{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZNFZTHZJX5H4TIIIDKDI7C4JWS","short_pith_number":"pith:ZNFZTHZJ","canonical_record":{"source":{"id":"1408.3344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-14T17:05:48Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"b7f96e259d9db264e809f2547bf3d5bf85c4b0f6160f224194c6e72f55de3efe","abstract_canon_sha256":"0f052169508390115bd725bab895d3f780149a526d71ac09c6153eb94577b682"},"schema_version":"1.0"},"canonical_sha256":"cb4b999f29bf4fc9a1081a868f8b89b4a37d7da4872fe07358ec5c5ad1d9c02b","source":{"kind":"arxiv","id":"1408.3344","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3344","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3344v1","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3344","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZNFZTHZJX5H4","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZNFZTHZJX5H4TIII","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZNFZTHZJ","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZNFZTHZJX5H4TIIIDKDI7C4JWS","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-14T17:05:48Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"b7f96e259d9db264e809f2547bf3d5bf85c4b0f6160f224194c6e72f55de3efe","abstract_canon_sha256":"0f052169508390115bd725bab895d3f780149a526d71ac09c6153eb94577b682"},"schema_version":"1.0"},"canonical_sha256":"cb4b999f29bf4fc9a1081a868f8b89b4a37d7da4872fe07358ec5c5ad1d9c02b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:55.387218Z","signature_b64":"u/kiEp2SkRiAd08g4ZZn07jNheFX/fxMucIZKA4MwpknabDGbOOYTl0nbP2WHML1upnzbG0+qkefCWS11v+iBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb4b999f29bf4fc9a1081a868f8b89b4a37d7da4872fe07358ec5c5ad1d9c02b","last_reissued_at":"2026-05-18T02:03:55.386341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:55.386341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3344","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":"2026-05-18T02:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZ/kqrDzfcpwrLyXB2+IXHGgGTzaw3lrmZ/9Y7KvXzWYYOK+HqWPN+ysa4gqdt5McBbJLG7tBEBMLk7uq9hCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:36:22.162805Z"},"content_sha256":"dc7407fac2513a63e69404da3090c3abf1738dc09fb31dece9d21fd1fb07a6c4","schema_version":"1.0","event_id":"sha256:dc7407fac2513a63e69404da3090c3abf1738dc09fb31dece9d21fd1fb07a6c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZNFZTHZJX5H4TIIIDKDI7C4JWS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic convergence to pushed wavefronts in a monostable equation with delayed reaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Abraham Solar, Sergei Trofimchuk","submitted_at":"2014-08-14T17:05:48Z","abstract_excerpt":"We study the asymptotic behaviour of solutions to the delayed monostable equation $(*)$: $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),$ $x \\in R,\\ t >0,$ with monotone reaction term $g: R_+ \\to R_+$. Our basic assumption is that this equation possesses pushed traveling fronts. First we prove that the pushed wavefronts are nonlinearly stable with asymptotic phase. Moreover, combinations of these waves attract, uniformly on $R$, every solution of equation $(*)$ with the initial datum sufficiently rapidly decaying at one (or at the both) infinities of the real line. These results provide a sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3344","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":"2026-05-18T02:03:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mn2gjHeh/CozLEVRuH+b4E3YmNo2nmifV28t6Ch9B9vNhE1GYnKP65AqR2VEBgQwEyLk8AnO1qRntBnnBBUxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:36:22.163381Z"},"content_sha256":"d974f90cf071accf537f38529a95d3a805687bbc8b01abd30dfb1c901ecf0121","schema_version":"1.0","event_id":"sha256:d974f90cf071accf537f38529a95d3a805687bbc8b01abd30dfb1c901ecf0121"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNFZTHZJX5H4TIIIDKDI7C4JWS/bundle.json","state_url":"https://pith.science/pith/ZNFZTHZJX5H4TIIIDKDI7C4JWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNFZTHZJX5H4TIIIDKDI7C4JWS/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":"2026-06-12T02:36:22Z","links":{"resolver":"https://pith.science/pith/ZNFZTHZJX5H4TIIIDKDI7C4JWS","bundle":"https://pith.science/pith/ZNFZTHZJX5H4TIIIDKDI7C4JWS/bundle.json","state":"https://pith.science/pith/ZNFZTHZJX5H4TIIIDKDI7C4JWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNFZTHZJX5H4TIIIDKDI7C4JWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZNFZTHZJX5H4TIIIDKDI7C4JWS","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":"0f052169508390115bd725bab895d3f780149a526d71ac09c6153eb94577b682","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-14T17:05:48Z","title_canon_sha256":"b7f96e259d9db264e809f2547bf3d5bf85c4b0f6160f224194c6e72f55de3efe"},"schema_version":"1.0","source":{"id":"1408.3344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3344","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3344v1","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3344","created_at":"2026-05-18T02:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"ZNFZTHZJX5H4","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZNFZTHZJX5H4TIII","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZNFZTHZJ","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:d974f90cf071accf537f38529a95d3a805687bbc8b01abd30dfb1c901ecf0121","target":"graph","created_at":"2026-05-18T02:03:55Z","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 study the asymptotic behaviour of solutions to the delayed monostable equation $(*)$: $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),$ $x \\in R,\\ t >0,$ with monotone reaction term $g: R_+ \\to R_+$. Our basic assumption is that this equation possesses pushed traveling fronts. First we prove that the pushed wavefronts are nonlinearly stable with asymptotic phase. Moreover, combinations of these waves attract, uniformly on $R$, every solution of equation $(*)$ with the initial datum sufficiently rapidly decaying at one (or at the both) infinities of the real line. These results provide a sh","authors_text":"Abraham Solar, Sergei Trofimchuk","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-14T17:05:48Z","title":"Asymptotic convergence to pushed wavefronts in a monostable equation with delayed reaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3344","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:dc7407fac2513a63e69404da3090c3abf1738dc09fb31dece9d21fd1fb07a6c4","target":"record","created_at":"2026-05-18T02:03:55Z","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":"0f052169508390115bd725bab895d3f780149a526d71ac09c6153eb94577b682","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-14T17:05:48Z","title_canon_sha256":"b7f96e259d9db264e809f2547bf3d5bf85c4b0f6160f224194c6e72f55de3efe"},"schema_version":"1.0","source":{"id":"1408.3344","kind":"arxiv","version":1}},"canonical_sha256":"cb4b999f29bf4fc9a1081a868f8b89b4a37d7da4872fe07358ec5c5ad1d9c02b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb4b999f29bf4fc9a1081a868f8b89b4a37d7da4872fe07358ec5c5ad1d9c02b","first_computed_at":"2026-05-18T02:03:55.386341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:55.386341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u/kiEp2SkRiAd08g4ZZn07jNheFX/fxMucIZKA4MwpknabDGbOOYTl0nbP2WHML1upnzbG0+qkefCWS11v+iBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:55.387218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc7407fac2513a63e69404da3090c3abf1738dc09fb31dece9d21fd1fb07a6c4","sha256:d974f90cf071accf537f38529a95d3a805687bbc8b01abd30dfb1c901ecf0121"],"state_sha256":"7f86fbaf04cb1d1410d442e77b7308c9029bc128329a1ff4811a7452b84d9bac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LKDcXHGthx+Ub5VOyY0+JrHMuHsUoUTYGCOy1x80sJXaEHSs+U8Y1Vf1FDFgjIqSVovkGfh7kHLgLXvkUnw4Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:36:22.167412Z","bundle_sha256":"0670149e76a81fe66c42a553dc6f7766b7f81679c38c956cf0a6761be6da48c5"}}