{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EZ3XF2PP3PNUE5ANCAO2DRSVNJ","short_pith_number":"pith:EZ3XF2PP","canonical_record":{"source":{"id":"1206.3756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-17T13:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"7a939706be9ad872cc8da0bb77bc4f17e79af6697aa4d3a8e6d72fdea982680c","abstract_canon_sha256":"1ebb022aeec3e990522d51640252dc5880b8ac97bfe3f32e7599afff4d5fc8b3"},"schema_version":"1.0"},"canonical_sha256":"267772e9efdbdb42740d101da1c6556a5fc5605706a9959644b98fb8daa00f86","source":{"kind":"arxiv","id":"1206.3756","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3756","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3756v1","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3756","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"EZ3XF2PP3PNU","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EZ3XF2PP3PNUE5AN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EZ3XF2PP","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EZ3XF2PP3PNUE5ANCAO2DRSVNJ","target":"record","payload":{"canonical_record":{"source":{"id":"1206.3756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-17T13:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"7a939706be9ad872cc8da0bb77bc4f17e79af6697aa4d3a8e6d72fdea982680c","abstract_canon_sha256":"1ebb022aeec3e990522d51640252dc5880b8ac97bfe3f32e7599afff4d5fc8b3"},"schema_version":"1.0"},"canonical_sha256":"267772e9efdbdb42740d101da1c6556a5fc5605706a9959644b98fb8daa00f86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:18.826875Z","signature_b64":"/Tmz7lxx5v5UujlGBipQttuQiCOKSWL8n532XigMlIEId4VoGaYWyKjQiw1mDW4N5gL+nFE2ADnYEJvHGpb0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"267772e9efdbdb42740d101da1c6556a5fc5605706a9959644b98fb8daa00f86","last_reissued_at":"2026-05-18T03:53:18.826259Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:18.826259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.3756","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":"2026-05-18T03:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqlKjdh4Qua6adn0Is65KNxnPV9CvBhHQx8LSmOfDNKl2KAafiwdvDQxFgWtYpaitQIdBurw7BeB57b9dxntCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:29:19.548532Z"},"content_sha256":"212a5a590bc1f05a0f12844145c41b6286f162ccdea24bb9537099cc00fc84ba","schema_version":"1.0","event_id":"sha256:212a5a590bc1f05a0f12844145c41b6286f162ccdea24bb9537099cc00fc84ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EZ3XF2PP3PNUE5ANCAO2DRSVNJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Cauchy problem for a Boussinesq type system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Linares, Jorge Drumond Silva, Mahendra Panthee","submitted_at":"2012-06-17T13:44:42Z","abstract_excerpt":"We consider the initial value problem (IVP) associated to a Boussinesq type system. After rewriting the system in an equivalent form of coupled KdV-type equations, we prove that this is locally well-posed in $(H^s(\\R^2))^4$, $s>3/2$, using sharp smoothing estimates. Consequently we obtain the local well-posedness result for the original system in $H^s\\times \\mathcal{V}^{s+1}$ for $s>3/2$ (see below for the definition of $\\mathcal{V}^{s}$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3756","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":"2026-05-18T03:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ZrUaoIjMHG0oKFe4FGjyAZpaTkVCc7QlH3L8mwvw+ZucedHTagV2/qWn+VuXrI/PdcHV2tlfFhz1EBWy5NwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:29:19.548879Z"},"content_sha256":"c5d997b36bc46a81f4d7bbef7cfac2021b5f713a803127c512c382126840a9e3","schema_version":"1.0","event_id":"sha256:c5d997b36bc46a81f4d7bbef7cfac2021b5f713a803127c512c382126840a9e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/bundle.json","state_url":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/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":"2026-06-24T21:29:19Z","links":{"resolver":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ","bundle":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/bundle.json","state":"https://pith.science/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EZ3XF2PP3PNUE5ANCAO2DRSVNJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EZ3XF2PP3PNUE5ANCAO2DRSVNJ","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":"1ebb022aeec3e990522d51640252dc5880b8ac97bfe3f32e7599afff4d5fc8b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-17T13:44:42Z","title_canon_sha256":"7a939706be9ad872cc8da0bb77bc4f17e79af6697aa4d3a8e6d72fdea982680c"},"schema_version":"1.0","source":{"id":"1206.3756","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3756","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3756v1","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3756","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"EZ3XF2PP3PNU","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EZ3XF2PP3PNUE5AN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EZ3XF2PP","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:c5d997b36bc46a81f4d7bbef7cfac2021b5f713a803127c512c382126840a9e3","target":"graph","created_at":"2026-05-18T03:53:18Z","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 consider the initial value problem (IVP) associated to a Boussinesq type system. After rewriting the system in an equivalent form of coupled KdV-type equations, we prove that this is locally well-posed in $(H^s(\\R^2))^4$, $s>3/2$, using sharp smoothing estimates. Consequently we obtain the local well-posedness result for the original system in $H^s\\times \\mathcal{V}^{s+1}$ for $s>3/2$ (see below for the definition of $\\mathcal{V}^{s}$).","authors_text":"Felipe Linares, Jorge Drumond Silva, Mahendra Panthee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-17T13:44:42Z","title":"On the Cauchy problem for a Boussinesq type system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3756","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":"sha256:212a5a590bc1f05a0f12844145c41b6286f162ccdea24bb9537099cc00fc84ba","target":"record","created_at":"2026-05-18T03:53:18Z","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":"1ebb022aeec3e990522d51640252dc5880b8ac97bfe3f32e7599afff4d5fc8b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-17T13:44:42Z","title_canon_sha256":"7a939706be9ad872cc8da0bb77bc4f17e79af6697aa4d3a8e6d72fdea982680c"},"schema_version":"1.0","source":{"id":"1206.3756","kind":"arxiv","version":1}},"canonical_sha256":"267772e9efdbdb42740d101da1c6556a5fc5605706a9959644b98fb8daa00f86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"267772e9efdbdb42740d101da1c6556a5fc5605706a9959644b98fb8daa00f86","first_computed_at":"2026-05-18T03:53:18.826259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:18.826259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Tmz7lxx5v5UujlGBipQttuQiCOKSWL8n532XigMlIEId4VoGaYWyKjQiw1mDW4N5gL+nFE2ADnYEJvHGpb0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:18.826875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3756","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:212a5a590bc1f05a0f12844145c41b6286f162ccdea24bb9537099cc00fc84ba","sha256:c5d997b36bc46a81f4d7bbef7cfac2021b5f713a803127c512c382126840a9e3"],"state_sha256":"40163749d8498024e33de21b96a5b2c4ca4c3960b8b9354ee960be13174780ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L2kbwllPdxHSy6z7X/NbMtDk/Hholr2GtQo2VPS4UwHskio0eApQH6qTFzffOQuH+ZBhfKU9VBsjMk9gSmfbDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:29:19.550827Z","bundle_sha256":"3bdbf8a2645a47794f8ae227a1c711515b38386e7893f52e643928bf6b480982"}}