{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7AZ4DUW7PROAXT55HOCSISZ4KV","short_pith_number":"pith:7AZ4DUW7","canonical_record":{"source":{"id":"1603.00452","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-03-01T20:44:34Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"8cd4ebee45fa78c23816d496fa78b2d07b47b1afc8661e6ab3a24d7c86a25395","abstract_canon_sha256":"7ca1dcac4673d25fbb00cc6ad91917c0691401a36dd739ad6bd9a8ec9ad40dbe"},"schema_version":"1.0"},"canonical_sha256":"f833c1d2df7c5c0bcfbd3b85244b3c5575a34163b31eca8f8f9fad02bf6dc579","source":{"kind":"arxiv","id":"1603.00452","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00452","created_at":"2026-05-18T01:18:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00452v2","created_at":"2026-05-18T01:18:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00452","created_at":"2026-05-18T01:18:37Z"},{"alias_kind":"pith_short_12","alias_value":"7AZ4DUW7PROA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7AZ4DUW7PROAXT55","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7AZ4DUW7","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7AZ4DUW7PROAXT55HOCSISZ4KV","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00452","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-03-01T20:44:34Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"8cd4ebee45fa78c23816d496fa78b2d07b47b1afc8661e6ab3a24d7c86a25395","abstract_canon_sha256":"7ca1dcac4673d25fbb00cc6ad91917c0691401a36dd739ad6bd9a8ec9ad40dbe"},"schema_version":"1.0"},"canonical_sha256":"f833c1d2df7c5c0bcfbd3b85244b3c5575a34163b31eca8f8f9fad02bf6dc579","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:37.029159Z","signature_b64":"Xv7sUnnOVTVgXx3wOygWpfRT1OVMzRsTexbwupz2Tzp6KcD7IOfoWh9hZ/2gvtS3PIZmbs4LdYqBDZ3z4CGHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f833c1d2df7c5c0bcfbd3b85244b3c5575a34163b31eca8f8f9fad02bf6dc579","last_reissued_at":"2026-05-18T01:18:37.028689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:37.028689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00452","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fl6J6yzgSdHYy/Noz9B2Op4Sl/B9FdxfqwywVajjmC4BXkqSzNzsgHwqH1PQw907aKk0otPrus03AUP48wNwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:26:35.706955Z"},"content_sha256":"491465ac1d83dbc0a3c6a396d3f062abc2d9df9d967c20620fce4f6f9b7dd6b0","schema_version":"1.0","event_id":"sha256:491465ac1d83dbc0a3c6a396d3f062abc2d9df9d967c20620fce4f6f9b7dd6b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7AZ4DUW7PROAXT55HOCSISZ4KV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On homology of complements of compact sets in Hilbert Cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GN","authors_text":"Alexander Dranishnikov, Ashwini Amarasinghe","submitted_at":"2016-03-01T20:44:34Z","abstract_excerpt":"We introduce the notion of spaces with weak relative cohomology and show the acyclicity of the complement $Q\\setminus X$ in the Hilbert cube $Q$ of a compactum $X$ with weak relative cohomology. As a corollary we obtain the acyclicity of the complement results when\n  (a) $X$ is weakly infinite dimensional;\n  (b) $X$ has finite cohomological dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00452","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:18:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LE9a4pdJ3mjblVl4Xh9yQdY6PRQMICSEkC1kgcDVH4XqxnNHXk+cMmd4dR2pyL9OSC2fay4J4gsagZ3+10vfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:26:35.707616Z"},"content_sha256":"ec21702490334ea69e08196957dab872b787c2db618601c6b07a6c20f596751f","schema_version":"1.0","event_id":"sha256:ec21702490334ea69e08196957dab872b787c2db618601c6b07a6c20f596751f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AZ4DUW7PROAXT55HOCSISZ4KV/bundle.json","state_url":"https://pith.science/pith/7AZ4DUW7PROAXT55HOCSISZ4KV