{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5BRE62XLUDU3KIVQZUJK2XCKVW","short_pith_number":"pith:5BRE62XL","canonical_record":{"source":{"id":"1511.09371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-30T16:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"651fb64a5c7b858d147c3bf17b266a103132ccfd5b21b8c29be2c01073ee04be","abstract_canon_sha256":"c3ba096a8c2e6056dd33b3a8f9c51ea117b6970d797598ec533a4f3788a79e03"},"schema_version":"1.0"},"canonical_sha256":"e8624f6aeba0e9b522b0cd12ad5c4aad9a96dc9146f128857aa8fac7db5381ec","source":{"kind":"arxiv","id":"1511.09371","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09371","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09371v2","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09371","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"5BRE62XLUDU3","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5BRE62XLUDU3KIVQ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5BRE62XL","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5BRE62XLUDU3KIVQZUJK2XCKVW","target":"record","payload":{"canonical_record":{"source":{"id":"1511.09371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-30T16:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"651fb64a5c7b858d147c3bf17b266a103132ccfd5b21b8c29be2c01073ee04be","abstract_canon_sha256":"c3ba096a8c2e6056dd33b3a8f9c51ea117b6970d797598ec533a4f3788a79e03"},"schema_version":"1.0"},"canonical_sha256":"e8624f6aeba0e9b522b0cd12ad5c4aad9a96dc9146f128857aa8fac7db5381ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:54.963348Z","signature_b64":"vzj4Oujo0OarWfdQKiI6EAu7fQbNzNBryxnn0ItifuELdHOyV+HVAJ0l22i/WaiuFhNoObd7S2X6pEE2XmbzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8624f6aeba0e9b522b0cd12ad5c4aad9a96dc9146f128857aa8fac7db5381ec","last_reissued_at":"2026-05-18T00:37:54.962767Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:54.962767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.09371","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:37:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W0MBauhrpyeVd/Fpcdo8FPZ6sgKkbCljzvbr257hkexQmb6NhS9jSmNum2KTbSfeVGnge8VKkf0gbO7JZ86fBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:09:49.542964Z"},"content_sha256":"4aff0fc856d2c7155a380fff0f15cdbd1df88235e4572a90e57cea4bef5d3a70","schema_version":"1.0","event_id":"sha256:4aff0fc856d2c7155a380fff0f15cdbd1df88235e4572a90e57cea4bef5d3a70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5BRE62XLUDU3KIVQZUJK2XCKVW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Scattering for Small Data of 2+1 Dimensional Equivariant Einstein-Wave Map System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Dodson, Nishanth Gudapati","submitted_at":"2015-11-30T16:27:48Z","abstract_excerpt":"We consider the Cauchy problem of 2+1 equivariant wave maps coupled to Einstein's equations of general relativity and prove that two separate (nonlinear) subclasses of the system disperse to their corresponding linearized equations in the large. Global asymptotic behaviour of 2+1 Einstein-wave map system is relevant because the system occurs naturally in 3+1 vacuum Einstein's equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09371","kind":"arxiv","version":2},"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":"2026-05-18T00:37:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N538zGmbCIfUJsfm8FCzaj6R7+/gqr0Cw8qTfWLa0Osb5+OthdbjCfrgoA5l84vf1I5vTLz7SZ88mftgkr+XCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:09:49.543353Z"},"content_sha256":"27cef33744c177168864213e5ec65ea9ca935f6559b6ae546cbbcdbc73fcda36","schema_version":"1.0","event_id":"sha256:27cef33744c177168864213e5ec65ea9ca935f6559b6ae546cbbcdbc73fcda36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5BRE62XLUDU3KIVQZUJK2XCKVW/bundle.json","state_url":"https://pith.science/pith/5BRE62XLUDU3KIVQZUJK2XCKVW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5BRE62XLUDU3KIVQZUJK2XCKVW/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":"2026-05-30T11:09:49Z","links":{"resolver":"https://pith.science/pith/5BRE62XLUDU3KIVQZUJK2XCKVW","bundle":"https://pith.science/pith/5BRE62XLUDU3KIVQZUJK2XCKVW/bundle.json","state":"https://pith.science/pith/5BRE62XLUDU3KIVQZUJK2XCKVW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5BRE62XLUDU3KIVQZUJK2XCKVW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5BRE62XLUDU3KIVQZUJK2XCKVW","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":"c3ba096a8c2e6056dd33b3a8f9c51ea117b6970d797598ec533a4f3788a79e03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-30T16:27:48Z","title_canon_sha256":"651fb64a5c7b858d147c3bf17b266a103132ccfd5b21b8c29be2c01073ee04be"},"schema_version":"1.0","source":{"id":"1511.09371","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.09371","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1511.09371v2","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.09371","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"5BRE62XLUDU3","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5BRE62XLUDU3KIVQ","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5BRE62XL","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:27cef33744c177168864213e5ec65ea9ca935f6559b6ae546cbbcdbc73fcda36","target":"graph","created_at":"2026-05-18T00:37:54Z","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 Cauchy problem of 2+1 equivariant wave maps coupled to Einstein's equations of general relativity and prove that two separate (nonlinear) subclasses of the system disperse to their corresponding linearized equations in the large. Global asymptotic behaviour of 2+1 Einstein-wave map system is relevant because the system occurs naturally in 3+1 vacuum Einstein's equations.","authors_text":"Benjamin Dodson, Nishanth Gudapati","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-30T16:27:48Z","title":"On Scattering for Small Data of 2+1 Dimensional Equivariant Einstein-Wave Map System"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09371","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":"sha256:4aff0fc856d2c7155a380fff0f15cdbd1df88235e4572a90e57cea4bef5d3a70","target":"record","created_at":"2026-05-18T00:37:54Z","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":"c3ba096a8c2e6056dd33b3a8f9c51ea117b6970d797598ec533a4f3788a79e03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-30T16:27:48Z","title_canon_sha256":"651fb64a5c7b858d147c3bf17b266a103132ccfd5b21b8c29be2c01073ee04be"},"schema_version":"1.0","source":{"id":"1511.09371","kind":"arxiv","version":2}},"canonical_sha256":"e8624f6aeba0e9b522b0cd12ad5c4aad9a96dc9146f128857aa8fac7db5381ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8624f6aeba0e9b522b0cd12ad5c4aad9a96dc9146f128857aa8fac7db5381ec","first_computed_at":"2026-05-18T00:37:54.962767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:54.962767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vzj4Oujo0OarWfdQKiI6EAu7fQbNzNBryxnn0ItifuELdHOyV+HVAJ0l22i/WaiuFhNoObd7S2X6pEE2XmbzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:54.963348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.09371","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aff0fc856d2c7155a380fff0f15cdbd1df88235e4572a90e57cea4bef5d3a70","sha256:27cef33744c177168864213e5ec65ea9ca935f6559b6ae546cbbcdbc73fcda36"],"state_sha256":"072fc55e59a2ff1b3baeaf5de45cfade6d50988ee4df9349c3a46d878cbc8a68"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P42TSVrh8Ywim+95KLcPfBfQ2+ceZpSHm8t0QFpqV/3KA3X1KEStvInbjcx2SGQJlV3Mh3gZYw/+DvB9FlIlDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:09:49.545465Z","bundle_sha256":"b59af38b51182a1b6b92229eb70b8d006231e862fac01bcd7732f63e229c878c"}}