{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AVBJCAK4KVENBHPFG3JSFNRZHZ","short_pith_number":"pith:AVBJCAK4","canonical_record":{"source":{"id":"1006.2525","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-13T11:03:08Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"fb593f126fecc38c1587a07a1024e83dcd1c33c3a5801cb728a1cac4d787fda5","abstract_canon_sha256":"37115506414dfbb8259d120d9cc70659de195bb17f89e800cfa5249ad890462d"},"schema_version":"1.0"},"canonical_sha256":"054291015c5548d09de536d322b6393e6e16debfb01673051e13b52ff21a98c7","source":{"kind":"arxiv","id":"1006.2525","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2525","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2525v2","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2525","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"AVBJCAK4KVEN","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AVBJCAK4KVENBHPF","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AVBJCAK4","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AVBJCAK4KVENBHPFG3JSFNRZHZ","target":"record","payload":{"canonical_record":{"source":{"id":"1006.2525","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-13T11:03:08Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"fb593f126fecc38c1587a07a1024e83dcd1c33c3a5801cb728a1cac4d787fda5","abstract_canon_sha256":"37115506414dfbb8259d120d9cc70659de195bb17f89e800cfa5249ad890462d"},"schema_version":"1.0"},"canonical_sha256":"054291015c5548d09de536d322b6393e6e16debfb01673051e13b52ff21a98c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:51.468603Z","signature_b64":"E0PzawKoUKcfVEa8xtUxoDRK8X3AYxgx/FU3RqTzvH8fPq9/D+bbcTy5bZxB3qPRyab/bzEkUuYJWCaMVXrkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"054291015c5548d09de536d322b6393e6e16debfb01673051e13b52ff21a98c7","last_reissued_at":"2026-05-18T04:31:51.468108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:51.468108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.2525","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":"2026-05-18T04:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ghhTwjNEvcEQZ1Z+yKTG8+bqfii0JLsX7bARoj+3pO5kUd8FdLnmjMvlplOMg6xzA8sjaCPdrqGwh1WaUD/2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:19:20.399731Z"},"content_sha256":"8325e0187285e07c6678393058a306dc8ed6bf3527647485901b8b789d67e972","schema_version":"1.0","event_id":"sha256:8325e0187285e07c6678393058a306dc8ed6bf3527647485901b8b789d67e972"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AVBJCAK4KVENBHPFG3JSFNRZHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second-order hyperbolic Fuchsian systems. Gowdy spacetimes and the Fuchsian numerical algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Florian Beyer, Philippe G. LeFloch","submitted_at":"2010-06-13T11:03:08Z","abstract_excerpt":"This is the second part of a series devoted to the singular initial value problem for second-order hyperbolic Fuchsian systems. In the first part, we defined and investigated this general class of systems, and we established a well-posedness theory in weighted Sobolev spaces. This theory is applied here to the vacuum Einstein equations for Gowdy spacetimes admitting, by definition, two Killing fields satisfying certain geometric conditions. We recover, by more direct and simpler arguments, the well-posedness results established earlier by Rendall and collaborators. In addition, in this paper w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2525","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":"2026-05-18T04:31:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mVfgNUsttggORYhY4PG6Sls/fUbAhSnrnOXh8xJqccp4Zsbg92v7vpAlR0xwuY0OkPcraLsiVUbrpNNJzynZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:19:20.400428Z"},"content_sha256":"3e381c4ea529527689349da5293fb01c4ee4b38f87e138c5afa706801c3ca6f7","schema_version":"1.0","event_id":"sha256:3e381c4ea529527689349da5293fb01c4ee4b38f87e138c5afa706801c3ca6f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AVBJCAK4KVENBHPFG3JSFNRZHZ/bundle.json","state_url":"https://pith.science/pith/AVBJCAK4KVENBHPFG3JSFNRZHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AVBJCAK4KVENBHPFG3JSFNRZHZ/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":"2026-05-30T09:19:20Z","links":{"resolver":"https://pith.science/pith/AVBJCAK4KVENBHPFG3JSFNRZHZ","bundle":"https://pith.science/pith/AVBJCAK4KVENBHPFG3JSFNRZHZ/bundle.json","state":"https://pith.science/pith/AVBJCAK4KVENBHPFG3JSFNRZHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AVBJCAK4KVENBHPFG3JSFNRZHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AVBJCAK4KVENBHPFG3JSFNRZHZ","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":"37115506414dfbb8259d120d9cc70659de195bb17f89e800cfa5249ad890462d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-13T11:03:08Z","title_canon_sha256":"fb593f126fecc38c1587a07a1024e83dcd1c33c3a5801cb728a1cac4d787fda5"},"schema_version":"1.0","source":{"id":"1006.2525","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2525","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2525v2","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2525","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"AVBJCAK4KVEN","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AVBJCAK4KVENBHPF","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AVBJCAK4","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:3e381c4ea529527689349da5293fb01c4ee4b38f87e138c5afa706801c3ca6f7","target":"graph","created_at":"2026-05-18T04:31:51Z","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":"This is the second part of a series devoted to the singular initial value problem for second-order hyperbolic Fuchsian systems. In the first part, we defined and investigated this general class of systems, and we established a well-posedness theory in weighted Sobolev spaces. This theory is applied here to the vacuum Einstein equations for Gowdy spacetimes admitting, by definition, two Killing fields satisfying certain geometric conditions. We recover, by more direct and simpler arguments, the well-posedness results established earlier by Rendall and collaborators. In addition, in this paper w","authors_text":"Florian Beyer, Philippe G. LeFloch","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-13T11:03:08Z","title":"Second-order hyperbolic Fuchsian systems. Gowdy spacetimes and the Fuchsian numerical algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2525","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":"sha256:8325e0187285e07c6678393058a306dc8ed6bf3527647485901b8b789d67e972","target":"record","created_at":"2026-05-18T04:31:51Z","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":"37115506414dfbb8259d120d9cc70659de195bb17f89e800cfa5249ad890462d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-06-13T11:03:08Z","title_canon_sha256":"fb593f126fecc38c1587a07a1024e83dcd1c33c3a5801cb728a1cac4d787fda5"},"schema_version":"1.0","source":{"id":"1006.2525","kind":"arxiv","version":2}},"canonical_sha256":"054291015c5548d09de536d322b6393e6e16debfb01673051e13b52ff21a98c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"054291015c5548d09de536d322b6393e6e16debfb01673051e13b52ff21a98c7","first_computed_at":"2026-05-18T04:31:51.468108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:51.468108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E0PzawKoUKcfVEa8xtUxoDRK8X3AYxgx/FU3RqTzvH8fPq9/D+bbcTy5bZxB3qPRyab/bzEkUuYJWCaMVXrkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:51.468603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2525","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8325e0187285e07c6678393058a306dc8ed6bf3527647485901b8b789d67e972","sha256:3e381c4ea529527689349da5293fb01c4ee4b38f87e138c5afa706801c3ca6f7"],"state_sha256":"7e4296eff9aea308da76add853ad76324071777074387a86ec1825131486af32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"naxzMFJdQw+tOfaO2ZhF1MUiN2IReEuw3L0VxOGQRp+yGivdqzXIFvLUVXToYAQIX4/bW4KAhRr73vhkonjFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:19:20.403190Z","bundle_sha256":"9999b0b44e15a753400f52baa8a219795c68d1c98dda87f4ca586fb897227605"}}