{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PX7TVQTM2MJ2KQQUERHDFZSGRF","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":"1b1f5ab34c4d51063c3b5dcea155101b223b3da2642603a660915296c20a9c27","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-06T14:40:11Z","title_canon_sha256":"246b76f16597e68331d5fa6db89b57356a57fbf5339892082e1dc97de729933e"},"schema_version":"1.0","source":{"id":"1908.02185","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.02185","created_at":"2026-07-05T01:10:26Z"},{"alias_kind":"arxiv_version","alias_value":"1908.02185v3","created_at":"2026-07-05T01:10:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02185","created_at":"2026-07-05T01:10:26Z"},{"alias_kind":"pith_short_12","alias_value":"PX7TVQTM2MJ2","created_at":"2026-07-05T01:10:26Z"},{"alias_kind":"pith_short_16","alias_value":"PX7TVQTM2MJ2KQQU","created_at":"2026-07-05T01:10:26Z"},{"alias_kind":"pith_short_8","alias_value":"PX7TVQTM","created_at":"2026-07-05T01:10:26Z"}],"graph_snapshots":[{"event_id":"sha256:cdb57b3635bdc06e3375b6dbd16977c8a02817b77f1264a13ce447c9a3436791","target":"graph","created_at":"2026-07-05T01:10:26Z","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/1908.02185/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the first part of this paper we consider expanding vacuum cosmological spacetimes with a free $T^N$-action. Among them, we give evidence that Gowdy spacetimes have AVTD (asymptotically velocity term dominated) behavior for their initial geometry, in any dimension. We then give sufficient conditions to reach a similar conclusion about a $T^2$-invariant four dimensional nonGowdy spacetime. In the second part of the paper we consider vacuum cosmological spacetimes with crushing singularities. We introduce a monotonic quantity to characterize Kasner spacetimes. Assuming scale-invariant curvatur","authors_text":"John Lott","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-06T14:40:11Z","title":"On the initial geometry of a vacuum cosmological spacetime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02185","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":"sha256:7053e3ef2056560cfbcecf7c846c02c8ea52bb10d2a24a62a910581a7979393d","target":"record","created_at":"2026-07-05T01:10:26Z","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":"1b1f5ab34c4d51063c3b5dcea155101b223b3da2642603a660915296c20a9c27","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-06T14:40:11Z","title_canon_sha256":"246b76f16597e68331d5fa6db89b57356a57fbf5339892082e1dc97de729933e"},"schema_version":"1.0","source":{"id":"1908.02185","kind":"arxiv","version":3}},"canonical_sha256":"7dff3ac26cd313a54214244e32e6468959ebb1ff9994a8384b0334c92e1cebd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dff3ac26cd313a54214244e32e6468959ebb1ff9994a8384b0334c92e1cebd4","first_computed_at":"2026-07-05T01:10:26.868201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:10:26.868201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qOiZeGcK514FP2A8pqd8xrh3vP6Fl4xPm3yqSBNjRVpXPl9JH1yW1b7NBfwfPhouKNIof9O5eYb5dRKMzaarCg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:10:26.868717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.02185","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7053e3ef2056560cfbcecf7c846c02c8ea52bb10d2a24a62a910581a7979393d","sha256:cdb57b3635bdc06e3375b6dbd16977c8a02817b77f1264a13ce447c9a3436791"],"state_sha256":"08015c0818589abea51b58c7b365b29c22b4f58747d70b557da049fb87c0417c"}