{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TZWVT6JBGUGAZCYXB4GVYG7T4F","short_pith_number":"pith:TZWVT6JB","canonical_record":{"source":{"id":"1903.03502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-03-08T15:28:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"fa091f7d8dcf9ea4b3759921a3e6c6572868b0feb2a178bb1fbd7f2a7dd27993","abstract_canon_sha256":"9db6cc89a12078aad940514a59931e7860c63866da8c7a17a73caf6bbffcfc54"},"schema_version":"1.0"},"canonical_sha256":"9e6d59f921350c0c8b170f0d5c1bf3e16c938f08be5ffb505dfe1c3f76f0d81a","source":{"kind":"arxiv","id":"1903.03502","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.03502","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"arxiv_version","alias_value":"1903.03502v2","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03502","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"pith_short_12","alias_value":"TZWVT6JBGUGA","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"TZWVT6JBGUGAZCYX","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"TZWVT6JB","created_at":"2026-07-05T01:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TZWVT6JBGUGAZCYXB4GVYG7T4F","target":"record","payload":{"canonical_record":{"source":{"id":"1903.03502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-03-08T15:28:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"fa091f7d8dcf9ea4b3759921a3e6c6572868b0feb2a178bb1fbd7f2a7dd27993","abstract_canon_sha256":"9db6cc89a12078aad940514a59931e7860c63866da8c7a17a73caf6bbffcfc54"},"schema_version":"1.0"},"canonical_sha256":"9e6d59f921350c0c8b170f0d5c1bf3e16c938f08be5ffb505dfe1c3f76f0d81a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:26:04.245881Z","signature_b64":"5+ZOemwBspJh71bfw47Yq1+zEDhbw0V0cRRpCCbsK0pnwqCQvEQm7yeg2fXGivmP5BAAmy6PRFuRQXWlnCirCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e6d59f921350c0c8b170f0d5c1bf3e16c938f08be5ffb505dfe1c3f76f0d81a","last_reissued_at":"2026-07-05T01:26:04.245386Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:26:04.245386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.03502","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":"2026-07-05T01:26:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5pIjc0SvaYFKR3/5Dn1myRx7+59i9t2e2CAmdxtWePxobCKusNEskM1be1dkyt3yCC48ZhTciG6GnZ4Dv87pAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:53:15.924098Z"},"content_sha256":"29f3bbece6fde0607f2417fca6b89fcdd57bd0e8379471e4bbe7060ffef767a0","schema_version":"1.0","event_id":"sha256:29f3bbece6fde0607f2417fca6b89fcdd57bd0e8379471e4bbe7060ffef767a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TZWVT6JBGUGAZCYXB4GVYG7T4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean curvature flow in asymptotically flat product spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"\\'Aron Szab\\'o, Boris Vertman, Felix Lubbe, Klaus Kroencke, Oliver C. Schn\\\"urer, Oliver Lindblad Petersen, Tobias Marxen, Wolfgang Maurer, Wolfgang Meiser","submitted_at":"2019-03-08T15:28:48Z","abstract_excerpt":"We consider the long-time behaviour of the mean curvature flow of spacelike hypersurfaces in the Lorentzian product manifold $M\\times\\mathbb{R}$, where $M$ is asymptotically flat. If the initial hypersurface $F_0\\subset M\\times\\mathbb{R}$ is uniformly spacelike and asymptotic to $M\\times\\left\\{s\\right\\}$ for some $s\\in\\mathbb{R}$ at infinity, we show that a mean curvature flow starting at $F_0$ exists for all times and converges uniformly to $M\\times\\left\\{s\\right\\}$ as $t\\to \\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03502","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.03502/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:26:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K9r06NqYe7GQYcCcYSMj24XvjrTlw17rLykUotjO+oWHppazrWYvPSq76Q7dCbg4rKuuIG7WsgIeUNbf8b+RBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:53:15.924489Z"},"content_sha256":"c08c5c2213f7a7721302b22df5febccf61624f56009328952b40a100d130a1b5","schema_version":"1.0","event_id":"sha256:c08c5c2213f7a7721302b22df5febccf61624f56009328952b40a100d130a1b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TZWVT6JBGUGAZCYXB4GVYG7T4F/bundle.json","state_url":"https://pith.science/pith/TZWVT6JBGUGAZCYXB4GVYG7T4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TZWVT6JBGUGAZCYXB4GVYG7T4F/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":"2026-07-06T08:53:15Z","links":{"resolver":"https://pith.science/pith/TZWVT6JBGUGAZCYXB4GVYG7T4F","bundle":"https://pith.science/pith/TZWVT6JBGUGAZCYXB4GVYG7T4F/bundle.json","state":"https://pith.science/pith/TZWVT6JBGUGAZCYXB4GVYG7T4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TZWVT6JBGUGAZCYXB4GVYG7T4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TZWVT6JBGUGAZCYXB4GVYG7T4F","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":"9db6cc89a12078aad940514a59931e7860c63866da8c7a17a73caf6bbffcfc54","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-03-08T15:28:48Z","title_canon_sha256":"fa091f7d8dcf9ea4b3759921a3e6c6572868b0feb2a178bb1fbd7f2a7dd27993"},"schema_version":"1.0","source":{"id":"1903.03502","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.03502","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"arxiv_version","alias_value":"1903.03502v2","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03502","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"pith_short_12","alias_value":"TZWVT6JBGUGA","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"TZWVT6JBGUGAZCYX","created_at":"2026-07-05T01:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"TZWVT6JB","created_at":"2026-07-05T01:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:c08c5c2213f7a7721302b22df5febccf61624f56009328952b40a100d130a1b5","target":"graph","created_at":"2026-07-05T01:26:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1903.03502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the long-time behaviour of the mean curvature flow of spacelike hypersurfaces in the Lorentzian product manifold $M\\times\\mathbb{R}$, where $M$ is asymptotically flat. If the initial hypersurface $F_0\\subset M\\times\\mathbb{R}$ is uniformly spacelike and asymptotic to $M\\times\\left\\{s\\right\\}$ for some $s\\in\\mathbb{R}$ at infinity, we show that a mean curvature flow starting at $F_0$ exists for all times and converges uniformly to $M\\times\\left\\{s\\right\\}$ as $t\\to \\infty$.","authors_text":"\\'Aron Szab\\'o, Boris Vertman, Felix Lubbe, Klaus Kroencke, Oliver C. Schn\\\"urer, Oliver Lindblad Petersen, Tobias Marxen, Wolfgang Maurer, Wolfgang Meiser","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-03-08T15:28:48Z","title":"Mean curvature flow in asymptotically flat product spacetimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03502","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":"sha256:29f3bbece6fde0607f2417fca6b89fcdd57bd0e8379471e4bbe7060ffef767a0","target":"record","created_at":"2026-07-05T01:26:04Z","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":"9db6cc89a12078aad940514a59931e7860c63866da8c7a17a73caf6bbffcfc54","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-03-08T15:28:48Z","title_canon_sha256":"fa091f7d8dcf9ea4b3759921a3e6c6572868b0feb2a178bb1fbd7f2a7dd27993"},"schema_version":"1.0","source":{"id":"1903.03502","kind":"arxiv","version":2}},"canonical_sha256":"9e6d59f921350c0c8b170f0d5c1bf3e16c938f08be5ffb505dfe1c3f76f0d81a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e6d59f921350c0c8b170f0d5c1bf3e16c938f08be5ffb505dfe1c3f76f0d81a","first_computed_at":"2026-07-05T01:26:04.245386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:26:04.245386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5+ZOemwBspJh71bfw47Yq1+zEDhbw0V0cRRpCCbsK0pnwqCQvEQm7yeg2fXGivmP5BAAmy6PRFuRQXWlnCirCg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:26:04.245881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.03502","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29f3bbece6fde0607f2417fca6b89fcdd57bd0e8379471e4bbe7060ffef767a0","sha256:c08c5c2213f7a7721302b22df5febccf61624f56009328952b40a100d130a1b5"],"state_sha256":"25b0968f964d5671eb98937dd2becd88153de77d29cec8d633aa5b849fcc2d36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MmpNU9P1LvqDe5SCIS1YsL8refyGI+d5yx4zbmZSXYl0gojfQ3g+dxkxj8RquvOzIzAW6m/g38C4+DYbmhbwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T08:53:15.926481Z","bundle_sha256":"4804c83cf8a65cad4b1603b3c3b60333f11ca3bf9a2e9e7babf090b3b89c6e20"}}