{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZFQ7AYUBJZIYCNYSRSWV6S2B4T","short_pith_number":"pith:ZFQ7AYUB","canonical_record":{"source":{"id":"1910.14116","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-10-30T20:16:17Z","cross_cats_sorted":["math.GT","math.SG"],"title_canon_sha256":"23dcd1148fe9859a314a60b05e49e0e85ced1a848fe02a39441df8f7e1d95240","abstract_canon_sha256":"3842556f4a386792d031c4e2c75a5224c2d0b96e4db1e891f80807d9c1dd9364"},"schema_version":"1.0"},"canonical_sha256":"c961f062814e518137128cad5f4b41e4d756c53188d27545e3dcfc85df799065","source":{"kind":"arxiv","id":"1910.14116","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.14116","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1910.14116v3","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.14116","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZFQ7AYUBJZIY","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"ZFQ7AYUBJZIYCNYS","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"ZFQ7AYUB","created_at":"2026-07-05T04:22:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZFQ7AYUBJZIYCNYSRSWV6S2B4T","target":"record","payload":{"canonical_record":{"source":{"id":"1910.14116","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-10-30T20:16:17Z","cross_cats_sorted":["math.GT","math.SG"],"title_canon_sha256":"23dcd1148fe9859a314a60b05e49e0e85ced1a848fe02a39441df8f7e1d95240","abstract_canon_sha256":"3842556f4a386792d031c4e2c75a5224c2d0b96e4db1e891f80807d9c1dd9364"},"schema_version":"1.0"},"canonical_sha256":"c961f062814e518137128cad5f4b41e4d756c53188d27545e3dcfc85df799065","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:22:13.941707Z","signature_b64":"6IBrqVr6H4W2ns2TvctFknNJ6VyWIM2Of2B59/RcjxnTedn9D5TAtgTc7rVQa0dTRb8U6VmeDdudn1MvqN02AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c961f062814e518137128cad5f4b41e4d756c53188d27545e3dcfc85df799065","last_reissued_at":"2026-07-05T04:22:13.941289Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:22:13.941289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1910.14116","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":"2026-07-05T04:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w9n2qbXpPCPcUXc0dUSgbTbofNhtPjX7tFTsI8f0nDDPNZFdSfZNcwZKQnpEIn2ltmYnrM3i+ufDdswCsT8kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T22:31:21.798514Z"},"content_sha256":"5dfedaa76cd4c6bc57247bf36a53fa706f632591077aab315704952bf38f0596","schema_version":"1.0","event_id":"sha256:5dfedaa76cd4c6bc57247bf36a53fa706f632591077aab315704952bf38f0596"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZFQ7AYUBJZIYCNYSRSWV6S2B4T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the boundaries of highly connected, almost closed manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.SG"],"primary_cat":"math.AT","authors_text":"Andrew Senger, Jeremy Hahn, Robert Burklund","submitted_at":"2019-10-30T20:16:17Z","abstract_excerpt":"Building on work of Stolz, we prove for integers $0 \\le d \\le 3$ and $k>232$ that the boundaries of $(k-1)$-connected, almost closed $(2k+d)$-manifolds also bound parallelizable manifolds. Away from finitely many dimensions, this settles longstanding questions of C.T.C. Wall, determines all Stein fillable homotopy spheres, and proves a conjecture of Galatius and Randal-Williams. Implications are drawn for both the classification of highly connected manifolds and, via work of Kreck and Krannich, the calculation of their mapping class groups.\n  Our technique is to recast the Galatius and Randal-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.14116","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1910.14116/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":"2026-07-05T04:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dqwmg6RX9kvDWAufixUXBF3wMrlhO+L0VykYt/is51L4W+kG+3hWw0Q34wobVD0JZjEp5yYF5gHJS5QjIjPQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T22:31:21.799368Z"},"content_sha256":"17cce12efc9e55e0ef92405b931e611cd1d43f4b4fa5f9940c291deb7eb0f5e8","schema_version":"1.0","event_id":"sha256:17cce12efc9e55e0ef92405b931e611cd1d43f4b4fa5f9940c291deb7eb0f5e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFQ7AYUBJZIYCNYSRSWV6S2B4T/bundle.json","state_url":"https://pith.science/pith/ZFQ7AYUBJZIYCNYSRSWV6S2B4T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFQ7AYUBJZIYCNYSRSWV6S2B4T/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":"2026-08-17T22:31:21Z","links":{"resolver":"https://pith.science/pith/ZFQ7AYUBJZIYCNYSRSWV6S2B4T","bundle":"https://pith.science/pith/ZFQ7AYUBJZIYCNYSRSWV6S2B4T/bundle.json","state":"https://pith.science/pith/ZFQ7AYUBJZIYCNYSRSWV6S2B4T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFQ7AYUBJZIYCNYSRSWV6S2B4T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZFQ7AYUBJZIYCNYSRSWV6S2B4T","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":"3842556f4a386792d031c4e2c75a5224c2d0b96e4db1e891f80807d9c1dd9364","cross_cats_sorted":["math.GT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-10-30T20:16:17Z","title_canon_sha256":"23dcd1148fe9859a314a60b05e49e0e85ced1a848fe02a39441df8f7e1d95240"},"schema_version":"1.0","source":{"id":"1910.14116","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.14116","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1910.14116v3","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.14116","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"ZFQ7AYUBJZIY","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"ZFQ7AYUBJZIYCNYS","created_at":"2026-07-05T04:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"ZFQ7AYUB","created_at":"2026-07-05T04:22:13Z"}],"graph_snapshots":[{"event_id":"sha256:17cce12efc9e55e0ef92405b931e611cd1d43f4b4fa5f9940c291deb7eb0f5e8","target":"graph","created_at":"2026-07-05T04:22:13Z","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/1910.14116/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building on work of Stolz, we prove for integers $0 \\le d \\le 3$ and $k>232$ that the boundaries of $(k-1)$-connected, almost closed $(2k+d)$-manifolds also bound parallelizable manifolds. Away from finitely many dimensions, this settles longstanding questions of C.T.C. Wall, determines all Stein fillable homotopy spheres, and proves a conjecture of Galatius and Randal-Williams. Implications are drawn for both the classification of highly connected manifolds and, via work of Kreck and Krannich, the calculation of their mapping class groups.\n  Our technique is to recast the Galatius and Randal-","authors_text":"Andrew Senger, Jeremy Hahn, Robert Burklund","cross_cats":["math.GT","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-10-30T20:16:17Z","title":"On the boundaries of highly connected, almost closed manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.14116","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":"sha256:5dfedaa76cd4c6bc57247bf36a53fa706f632591077aab315704952bf38f0596","target":"record","created_at":"2026-07-05T04:22:13Z","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":"3842556f4a386792d031c4e2c75a5224c2d0b96e4db1e891f80807d9c1dd9364","cross_cats_sorted":["math.GT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-10-30T20:16:17Z","title_canon_sha256":"23dcd1148fe9859a314a60b05e49e0e85ced1a848fe02a39441df8f7e1d95240"},"schema_version":"1.0","source":{"id":"1910.14116","kind":"arxiv","version":3}},"canonical_sha256":"c961f062814e518137128cad5f4b41e4d756c53188d27545e3dcfc85df799065","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c961f062814e518137128cad5f4b41e4d756c53188d27545e3dcfc85df799065","first_computed_at":"2026-07-05T04:22:13.941289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:22:13.941289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6IBrqVr6H4W2ns2TvctFknNJ6VyWIM2Of2B59/RcjxnTedn9D5TAtgTc7rVQa0dTRb8U6VmeDdudn1MvqN02AA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:22:13.941707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.14116","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dfedaa76cd4c6bc57247bf36a53fa706f632591077aab315704952bf38f0596","sha256:17cce12efc9e55e0ef92405b931e611cd1d43f4b4fa5f9940c291deb7eb0f5e8"],"state_sha256":"b74009c879d343e2f50beef6862c5ce279e9f8cea7bc75fce266bd9d4bcd014f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9UVQ3r1LAepAGKWYQh9elSBwzHUkgG60c3finHzuwFH3eSDERxVXpHCE+hBLEdHM5QGYKmfKia8YYpmrlIhOCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T22:31:21.804782Z","bundle_sha256":"3b045096cde6326ecc435b0ab5a6c000cd5611efc775887ec0aaba16779b8cc4"}}