{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CKIEYUHDTVU3TKXO6CMHXHI5HY","short_pith_number":"pith:CKIEYUHD","canonical_record":{"source":{"id":"2606.09519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-08T14:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"973a92d4cda84cd5e26819ced687fd38bf6f3d782d356a540bac6f3824ab5f2d","abstract_canon_sha256":"aeec2f07a11dd35d373472a2b2e8d57c8cc9e93d15211313af8564ca2593f634"},"schema_version":"1.0"},"canonical_sha256":"12904c50e39d69b9aaeef0987b9d1d3e22d762ab3667c79e0b7513a52ae412d6","source":{"kind":"arxiv","id":"2606.09519","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09519","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09519v1","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09519","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"CKIEYUHDTVU3","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"pith_short_16","alias_value":"CKIEYUHDTVU3TKXO","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"pith_short_8","alias_value":"CKIEYUHD","created_at":"2026-06-09T02:08:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CKIEYUHDTVU3TKXO6CMHXHI5HY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.09519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-08T14:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"973a92d4cda84cd5e26819ced687fd38bf6f3d782d356a540bac6f3824ab5f2d","abstract_canon_sha256":"aeec2f07a11dd35d373472a2b2e8d57c8cc9e93d15211313af8564ca2593f634"},"schema_version":"1.0"},"canonical_sha256":"12904c50e39d69b9aaeef0987b9d1d3e22d762ab3667c79e0b7513a52ae412d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:08:53.076021Z","signature_b64":"TFol99OIforb3wmaEsda6R/6L8tGtxijnESda9Tu2mztjs12LfD0V7m6NRtHjQ8GRBF11Ew8R8SmhslTPQNDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12904c50e39d69b9aaeef0987b9d1d3e22d762ab3667c79e0b7513a52ae412d6","last_reissued_at":"2026-06-09T02:08:53.075177Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:08:53.075177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.09519","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":"2026-06-09T02:08:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4H9DbPVYfFkj8KQkMtbtgaeWYTlbF13RQMfM0/2NFUL9ZZrlUlnJO3NZ6Roe8xcLOTf8HqqV7n0Qb9F5lNSGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T07:06:11.386132Z"},"content_sha256":"2c5457a8616c24ce3e1c44201102da13eb4567da64ba1c2341322f864a54fb7d","schema_version":"1.0","event_id":"sha256:2c5457a8616c24ce3e1c44201102da13eb4567da64ba1c2341322f864a54fb7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CKIEYUHDTVU3TKXO6CMHXHI5HY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global existence for a Zakharov type system in a domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masahito Ohta, Nobutatsu Kobayashi","submitted_at":"2026-06-08T14:09:30Z","abstract_excerpt":"We study an initial-boundary value problem for a Zakharov type system in three space dimensions in a general domain. Under a smallness assumption on the initial data, we construct a unique global strong solution. The solution is obtained by a direct approach based on higher-order energy estimates and the construction of a Cauchy sequence in suitable Banach spaces, without employing compactness methods. Furthermore, we obtain estimates on the growth of higher-order Sobolev norms of solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09519","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/2606.09519/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":"2026-06-09T02:08:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mbV60NEkRF7JG0pqIOecID3+sXckhyU2Q6a+QQMf4s/qeBLLV3CnZVQpNKE3bR4l8DINaNFNSHdrvc9qxhYrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T07:06:11.386513Z"},"content_sha256":"14f230b894714124bb9bdfdc56a98f0ada0d2bc24ec6261222a79b5756d17228","schema_version":"1.0","event_id":"sha256:14f230b894714124bb9bdfdc56a98f0ada0d2bc24ec6261222a79b5756d17228"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKIEYUHDTVU3TKXO6CMHXHI5HY/bundle.json","state_url":"https://pith.