{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YHVTFQ3GAOGLWJQ6JRMMWKV7TH","short_pith_number":"pith:YHVTFQ3G","canonical_record":{"source":{"id":"1310.1318","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-10-04T15:26:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"15c17d4415cd136af8e23faf867a0a92de8133bc5985034360799f5c97b901c3","abstract_canon_sha256":"8676785c5a4fd0b0d44e5e603586ed1111049f43c45e9817d84551aa4118639f"},"schema_version":"1.0"},"canonical_sha256":"c1eb32c366038cbb261e4c58cb2abf99c91b0540b0b604848de0be68163d4c40","source":{"kind":"arxiv","id":"1310.1318","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1318","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1318v3","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1318","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"YHVTFQ3GAOGL","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YHVTFQ3GAOGLWJQ6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YHVTFQ3G","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YHVTFQ3GAOGLWJQ6JRMMWKV7TH","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1318","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-10-04T15:26:48Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"15c17d4415cd136af8e23faf867a0a92de8133bc5985034360799f5c97b901c3","abstract_canon_sha256":"8676785c5a4fd0b0d44e5e603586ed1111049f43c45e9817d84551aa4118639f"},"schema_version":"1.0"},"canonical_sha256":"c1eb32c366038cbb261e4c58cb2abf99c91b0540b0b604848de0be68163d4c40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:04.707184Z","signature_b64":"466r+vARMaTp2cff0Nn24ln7IXiL8qYpJa2DQuwYLtYjnpLlobRQUgWlHkGq/61zLmS0tE5WDGeQpxkDBz3gAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1eb32c366038cbb261e4c58cb2abf99c91b0540b0b604848de0be68163d4c40","last_reissued_at":"2026-05-18T03:06:04.706621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:04.706621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1318","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9MHmOSuxkKsIoQqvYoYFReNZkFE7harsRmlk8bh0lLZiOhm1auqhFSFZgHdgtnTutbqIo3CncE5Bb6A1rulBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:03:48.116550Z"},"content_sha256":"baf0c0dfb1262ae4a5af988e5235156587863ed0fbe5c63bc966b58ef62f4726","schema_version":"1.0","event_id":"sha256:baf0c0dfb1262ae4a5af988e5235156587863ed0fbe5c63bc966b58ef62f4726"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YHVTFQ3GAOGLWJQ6JRMMWKV7TH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A comment on the construction of the maximal globally hyperbolic Cauchy development","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Willie Wai-Yeung Wong","submitted_at":"2013-10-04T15:26:48Z","abstract_excerpt":"Under mild assumptions, we remove all traces of the axiom of choice from the construction of the maximal globally hyperbolic Cauchy development in general relativity. The construction relies on the notion of direct union manifolds, which we review. The construction given is very general: any physical theory with a suitable geometric representation (in particular all classical fields), and such that a strong notion of \"local existence and uniqueness\" of solutions for the corresponding initial value problem is available, is amenable to the same treatment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1318","kind":"arxiv","version":3},"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":"2026-05-18T03:06:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2yjaaiYo8C0Pdf0AwwwiZ8UXP8/2ZHdcU7hEObMTCFP2SQ1sJdzoWYH1JlxLMARSYJscqbyYRUd6o7X479FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:03:48.117436Z"},"content_sha256":"c22cd54bf0f513a749915c1c567bc08625a9d07922f2fdcb364442c85f0533d8","schema_version":"1.0","event_id":"sha256:c22cd54bf0f513a749915c1c567bc08625a9d07922f2fdcb364442c85f0533d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YHVTFQ3GAOGLWJQ6JRMMWKV7TH/bundle.json","state_url":"https://pith.science/pith/YHVTFQ3GAOGLWJQ6JRMMWKV7TH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YHVTFQ3GAOGLWJQ6JRMMWKV7TH/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":"2026-05-30T20:03:48Z","links":{"resolver":"https://pith.science/pith/YHVTFQ3GAOGLWJQ6JRMMWKV7TH","bundle":"https://pith.science/pith/YHVTFQ3GAOGLWJQ6JRMMWKV7TH/bundle.json","state":"https://pith.science/pith/YHVTFQ3GAOGLWJQ6JRMMWKV7TH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YHVTFQ3GAOGLWJQ6JRMMWKV7TH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YHVTFQ3GAOGLWJQ6JRMMWKV7TH","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":"8676785c5a4fd0b0d44e5e603586ed1111049f43c45e9817d84551aa4118639f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-10-04T15:26:48Z","title_canon_sha256":"15c17d4415cd136af8e23faf867a0a92de8133bc5985034360799f5c97b901c3"},"schema_version":"1.0","source":{"id":"1310.1318","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1318","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1318v3","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1318","created_at":"2026-05-18T03:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"YHVTFQ3GAOGL","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YHVTFQ3GAOGLWJQ6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YHVTFQ3G","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:c22cd54bf0f513a749915c1c567bc08625a9d07922f2fdcb364442c85f0533d8","target":"graph","created_at":"2026-05-18T03:06:04Z","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":"Under mild assumptions, we remove all traces of the axiom of choice from the construction of the maximal globally hyperbolic Cauchy development in general relativity. The construction relies on the notion of direct union manifolds, which we review. The construction given is very general: any physical theory with a suitable geometric representation (in particular all classical fields), and such that a strong notion of \"local existence and uniqueness\" of solutions for the corresponding initial value problem is available, is amenable to the same treatment.","authors_text":"Willie Wai-Yeung Wong","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-10-04T15:26:48Z","title":"A comment on the construction of the maximal globally hyperbolic Cauchy development"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1318","kind":"arxiv","version":3},"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:baf0c0dfb1262ae4a5af988e5235156587863ed0fbe5c63bc966b58ef62f4726","target":"record","created_at":"2026-05-18T03:06:04Z","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":"8676785c5a4fd0b0d44e5e603586ed1111049f43c45e9817d84551aa4118639f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-10-04T15:26:48Z","title_canon_sha256":"15c17d4415cd136af8e23faf867a0a92de8133bc5985034360799f5c97b901c3"},"schema_version":"1.0","source":{"id":"1310.1318","kind":"arxiv","version":3}},"canonical_sha256":"c1eb32c366038cbb261e4c58cb2abf99c91b0540b0b604848de0be68163d4c40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1eb32c366038cbb261e4c58cb2abf99c91b0540b0b604848de0be68163d4c40","first_computed_at":"2026-05-18T03:06:04.706621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:04.706621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"466r+vARMaTp2cff0Nn24ln7IXiL8qYpJa2DQuwYLtYjnpLlobRQUgWlHkGq/61zLmS0tE5WDGeQpxkDBz3gAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:04.707184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1318","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baf0c0dfb1262ae4a5af988e5235156587863ed0fbe5c63bc966b58ef62f4726","sha256:c22cd54bf0f513a749915c1c567bc08625a9d07922f2fdcb364442c85f0533d8"],"state_sha256":"3bd42fa06e97be2f20a8043ade31ce1f539b7a00ba245f2126c553df0706d487"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sHw1nz0KmovkpkgyO+bkei58a0Dj7dg5xK4WzlCOErjMypFRjOOmSv+OVFuWeg8gg1kygn35bdmRfQDaCLWzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:03:48.122294Z","bundle_sha256":"35063644221165ae9fb1ddead33d5dd82d15614d5c10fab8f86b0ff168ff1b2b"}}