{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:53UZCXN7NAO4RS4FP24KOODRXZ","short_pith_number":"pith:53UZCXN7","canonical_record":{"source":{"id":"1503.06114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-20T15:35:50Z","cross_cats_sorted":[],"title_canon_sha256":"dd03119a5552d57096b75d67d99ea4f11beddfeda9b0ac54c4473355cb8bc114","abstract_canon_sha256":"d9ae0797200d08d298a57baedb790a66dba932bb68609199951f9baa935b5b69"},"schema_version":"1.0"},"canonical_sha256":"eee9915dbf681dc8cb857eb8a73871be6ea8a641c5b26962bea6a32bf0f233a4","source":{"kind":"arxiv","id":"1503.06114","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06114","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06114v1","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06114","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"53UZCXN7NAO4","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"53UZCXN7NAO4RS4F","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"53UZCXN7","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:53UZCXN7NAO4RS4FP24KOODRXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-20T15:35:50Z","cross_cats_sorted":[],"title_canon_sha256":"dd03119a5552d57096b75d67d99ea4f11beddfeda9b0ac54c4473355cb8bc114","abstract_canon_sha256":"d9ae0797200d08d298a57baedb790a66dba932bb68609199951f9baa935b5b69"},"schema_version":"1.0"},"canonical_sha256":"eee9915dbf681dc8cb857eb8a73871be6ea8a641c5b26962bea6a32bf0f233a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:48.587092Z","signature_b64":"UiJNjs3FRsAsq4kuNlU2q3hljg0xhd4H0WL9oW0CbOyg8n3GfXRBIGZZxmCMNeZwEJlF2+t9+SDIzzcho3+QDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eee9915dbf681dc8cb857eb8a73871be6ea8a641c5b26962bea6a32bf0f233a4","last_reissued_at":"2026-05-18T02:20:48.586520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:48.586520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06114","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":"2026-05-18T02:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PbvBrHqHD0wbxGYubVihd65l54Exks9OeDWaAb8s2MY6uDXAh0F3enasWOE/XOk7626jypIcc5kycQj04RTdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:40:18.786793Z"},"content_sha256":"5eefac2d19217b4f24744842449d8a79e5d4bccd4f28ff7897c1adc827f5d4a0","schema_version":"1.0","event_id":"sha256:5eefac2d19217b4f24744842449d8a79e5d4bccd4f28ff7897c1adc827f5d4a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:53UZCXN7NAO4RS4FP24KOODRXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the propagation of regularity of solutions of the Kadomtsev-Petviashvilli (KPII) equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Linares, Gustavo Ponce, Pedro Isaza","submitted_at":"2015-03-20T15:35:50Z","abstract_excerpt":"We shall deduce some special regularity properties of solutions to the IVP associated to the KPII equation. Mainly, for datum $u_0\\in X_s(\\mathbb R^2)$, $s>2$, (see (1.2) below) whose restriction belongs to $H^m((x_0,\\infty)\\times\\mathbb R)$ for some $m\\in\\mathbb Z^+,\\,m\\geq 3,$ and $x_0\\in \\mathbb R$, we shall prove that the restriction of the corresponding solution $u(\\cdot,t)$ belongs to $H^m((\\beta,\\infty)\\times\\mathbb R)$ for any $\\beta\\in \\mathbb R$ and any $t>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06114","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":"2026-05-18T02:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wfM9SxbTmLBJp/UTYmeNJujBk5vAv0LegRldNFuIubqi13dhqrISoglXoQeVbZmBQmmzAoJ++SCPoEZfa8XUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:40:18.787129Z"},"content_sha256":"17679a15d51102658e5b1a9c97821b28cca9cde6c35727f1ce0464a289eac14a","schema_version":"1.0","event_id":"sha256:17679a15d51102658e5b1a9c97821b28cca9cde6c35727f1ce0464a289eac14a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53UZCXN7NAO4RS4FP24KOODRXZ/bundle.json","state_url":"https://pith.science/pith/53UZCXN7NAO4RS4FP24KOODRXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