source":{"id":"1609.04475","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-14T23:23:30Z","cross_cats_sorted":[],"title_canon_sha256":"3c74c3836d01def6606f336181f3960619f079ad5d9f3d2c26bb9f3fc7005371","abstract_canon_sha256":"ef21a0201c796d5f6bce1679727f7ab61451397324893ef46157dbd808b2be10"},"schema_version":"1.0"},"canonical_sha256":"3b6699dc968d432a10d801593d632308fb5380bd6b60efe68a919f9630dcd5db","source":{"kind":"arxiv","id":"1609.04475","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04475","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04475v3","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04475","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"HNTJTXEWRVBS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HNTJTXEWRVBSUEGY","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HNTJTXEW","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HNTJTXEWRVBSUEGYAFMT2YZDBD","target":"record","payload":{"canonical_record":{"source":{"id":"1609.04475","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-14T23:23:30Z","cross_cats_sorted":[],"title_canon_sha256":"3c74c3836d01def6606f336181f3960619f079ad5d9f3d2c26bb9f3fc7005371","abstract_canon_sha256":"ef21a0201c796d5f6bce1679727f7ab61451397324893ef46157dbd808b2be10"},"schema_version":"1.0"},"canonical_sha256":"3b6699dc968d432a10d801593d632308fb5380bd6b60efe68a919f9630dcd5db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:24.649674Z","signature_b64":"HhBPvwptveHmqYmzUJQ+7J2INdIZUtuuGiEckfiAjGlnpEe2jE7BL0ydr5X2OeJ+NhyntbVBQldZkHh4pb80Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b6699dc968d432a10d801593d632308fb5380bd6b60efe68a919f9630dcd5db","last_reissued_at":"2026-05-18T00:35:24.649183Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:24.649183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.04475","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2yXlxBG7s6aGIx8eDHpn7KH3KxdAZ/cFf5w1C9eIz4sUSexZ0cATemsdWjVw45FhA6xL02kP6CCvZ/XMWY3ACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:48:01.597675Z"},"content_sha256":"4d9024ab56b8f2a14e9cf22869a885623beedef08eee5feba9d38269ece3ee60","schema_version":"1.0","event_id":"sha256:4d9024ab56b8f2a14e9cf22869a885623beedef08eee5feba9d38269ece3ee60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HNTJTXEWRVBSUEGYAFMT2YZDBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wenxian Shen","submitted_at":"2016-09-14T23:23:30Z","abstract_excerpt":"This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or almost periodic dependence as special cases. We first show the existence, uniqueness, and stability of strictly positive entire solutions of such equations. Next, we show the stability of uniformly continuous transition waves connecting the unique strictly positive entire solution and the trivial solution zero and satisfying certain decay property"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04475","kind":"arxiv","version":3},"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":"2026-05-18T00:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e+mUk7OiHRdZoyba/6iV6lKwNVXoGPlK0uLExgL8gdVZzKuqaThLs9qKmMDbEVVfiL7gyIAQYDfFHDneE+wwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:48:01.598018Z"},"content_sha256":"290b458733a5a32167293abd222185b705d6d49626137bef53c0e332c34caf6f","schema_version":"1.0","event_id":"sha256:290b458733a5a32167293abd222185b705d6d49626137bef53c0e332c34caf6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HNTJTXEWRVBSUEGYAFMT2YZDBD/bundle.json","state_url":"https://pith.science/pith/HNTJTXEWRVBSUEGYAFMT2YZDBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HNTJTXEWRVBSUEGYAFMT2YZDBD/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":"2026-06-01T03:48:01Z","links":{"resolver":"https://pith.science/pith/HNTJTXEWRVBSUEGYAFMT2YZDBD","bundle":"https://pith.science/pith/HNTJTXEWRVBSUEGYAFMT2YZDBD/bundle.json","state":"https://pith.science/pith/HNTJTXEWRVBSUEGYAFMT2YZDBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HNTJTXEWRVBSUEGYAFMT2YZDBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HNTJTXEWRVBSUEGYAFMT2YZDBD","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":"ef21a0201c796d5f6bce1679727f7ab61451397324893ef46157dbd808b2be10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-14T23:23:30Z","title_canon_sha256":"3c74c3836d01def6606f336181f3960619f079ad5d9f3d2c26bb9f3fc7005371"},"schema_version":"1.0","source":{"id":"1609.04475","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04475","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04475v3","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04475","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"HNTJTXEWRVBS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HNTJTXEWRVBSUEGY","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HNTJTXEW","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:290b458733a5a32167293abd222185b705d6d49626137bef53c0e332c34caf6f","target":"graph","created_at":"2026-05-18T00:35:24Z","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":"This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or almost periodic dependence as special cases. We first show the existence, uniqueness, and stability of strictly positive entire solutions of such equations. Next, we show the stability of uniformly continuous transition waves connecting the unique strictly positive entire solution and the trivial solution zero and satisfying certain decay property","authors_text":"Wenxian Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-14T23:23:30Z","title":"Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04475","kind":"arxiv","version":3},"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":"sha256:4d9024ab56b8f2a14e9cf22869a885623beedef08eee5feba9d38269ece3ee60","target":"record","created_at":"2026-05-18T00:35:24Z","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":"ef21a0201c796d5f6bce1679727f7ab61451397324893ef46157dbd808b2be10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-14T23:23:30Z","title_canon_sha256":"3c74c3836d01def6606f336181f3960619f079ad5d9f3d2c26bb9f3fc7005371"},"schema_version":"1.0","source":{"id":"1609.04475","kind":"arxiv","version":3}},"canonical_sha256":"3b6699dc968d432a10d801593d632308fb5380bd6b60efe68a919f9630dcd5db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b6699dc968d432a10d801593d632308fb5380bd6b60efe68a919f9630dcd5db","first_computed_at":"2026-05-18T00:35:24.649183Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:24.649183Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HhBPvwptveHmqYmzUJQ+7J2INdIZUtuuGiEckfiAjGlnpEe2jE7BL0ydr5X2OeJ+NhyntbVBQldZkHh4pb80Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:24.649674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04475","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d9024ab56b8f2a14e9cf22869a885623beedef08eee5feba9d38269ece3ee60","sha256:290b458733a5a32167293abd222185b705d6d49626137bef53c0e332c34caf6f"],"state_sha256":"62a7ecee4bf749f3a4f821b6ed1f63fca503e001787666b6f02f587770435795"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HrpITxykWuLuHdoQ0pKmZKucfkLeX5nWPhsjotca/TtTUsu5/UD5FwRzrjUAybZP/N3bZdwIoy2pCZ+/+qNVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:48:01.599995Z","bundle_sha256":"aa151fc2a8223d6e72a38901e15c18275665b5453a6077cf232d7a8aab683b78"}}