{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NBHL7UDLWO765P6E2UM5K3GFFV","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":"01352128b7aac171ae79f22bd1b0b51133348df890c3887f462725f4a5e65746","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T11:57:27Z","title_canon_sha256":"49a487635b5dd1ab8f8e69e93052fd35b19238fd86361c8b36e3a9e29e16a7bd"},"schema_version":"1.0","source":{"id":"1508.06120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06120","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06120v2","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06120","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"NBHL7UDLWO76","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NBHL7UDLWO765P6E","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NBHL7UDL","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:fc6f4cea2f09fd161143738716f8b086ebc0e2095ae852ca34611168b9e3629d","target":"graph","created_at":"2026-05-18T01:07:49Z","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 prove the existence of an infinite family of smooth positive bound states for (N +1)-coupled long-wave--short-wave interaction equations. The system describes the interaction between N short waves and a long wave and is of interest in physics and fluid dynamics.","authors_text":"Sharad Silwal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T11:57:27Z","title":"Existence of bound states for (N+1)-coupled long-wave--short-wave interaction equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06120","kind":"arxiv","version":2},"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:f2747909f896de4e6ede1341f73fce5440860fa7ad35b6d5a6c2401562630c87","target":"record","created_at":"2026-05-18T01:07:49Z","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":"01352128b7aac171ae79f22bd1b0b51133348df890c3887f462725f4a5e65746","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-25T11:57:27Z","title_canon_sha256":"49a487635b5dd1ab8f8e69e93052fd35b19238fd86361c8b36e3a9e29e16a7bd"},"schema_version":"1.0","source":{"id":"1508.06120","kind":"arxiv","version":2}},"canonical_sha256":"684ebfd06bb3bfeebfc4d519d56cc52d7a87e9fc89b895bb7ed03e53ad08d1f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"684ebfd06bb3bfeebfc4d519d56cc52d7a87e9fc89b895bb7ed03e53ad08d1f3","first_computed_at":"2026-05-18T01:07:49.061095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:49.061095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JaL9vGpyvzuz745gG5D7cyw1GfcJm1gikZ7smEmTAtXp35aS9BULquev9CIBTiyCJYryicKUsQIkaQsn9o4qDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:49.061724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2747909f896de4e6ede1341f73fce5440860fa7ad35b6d5a6c2401562630c87","sha256:fc6f4cea2f09fd161143738716f8b086ebc0e2095ae852ca34611168b9e3629d"],"state_sha256":"e5704fc45cf6e9480eb24aa1d62d48a6245497d38d35e1aaa44b27a8bda8182e"}