{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VBROYSE4OWSFKNAZSNGWPGRXEA","short_pith_number":"pith:VBROYSE4","canonical_record":{"source":{"id":"2606.00638","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-30T09:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"122962e0a140d47a7283a8275fe75bbdbbe28bf9e1f93bfa90a61ff6c08c0019","abstract_canon_sha256":"75e83852d754184c3cbb710f9a62597f95d5ac53e8a9b39a1c666475a7bd0123"},"schema_version":"1.0"},"canonical_sha256":"a862ec489c75a4553419934d679a372023109b0fb28fe8164b802ed73a28ed7e","source":{"kind":"arxiv","id":"2606.00638","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00638","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00638v1","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00638","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"VBROYSE4OWSF","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"VBROYSE4OWSFKNAZ","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"VBROYSE4","created_at":"2026-06-02T01:04:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VBROYSE4OWSFKNAZSNGWPGRXEA","target":"record","payload":{"canonical_record":{"source":{"id":"2606.00638","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-30T09:26:33Z","cross_cats_sorted":[],"title_canon_sha256":"122962e0a140d47a7283a8275fe75bbdbbe28bf9e1f93bfa90a61ff6c08c0019","abstract_canon_sha256":"75e83852d754184c3cbb710f9a62597f95d5ac53e8a9b39a1c666475a7bd0123"},"schema_version":"1.0"},"canonical_sha256":"a862ec489c75a4553419934d679a372023109b0fb28fe8164b802ed73a28ed7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:00.560497Z","signature_b64":"zI7I8Jxa5d9p1zNH6zS1VsVFDqJDEfyJ5lckmLtS4cbjcfBKZZ2hBkq8cgrd1f+nSLilfqolsgiTZSc8bIHBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a862ec489c75a4553419934d679a372023109b0fb28fe8164b802ed73a28ed7e","last_reissued_at":"2026-06-02T01:04:00.560010Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:00.560010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.00638","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":"2026-06-02T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"czoV4Kg8GtRlV+Fi4dyajrz4tGFcSxzmzSosMwnsg/P311zXFvepKAd2ayECKTUDtqCCw/ycrSi8sYY2UvWhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:12:19.711660Z"},"content_sha256":"ad866c26f6f6f896e3bd153840f91c6be699dcdde14d0b6aa16c94e2fc90d9ba","schema_version":"1.0","event_id":"sha256:ad866c26f6f6f896e3bd153840f91c6be699dcdde14d0b6aa16c94e2fc90d9ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VBROYSE4OWSFKNAZSNGWPGRXEA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Traveling waves for combustion reaction-diffusion-convection equations: the full range of wave speeds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eunkyung Ko, Michaela Zahradn\\'ikov\\'a, Pavel Dr\\'abek, Soyeun Jung","submitted_at":"2026-05-30T09:26:33Z","abstract_excerpt":"We consider traveling wave solutions to a reaction--diffusion--convection equation with a combustion-type reaction term. While a necessary condition for the existence of traveling waves is $c \\geq H^*:=\\sup_{0<u \\leq \\theta} \\big(-\\frac{1}{u} \\int_0^u h(\\sigma)\\,d\\sigma \\big)$, where $c$ denotes the wave speed, $\\theta\\in(0,1)$ the ignition threshold, and $h$ the convective term, the available results in \\cite{DZ25,MM03} establish existence and nonexistence only under the restriction $c \\geq -\\min_{u\\in[0,1]} h(u)$. In this note, we close this gap by covering the entire range $c\\ge H^*$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00638","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00638/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-02T01:04:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpOTcvfbVwbxM64GxdoNneuPjabJ2/610YF3dztHZZYV+zlg94C1SQ/KliNTiVle2/AKqxgY0mUyhGRdM+7TDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:12:19.712040Z"},"content_sha256":"5798fdecfe7872068a0c63d3832325d8c47fc29d777f2c3ab93f87eb1a93e5ba","schema_version":"1.0","event_id":"sha256:5798fdecfe7872068a0c63d3832325d8c47fc29d777f2c3ab93f87eb1a93e5ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VBROYSE4OWSFKNAZSNGWPGRXEA/bundle.json","state_url":"https://pith.science/pith/VBROYSE4OWSFKNAZSNGWPGRXEