{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:4M2V2422Q4WHKBK4XTIQNS3XW7","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":"6bcc47d3ddc4d10d877a41c582cf87b1e2862ef3629e98ffc40aeb427a6d0d7c","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.AP","submitted_at":"2005-03-23T14:47:36Z","title_canon_sha256":"6c5576681e1ec0e0c85025e3fd0d6b8b4efdee198c6b2c7f1d0bd15dc0a68f71"},"schema_version":"1.0","source":{"id":"math/0503493","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0503493","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0503493v1","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0503493","created_at":"2026-05-18T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"4M2V2422Q4WH","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"4M2V2422Q4WHKBK4","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"4M2V2422","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:64640c61c35b2280f607fb1e5eabee7adc9d6a9f239886ef17a5275e449935a4","target":"graph","created_at":"2026-05-18T01:05:23Z","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 a semilinear elliptic system which include the model system of the $W-$strings in the cosmology as a special case. We prove existence of multi-string solutions and obtain precise asymptotic decay estimates near infinity for the solutions.\n As a special case of this result we solve an open problem posed in\n \\cite{yan}","authors_text":"Dongho Chae","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2005-03-23T14:47:36Z","title":"Existence of Multistring Solutions of the Self-Gravitating Massive $W-$Boson"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503493","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":"sha256:9875f2aed8857e4e122b4ce8bbf2515af01d3a0e68ddec97d404277ac3c28d47","target":"record","created_at":"2026-05-18T01:05:23Z","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":"6bcc47d3ddc4d10d877a41c582cf87b1e2862ef3629e98ffc40aeb427a6d0d7c","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.AP","submitted_at":"2005-03-23T14:47:36Z","title_canon_sha256":"6c5576681e1ec0e0c85025e3fd0d6b8b4efdee198c6b2c7f1d0bd15dc0a68f71"},"schema_version":"1.0","source":{"id":"math/0503493","kind":"arxiv","version":1}},"canonical_sha256":"e3355d735a872c75055cbcd106cb77b7c535d412b480f1e9fadeb073c9edfefb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3355d735a872c75055cbcd106cb77b7c535d412b480f1e9fadeb073c9edfefb","first_computed_at":"2026-05-18T01:05:23.576703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:23.576703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YBOli5SyickYPlLsjxQgJyaVH3PiO4AyGoq4PQL6SpaJCCuHqgtx3twic3pGBh9k84J807OZZxLkQhJJfxeGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:23.577164Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0503493","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9875f2aed8857e4e122b4ce8bbf2515af01d3a0e68ddec97d404277ac3c28d47","sha256:64640c61c35b2280f607fb1e5eabee7adc9d6a9f239886ef17a5275e449935a4"],"state_sha256":"bc5094f8bbbf78cfdb7d4e989b07520680154c750e9f519e125f7a5ab355f1a5"}