53UZCXN7NAO4RS4FP24KOODRXZ/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":"2026-06-25T19:40:18Z","links":{"resolver":"https://pith.science/pith/53UZCXN7NAO4RS4FP24KOODRXZ","bundle":"https://pith.science/pith/53UZCXN7NAO4RS4FP24KOODRXZ/bundle.json","state":"https://pith.science/pith/53UZCXN7NAO4RS4FP24KOODRXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53UZCXN7NAO4RS4FP24KOODRXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:53UZCXN7NAO4RS4FP24KOODRXZ","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":"d9ae0797200d08d298a57baedb790a66dba932bb68609199951f9baa935b5b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-20T15:35:50Z","title_canon_sha256":"dd03119a5552d57096b75d67d99ea4f11beddfeda9b0ac54c4473355cb8bc114"},"schema_version":"1.0","source":{"id":"1503.06114","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06114","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06114v1","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06114","created_at":"2026-05-18T02:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"53UZCXN7NAO4","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"53UZCXN7NAO4RS4F","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"53UZCXN7","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:17679a15d51102658e5b1a9c97821b28cca9cde6c35727f1ce0464a289eac14a","target":"graph","created_at":"2026-05-18T02:20:48Z","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 shall deduce some special regularity properties of solutions to the IVP associated to the KPII equation. Mainly, for datum $u_0\\in X_s(\\mathbb R^2)$, $s>2$, (see (1.2) below) whose restriction belongs to $H^m((x_0,\\infty)\\times\\mathbb R)$ for some $m\\in\\mathbb Z^+,\\,m\\geq 3,$ and $x_0\\in \\mathbb R$, we shall prove that the restriction of the corresponding solution $u(\\cdot,t)$ belongs to $H^m((\\beta,\\infty)\\times\\mathbb R)$ for any $\\beta\\in \\mathbb R$ and any $t>0$.","authors_text":"Felipe Linares, Gustavo Ponce, Pedro Isaza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-20T15:35:50Z","title":"On the propagation of regularity of solutions of the Kadomtsev-Petviashvilli (KPII) equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06114","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":"sha256:5eefac2d19217b4f24744842449d8a79e5d4bccd4f28ff7897c1adc827f5d4a0","target":"record","created_at":"2026-05-18T02:20:48Z","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":"d9ae0797200d08d298a57baedb790a66dba932bb68609199951f9baa935b5b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-20T15:35:50Z","title_canon_sha256":"dd03119a5552d57096b75d67d99ea4f11beddfeda9b0ac54c4473355cb8bc114"},"schema_version":"1.0","source":{"id":"1503.06114","kind":"arxiv","version":1}},"canonical_sha256":"eee9915dbf681dc8cb857eb8a73871be6ea8a641c5b26962bea6a32bf0f233a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eee9915dbf681dc8cb857eb8a73871be6ea8a641c5b26962bea6a32bf0f233a4","first_computed_at":"2026-05-18T02:20:48.586520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:48.586520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UiJNjs3FRsAsq4kuNlU2q3hljg0xhd4H0WL9oW0CbOyg8n3GfXRBIGZZxmCMNeZwEJlF2+t9+SDIzzcho3+QDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:48.587092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06114","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5eefac2d19217b4f24744842449d8a79e5d4bccd4f28ff7897c1adc827f5d4a0","sha256:17679a15d51102658e5b1a9c97821b28cca9cde6c35727f1ce0464a289eac14a"],"state_sha256":"48bc65a3c05408fd93456a3e5cbdd474c985719905db9d2f3b52192b441d89d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kXcTmOyE1imbmFobX+D2KpDTo7uOVMOvhv5ILlsgeqMRgIOfhs4VHekdO83GoHqGEl+BA/Kp9TMHkp0mWYXQBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:40:18.788949Z","bundle_sha256":"8965f0417b08046797220de5b96cc77474941f86a7a545cdeae2ee2b2205cd27"}}