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AZ4DUW7PROAXT55HOCSISZ4KV/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":"2026-06-06T16:26:35Z","links":{"resolver":"https://pith.science/pith/7AZ4DUW7PROAXT55HOCSISZ4KV","bundle":"https://pith.science/pith/7AZ4DUW7PROAXT55HOCSISZ4KV/bundle.json","state":"https://pith.science/pith/7AZ4DUW7PROAXT55HOCSISZ4KV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AZ4DUW7PROAXT55HOCSISZ4KV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7AZ4DUW7PROAXT55HOCSISZ4KV","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":"7ca1dcac4673d25fbb00cc6ad91917c0691401a36dd739ad6bd9a8ec9ad40dbe","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-03-01T20:44:34Z","title_canon_sha256":"8cd4ebee45fa78c23816d496fa78b2d07b47b1afc8661e6ab3a24d7c86a25395"},"schema_version":"1.0","source":{"id":"1603.00452","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00452","created_at":"2026-05-18T01:18:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00452v2","created_at":"2026-05-18T01:18:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00452","created_at":"2026-05-18T01:18:37Z"},{"alias_kind":"pith_short_12","alias_value":"7AZ4DUW7PROA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7AZ4DUW7PROAXT55","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7AZ4DUW7","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:ec21702490334ea69e08196957dab872b787c2db618601c6b07a6c20f596751f","target":"graph","created_at":"2026-05-18T01:18:37Z","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":"We introduce the notion of spaces with weak relative cohomology and show the acyclicity of the complement $Q\\setminus X$ in the Hilbert cube $Q$ of a compactum $X$ with weak relative cohomology. As a corollary we obtain the acyclicity of the complement results when\n  (a) $X$ is weakly infinite dimensional;\n  (b) $X$ has finite cohomological dimension.","authors_text":"Alexander Dranishnikov, Ashwini Amarasinghe","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-03-01T20:44:34Z","title":"On homology of complements of compact sets in Hilbert Cube"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00452","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":"sha256:491465ac1d83dbc0a3c6a396d3f062abc2d9df9d967c20620fce4f6f9b7dd6b0","target":"record","created_at":"2026-05-18T01:18:37Z","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":"7ca1dcac4673d25fbb00cc6ad91917c0691401a36dd739ad6bd9a8ec9ad40dbe","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-03-01T20:44:34Z","title_canon_sha256":"8cd4ebee45fa78c23816d496fa78b2d07b47b1afc8661e6ab3a24d7c86a25395"},"schema_version":"1.0","source":{"id":"1603.00452","kind":"arxiv","version":2}},"canonical_sha256":"f833c1d2df7c5c0bcfbd3b85244b3c5575a34163b31eca8f8f9fad02bf6dc579","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f833c1d2df7c5c0bcfbd3b85244b3c5575a34163b31eca8f8f9fad02bf6dc579","first_computed_at":"2026-05-18T01:18:37.028689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:37.028689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xv7sUnnOVTVgXx3wOygWpfRT1OVMzRsTexbwupz2Tzp6KcD7IOfoWh9hZ/2gvtS3PIZmbs4LdYqBDZ3z4CGHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:37.029159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00452","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:491465ac1d83dbc0a3c6a396d3f062abc2d9df9d967c20620fce4f6f9b7dd6b0","sha256:ec21702490334ea69e08196957dab872b787c2db618601c6b07a6c20f596751f"],"state_sha256":"83d9bfeb696740538c59707b077030277bd02dd2802bc0aa31591a4fbb4ed904"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qp7s1mwczfylpholhTD6/q8fCWiF+ZMOyoxaXwP6sQ5WrvHQ1STfIOMrlxeA9/W2oUt52mjHcwLvpowtRl2XCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:26:35.711233Z","bundle_sha256":"bcf5c8498d3f8235a8390be1f8a801ca726755332bb604a2990e44d52a59a3d0"}}