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VBROYSE4OWSFKNAZSNGWPGRXEA/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":"2026-06-04T03:12:19Z","links":{"resolver":"https://pith.science/pith/VBROYSE4OWSFKNAZSNGWPGRXEA","bundle":"https://pith.science/pith/VBROYSE4OWSFKNAZSNGWPGRXEA/bundle.json","state":"https://pith.science/pith/VBROYSE4OWSFKNAZSNGWPGRXEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VBROYSE4OWSFKNAZSNGWPGRXEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VBROYSE4OWSFKNAZSNGWPGRXEA","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":"75e83852d754184c3cbb710f9a62597f95d5ac53e8a9b39a1c666475a7bd0123","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-30T09:26:33Z","title_canon_sha256":"122962e0a140d47a7283a8275fe75bbdbbe28bf9e1f93bfa90a61ff6c08c0019"},"schema_version":"1.0","source":{"id":"2606.00638","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00638","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00638v1","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00638","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"pith_short_12","alias_value":"VBROYSE4OWSF","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"pith_short_16","alias_value":"VBROYSE4OWSFKNAZ","created_at":"2026-06-02T01:04:00Z"},{"alias_kind":"pith_short_8","alias_value":"VBROYSE4","created_at":"2026-06-02T01:04:00Z"}],"graph_snapshots":[{"event_id":"sha256:5798fdecfe7872068a0c63d3832325d8c47fc29d777f2c3ab93f87eb1a93e5ba","target":"graph","created_at":"2026-06-02T01:04:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.00638/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider traveling wave solutions to a reaction--diffusion--convection equation with a combustion-type reaction term. While a necessary condition for the existence of traveling waves is $c \\geq H^*:=\\sup_{0<u \\leq \\theta} \\big(-\\frac{1}{u} \\int_0^u h(\\sigma)\\,d\\sigma \\big)$, where $c$ denotes the wave speed, $\\theta\\in(0,1)$ the ignition threshold, and $h$ the convective term, the available results in \\cite{DZ25,MM03} establish existence and nonexistence only under the restriction $c \\geq -\\min_{u\\in[0,1]} h(u)$. In this note, we close this gap by covering the entire range $c\\ge H^*$.","authors_text":"Eunkyung Ko, Michaela Zahradn\\'ikov\\'a, Pavel Dr\\'abek, Soyeun Jung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-30T09:26:33Z","title":"Traveling waves for combustion reaction-diffusion-convection equations: the full range of wave speeds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00638","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:ad866c26f6f6f896e3bd153840f91c6be699dcdde14d0b6aa16c94e2fc90d9ba","target":"record","created_at":"2026-06-02T01:04:00Z","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":"75e83852d754184c3cbb710f9a62597f95d5ac53e8a9b39a1c666475a7bd0123","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-30T09:26:33Z","title_canon_sha256":"122962e0a140d47a7283a8275fe75bbdbbe28bf9e1f93bfa90a61ff6c08c0019"},"schema_version":"1.0","source":{"id":"2606.00638","kind":"arxiv","version":1}},"canonical_sha256":"a862ec489c75a4553419934d679a372023109b0fb28fe8164b802ed73a28ed7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a862ec489c75a4553419934d679a372023109b0fb28fe8164b802ed73a28ed7e","first_computed_at":"2026-06-02T01:04:00.560010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:04:00.560010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zI7I8Jxa5d9p1zNH6zS1VsVFDqJDEfyJ5lckmLtS4cbjcfBKZZ2hBkq8cgrd1f+nSLilfqolsgiTZSc8bIHBAg==","signature_status":"signed_v1","signed_at":"2026-06-02T01:04:00.560497Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00638","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad866c26f6f6f896e3bd153840f91c6be699dcdde14d0b6aa16c94e2fc90d9ba","sha256:5798fdecfe7872068a0c63d3832325d8c47fc29d777f2c3ab93f87eb1a93e5ba"],"state_sha256":"c4f1af4daf94568d26fe1bde3e2cfda5a7a1e5e34c9033fbe0bdb061e54abc66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"33xaLpZVMOW99bIfx58Wkxyr2NmsqMSkK3mBigYte3ToujiGtj3FCVk5+Nd2xC6LhpETO+Jg/EkBLVHBEsCmAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:12:19.715569Z","bundle_sha256":"9eab8ac7ecd734830a5b1e4dc9253cd77764f6867ae5bb3ed259a80424ea871c"}}