science/pith/CKIEYUHDTVU3TKXO6CMHXHI5HY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKIEYUHDTVU3TKXO6CMHXHI5HY/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":"2026-06-29T07:06:11Z","links":{"resolver":"https://pith.science/pith/CKIEYUHDTVU3TKXO6CMHXHI5HY","bundle":"https://pith.science/pith/CKIEYUHDTVU3TKXO6CMHXHI5HY/bundle.json","state":"https://pith.science/pith/CKIEYUHDTVU3TKXO6CMHXHI5HY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKIEYUHDTVU3TKXO6CMHXHI5HY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CKIEYUHDTVU3TKXO6CMHXHI5HY","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":"aeec2f07a11dd35d373472a2b2e8d57c8cc9e93d15211313af8564ca2593f634","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-08T14:09:30Z","title_canon_sha256":"973a92d4cda84cd5e26819ced687fd38bf6f3d782d356a540bac6f3824ab5f2d"},"schema_version":"1.0","source":{"id":"2606.09519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09519","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09519v1","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09519","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"pith_short_12","alias_value":"CKIEYUHDTVU3","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"pith_short_16","alias_value":"CKIEYUHDTVU3TKXO","created_at":"2026-06-09T02:08:53Z"},{"alias_kind":"pith_short_8","alias_value":"CKIEYUHD","created_at":"2026-06-09T02:08:53Z"}],"graph_snapshots":[{"event_id":"sha256:14f230b894714124bb9bdfdc56a98f0ada0d2bc24ec6261222a79b5756d17228","target":"graph","created_at":"2026-06-09T02:08:53Z","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/2606.09519/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study an initial-boundary value problem for a Zakharov type system in three space dimensions in a general domain. Under a smallness assumption on the initial data, we construct a unique global strong solution. The solution is obtained by a direct approach based on higher-order energy estimates and the construction of a Cauchy sequence in suitable Banach spaces, without employing compactness methods. Furthermore, we obtain estimates on the growth of higher-order Sobolev norms of solutions.","authors_text":"Masahito Ohta, Nobutatsu Kobayashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-08T14:09:30Z","title":"Global existence for a Zakharov type system in a domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09519","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":"sha256:2c5457a8616c24ce3e1c44201102da13eb4567da64ba1c2341322f864a54fb7d","target":"record","created_at":"2026-06-09T02:08:53Z","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":"aeec2f07a11dd35d373472a2b2e8d57c8cc9e93d15211313af8564ca2593f634","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-08T14:09:30Z","title_canon_sha256":"973a92d4cda84cd5e26819ced687fd38bf6f3d782d356a540bac6f3824ab5f2d"},"schema_version":"1.0","source":{"id":"2606.09519","kind":"arxiv","version":1}},"canonical_sha256":"12904c50e39d69b9aaeef0987b9d1d3e22d762ab3667c79e0b7513a52ae412d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12904c50e39d69b9aaeef0987b9d1d3e22d762ab3667c79e0b7513a52ae412d6","first_computed_at":"2026-06-09T02:08:53.075177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:08:53.075177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TFol99OIforb3wmaEsda6R/6L8tGtxijnESda9Tu2mztjs12LfD0V7m6NRtHjQ8GRBF11Ew8R8SmhslTPQNDAg==","signature_status":"signed_v1","signed_at":"2026-06-09T02:08:53.076021Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c5457a8616c24ce3e1c44201102da13eb4567da64ba1c2341322f864a54fb7d","sha256:14f230b894714124bb9bdfdc56a98f0ada0d2bc24ec6261222a79b5756d17228"],"state_sha256":"f00c3781c2a6f5d7e2933ec0601788a73028f8d65ea699b6c276a5b2e547d289"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7djYyeMAXO8HR9aC40KIN9ODgr0HKed/QNu5HLTE7QJHfh+bmFo7Qagfdiq/FeTY35LsKyxebRBysrTRyn/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T07:06:11.388402Z","bundle_sha256":"4680ef2a074e21afbb566d99654722dbc15c045a8c3768f6c4278485829d489b"}}