{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FBY5HUPFO4IOACCKYGWTEVTCU4","short_pith_number":"pith:FBY5HUPF","canonical_record":{"source":{"id":"1703.05151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-15T13:42:35Z","cross_cats_sorted":[],"title_canon_sha256":"b0c30ad5b0a09bd3bee5096f52833e125c5124833a493535c151b7d774e7cee2","abstract_canon_sha256":"c74cf64238ec00eccebb1371d5f91a7072b28628d23e92e12abd75522a21665f"},"schema_version":"1.0"},"canonical_sha256":"2871d3d1e57710e0084ac1ad325662a72008262956686fbd365e347f27e59c27","source":{"kind":"arxiv","id":"1703.05151","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05151","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05151v1","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05151","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"FBY5HUPFO4IO","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FBY5HUPFO4IOACCK","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FBY5HUPF","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FBY5HUPFO4IOACCKYGWTEVTCU4","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-15T13:42:35Z","cross_cats_sorted":[],"title_canon_sha256":"b0c30ad5b0a09bd3bee5096f52833e125c5124833a493535c151b7d774e7cee2","abstract_canon_sha256":"c74cf64238ec00eccebb1371d5f91a7072b28628d23e92e12abd75522a21665f"},"schema_version":"1.0"},"canonical_sha256":"2871d3d1e57710e0084ac1ad325662a72008262956686fbd365e347f27e59c27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:38.243013Z","signature_b64":"j4bX4fvDUDUPoPhBi83EixmrI46SmoWoPAtb9DCz/8li8rybhWLl/C1hBoWiSyMOOmBtVAw4ULhqXzcHlv3EBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2871d3d1e57710e0084ac1ad325662a72008262956686fbd365e347f27e59c27","last_reissued_at":"2026-05-18T00:48:38.242479Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:38.242479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05151","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":"2026-05-18T00:48:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HOvBjRYacjBr1KBPWLUY9L6H37zKyFdlPVl+BzVs8HF6Xb20yTblM35mC4cfPbzTrPdpuwyfySXGbSI9m3n7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:26:12.997565Z"},"content_sha256":"8d28cd9158192816ec5773013e0c1d46708ce876033537ac72794bb84a9259e4","schema_version":"1.0","event_id":"sha256:8d28cd9158192816ec5773013e0c1d46708ce876033537ac72794bb84a9259e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FBY5HUPFO4IOACCKYGWTEVTCU4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotone wave fronts for $(p, q)$-Laplacian driven reaction-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marta Strani, Maurizio Garrione","submitted_at":"2017-03-15T13:42:35Z","abstract_excerpt":"We study the existence of monotone heteroclinic traveling waves for the $1$-dimensional reaction-diffusion equation $$ u_t = (| u_x |^{p-2} u_x + | u_x |^{q-2} u_x)_x + f(u), $$ where the non-homogeneous operator appearing on the right-hand side is known as $(p, q)$-Laplacian. Here we assume that $2 \\leq q < p$ and $f$ is a nonlinearity of Fisher type, namely it is always positive out of its zeros. We give an estimate of the critical speed and we comment on the roles of $p$ and $q$ in the dynamics, providing some numerical simulations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05151","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":"2026-05-18T00:48:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xioEGqkuUvcEBkvt3eZCUM+hj3CUWkgBnfbt44yom4N2bx89br0cpHzRfJmeUjlRDxLqqhalUHA87mwLK2YRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:26:12.997910Z"},"content_sha256":"c7b4682c9c7e7daea41666b617933a325e3b7543af2827c51c32b614852762bc","schema_version":"1.0","event_id":"sha256:c7b4682c9c7e7daea41666b617933a325e3b7543af2827c51c32b614852762bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FBY5HUPFO4IOACCKYGWTEVTCU4/bundle.json","state_url":"https://pith.science/pith/FBY5HUPFO4IOACCKYGWTEVTCU4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FBY5HUPFO4IOACCKYGWTEVTCU4/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":"2026-05-31T00:26:12Z","links":{"resolver":"https://pith.science/pith/FBY5HUPFO4IOACCKYGWTEVTCU4","bundle":"https://pith.science/pith/FBY5HUPFO4IOACCKYGWTEVTCU4/bundle.json","state":"https://pith.science/pith/FBY5HUPFO4IOACCKYGWTEVTCU4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FBY5HUPFO4IOACCKYGWTEVTCU4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FBY5HUPFO4IOACCKYGWTEVTCU4","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":"c74cf64238ec00eccebb1371d5f91a7072b28628d23e92e12abd75522a21665f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-15T13:42:35Z","title_canon_sha256":"b0c30ad5b0a09bd3bee5096f52833e125c5124833a493535c151b7d774e7cee2"},"schema_version":"1.0","source":{"id":"1703.05151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05151","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05151v1","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05151","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"FBY5HUPFO4IO","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FBY5HUPFO4IOACCK","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FBY5HUPF","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:c7b4682c9c7e7daea41666b617933a325e3b7543af2827c51c32b614852762bc","target":"graph","created_at":"2026-05-18T00:48:38Z","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 existence of monotone heteroclinic traveling waves for the $1$-dimensional reaction-diffusion equation $$ u_t = (| u_x |^{p-2} u_x + | u_x |^{q-2} u_x)_x + f(u), $$ where the non-homogeneous operator appearing on the right-hand side is known as $(p, q)$-Laplacian. Here we assume that $2 \\leq q < p$ and $f$ is a nonlinearity of Fisher type, namely it is always positive out of its zeros. We give an estimate of the critical speed and we comment on the roles of $p$ and $q$ in the dynamics, providing some numerical simulations.","authors_text":"Marta Strani, Maurizio Garrione","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-15T13:42:35Z","title":"Monotone wave fronts for $(p, q)$-Laplacian driven reaction-diffusion equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05151","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":"sha256:8d28cd9158192816ec5773013e0c1d46708ce876033537ac72794bb84a9259e4","target":"record","created_at":"2026-05-18T00:48:38Z","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":"c74cf64238ec00eccebb1371d5f91a7072b28628d23e92e12abd75522a21665f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-15T13:42:35Z","title_canon_sha256":"b0c30ad5b0a09bd3bee5096f52833e125c5124833a493535c151b7d774e7cee2"},"schema_version":"1.0","source":{"id":"1703.05151","kind":"arxiv","version":1}},"canonical_sha256":"2871d3d1e57710e0084ac1ad325662a72008262956686fbd365e347f27e59c27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2871d3d1e57710e0084ac1ad325662a72008262956686fbd365e347f27e59c27","first_computed_at":"2026-05-18T00:48:38.242479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:38.242479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j4bX4fvDUDUPoPhBi83EixmrI46SmoWoPAtb9DCz/8li8rybhWLl/C1hBoWiSyMOOmBtVAw4ULhqXzcHlv3EBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:38.243013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d28cd9158192816ec5773013e0c1d46708ce876033537ac72794bb84a9259e4","sha256:c7b4682c9c7e7daea41666b617933a325e3b7543af2827c51c32b614852762bc"],"state_sha256":"fb9fa27707b28edcceebacc0cada7de11e6365738b4c2b66851a17802e3ad742"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WTWp951n5YSdk4ljXSmuH5aFmsRPvYQsopWJGxizzv9RZeEXefIbEdwTCNz37svkLe6Bg7qk1+PzT4wbSxbaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:26:12.999934Z","bundle_sha256":"90778ccf95ace9dc8821e4570b0c3bcb052902b34d1870d867457a30f0774380"}}