{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OMF4KEA3UI7BS7O7VAA5POCI5F","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":"5c25d40c5f67ef9b7983b072d86f9c37325133b9c978990824a2b71c1a280b0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-04T05:40:12Z","title_canon_sha256":"4d73eccf4894273c987c2d3b9ebd9e6b36134329bdecbfc047283e97fa17cb9c"},"schema_version":"1.0","source":{"id":"1902.01039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01039","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01039v2","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01039","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"OMF4KEA3UI7B","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OMF4KEA3UI7BS7O7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OMF4KEA3","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:a404c87cba37e89704e56f033666ed573040d2c07730ddc76ef8314160791a9f","target":"graph","created_at":"2026-05-17T23:40:17Z","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":"In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy equivalent to that of a single path; we call this the trivial space of directed paths. Directed spaces that are topologically trivial may have non-trivial spaces of directed paths, which means that information is lost when the direction of these topological spaces is ignored. We define a notion of directed collapsibility in the setting of a directed Euclidean cubic","authors_text":"Brittany Terese Fasy, Catherine Ray, Elizabeth Vidaurre, Lisbeth Fajstrup, Nicole Sanderson, Robin Belton, Robyn Brooks, Stefania Ebli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-04T05:40:12Z","title":"Towards Directed Collapsibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01039","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":"sha256:2e62926ac03f28ee41ee85b1150c2759944ac898e4fad93c5e5c7b59d1e547bb","target":"record","created_at":"2026-05-17T23:40:17Z","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":"5c25d40c5f67ef9b7983b072d86f9c37325133b9c978990824a2b71c1a280b0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-02-04T05:40:12Z","title_canon_sha256":"4d73eccf4894273c987c2d3b9ebd9e6b36134329bdecbfc047283e97fa17cb9c"},"schema_version":"1.0","source":{"id":"1902.01039","kind":"arxiv","version":2}},"canonical_sha256":"730bc5101ba23e197ddfa801d7b848e95d45bc52a605ffeddd9e96ed338b5081","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"730bc5101ba23e197ddfa801d7b848e95d45bc52a605ffeddd9e96ed338b5081","first_computed_at":"2026-05-17T23:40:17.517774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:17.517774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v7lc7M2CWQ5HQ83Ar2yF3eGjnEqsfo+1Qq5uzf3f2PZQ5C/KtexgZ+JpaWBtRuC35pyu45CTmqVcDUN/fBCeDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:17.518462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e62926ac03f28ee41ee85b1150c2759944ac898e4fad93c5e5c7b59d1e547bb","sha256:a404c87cba37e89704e56f033666ed573040d2c07730ddc76ef8314160791a9f"],"state_sha256":"4421cfbb9b6ddbbfcb94152002fbc22aeb3eef0c3deca95024684e0e1eff1aa8"}