{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SICFVM2TXVUQ2SDNM7DRQF5QLJ","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":"e99f32d9b549fafe6330409b4f0f22ec79d0259afb2199f14006497f069ba92a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-27T23:46:17Z","title_canon_sha256":"ff7acb7418053b47989c98d4af446cfa2c7b1da82f32fd55e3f1f50a80eea7e8"},"schema_version":"1.0","source":{"id":"1806.11104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.11104","created_at":"2026-05-18T00:12:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.11104v1","created_at":"2026-05-18T00:12:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.11104","created_at":"2026-05-18T00:12:03Z"},{"alias_kind":"pith_short_12","alias_value":"SICFVM2TXVUQ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SICFVM2TXVUQ2SDN","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SICFVM2T","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:ea884848437ad20d700d4f73b52ffa5b6ee5b056e98b946ad365816ee28c7a48","target":"graph","created_at":"2026-05-18T00:12:03Z","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":"Any traversally generic vector flow on a compact manifold $X$ with boundary leaves some residual structure on its boundary $\\d X$. A part of this structure is the flow-generated causality map $C_v$, which takes a region of $\\d X$ to the complementary region. By the Holography Theorem from \\cite{K4}, the map $C_v$ allows to reconstruct $X$ together with the unparametrized flow. The reconstruction is a manifestation of holographic description of the flow.\n  In the paper, we introduce and study the holographic structures on a given closed manifold $Y$, which mimics $\\d X$. We generalize the Holog","authors_text":"Gabriel Katz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-27T23:46:17Z","title":"On Holographic Structures, Traversing Flows, and Exotic Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11104","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:f3a86b38a4e5af45df01b00f4fe1b46934782aae25e4105efc92779aa4dc558c","target":"record","created_at":"2026-05-18T00:12:03Z","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":"e99f32d9b549fafe6330409b4f0f22ec79d0259afb2199f14006497f069ba92a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-06-27T23:46:17Z","title_canon_sha256":"ff7acb7418053b47989c98d4af446cfa2c7b1da82f32fd55e3f1f50a80eea7e8"},"schema_version":"1.0","source":{"id":"1806.11104","kind":"arxiv","version":1}},"canonical_sha256":"92045ab353bd690d486d67c71817b05a6c1ce4fbd1c3956a3dd3a861f435fb5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92045ab353bd690d486d67c71817b05a6c1ce4fbd1c3956a3dd3a861f435fb5c","first_computed_at":"2026-05-18T00:12:03.545635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:03.545635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1KfE+kI4Um0Ah1AmTRpQC4A5BMIiQiYsUfnSrXP+8Nl4HH08Z2jhZMb+8s7rjx/Tzwd9925H16buqLtYZdOjCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:03.546265Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.11104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3a86b38a4e5af45df01b00f4fe1b46934782aae25e4105efc92779aa4dc558c","sha256:ea884848437ad20d700d4f73b52ffa5b6ee5b056e98b946ad365816ee28c7a48"],"state_sha256":"5d4fea852c3844f9f1696b92a25c728d55cf5512a6c8ac31b92f11d91b86b910"}