{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OIIWBPRDSSOA7G3DEOBGTNEYTT","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":"2787a439534661384026748037b8980926fee4a1d04cadd36283b42d53a44efd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-16T07:04:04Z","title_canon_sha256":"b25d36764d058858c8c3a1f4bc20e745a9dd2972491fa063600304cb5a2ccadb"},"schema_version":"1.0","source":{"id":"2606.17597","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17597","created_at":"2026-06-19T16:10:16Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17597v1","created_at":"2026-06-19T16:10:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17597","created_at":"2026-06-19T16:10:16Z"},{"alias_kind":"pith_short_12","alias_value":"OIIWBPRDSSOA","created_at":"2026-06-19T16:10:16Z"},{"alias_kind":"pith_short_16","alias_value":"OIIWBPRDSSOA7G3D","created_at":"2026-06-19T16:10:16Z"},{"alias_kind":"pith_short_8","alias_value":"OIIWBPRD","created_at":"2026-06-19T16:10:16Z"}],"graph_snapshots":[{"event_id":"sha256:753901746793c5e7e15e1cc458dfae7e86c852c2fc1ca439a48d29db5aa2d8ff","target":"graph","created_at":"2026-06-19T16:10:16Z","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/2606.17597/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For a manifold $\\overline{M}$ with boundary $\\partial M$ and interior $M$, we introduce and study a weakening of the concept of projective compactness for torsion-free linear connections on $M$, which we call projective pre-compactness. Via the Levi-Civita connection, this concept applies to pseudo-Riemannian metrics on $M$. This is motivated by scattering theory and general relativity (GR), via asymptotic forms of metrics used in these areas.\n  In the general setting of a projectively pre-compact connection $\\nabla$ we show that, assuming weak asymptotic conditions on the Ricci curvature, the","authors_text":"Andreas Cap, A. Rod Gover","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-16T07:04:04Z","title":"Projective Infinities and b-Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17597","kind":"arxiv","version":1},"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":"sha256:6ff572baf566f8bc512543f2c42b059ec1e66864534c5b7afd92b8934c7b6db4","target":"record","created_at":"2026-06-19T16:10:16Z","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":"2787a439534661384026748037b8980926fee4a1d04cadd36283b42d53a44efd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-06-16T07:04:04Z","title_canon_sha256":"b25d36764d058858c8c3a1f4bc20e745a9dd2972491fa063600304cb5a2ccadb"},"schema_version":"1.0","source":{"id":"2606.17597","kind":"arxiv","version":1}},"canonical_sha256":"721160be23949c0f9b63238269b4989cdb18913c7832adf97e229f37075126a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"721160be23949c0f9b63238269b4989cdb18913c7832adf97e229f37075126a3","first_computed_at":"2026-06-19T16:10:16.911333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:16.911333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RKyTk4c6c1U5Np+KM3k8WaRtRT+P18nbkqOnwd+brk38kiX0gfehicngZu2dzNtXAEal+khz5LGr3ns1SgMjBQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:16.911709Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17597","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ff572baf566f8bc512543f2c42b059ec1e66864534c5b7afd92b8934c7b6db4","sha256:753901746793c5e7e15e1cc458dfae7e86c852c2fc1ca439a48d29db5aa2d8ff"],"state_sha256":"38e547aa10ab0694e8ed3db1c868e1673243495f60d49da207a57b49fe1ae3d3"}