{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3DBEDJBMQFZS2VMCPA6AVTZI4K","short_pith_number":"pith:3DBEDJBM","canonical_record":{"source":{"id":"1904.00380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-03-31T11:07:46Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"2748b2c9d08f9b76e3b27003c1d2929404bdafdc63adfdfaea3ff0c65ced633e","abstract_canon_sha256":"6a5e649d119d83bce8d7ba5d74999a0b63f6cebe768e0371c1e2146ab465759b"},"schema_version":"1.0"},"canonical_sha256":"d8c241a42c81732d5582783c0acf28e29b9167a097201dd6d13ecf6be34145b5","source":{"kind":"arxiv","id":"1904.00380","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00380","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00380v1","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00380","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"3DBEDJBMQFZS","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3DBEDJBMQFZS2VMC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3DBEDJBM","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3DBEDJBMQFZS2VMCPA6AVTZI4K","target":"record","payload":{"canonical_record":{"source":{"id":"1904.00380","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-03-31T11:07:46Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"2748b2c9d08f9b76e3b27003c1d2929404bdafdc63adfdfaea3ff0c65ced633e","abstract_canon_sha256":"6a5e649d119d83bce8d7ba5d74999a0b63f6cebe768e0371c1e2146ab465759b"},"schema_version":"1.0"},"canonical_sha256":"d8c241a42c81732d5582783c0acf28e29b9167a097201dd6d13ecf6be34145b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:48.533861Z","signature_b64":"qlAWtfC6QSez9sJDuiSjsBNyywvqTFEirlbUc2YwLp4TIH7wCnFISH/wlGPYRt3jJk+4x2xNufdkMOJaeaq5DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8c241a42c81732d5582783c0acf28e29b9167a097201dd6d13ecf6be34145b5","last_reissued_at":"2026-05-17T23:49:48.533204Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:48.533204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.00380","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h3hpiMjOXTB2xG0RRW91AONJdC1ICD4Y2FV+9Ay70qiuDTLy2C6/SCBVCWqamFq9bNEMLR3aHOffy8r8QI0gAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:25:59.836394Z"},"content_sha256":"f118515a32f5ef2f715fdde6d4ab3cd554e5b3a10ad2687e598d08b3dd90cb9a","schema_version":"1.0","event_id":"sha256:f118515a32f5ef2f715fdde6d4ab3cd554e5b3a10ad2687e598d08b3dd90cb9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3DBEDJBMQFZS2VMCPA6AVTZI4K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twisted Coefficients on coarse Spaces and their Corona","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.MG","authors_text":"Elisa Hartmann","submitted_at":"2019-03-31T11:07:46Z","abstract_excerpt":"To a metric space $X$ we associate a compact topological space $\\nu' X$ called the corona of $X$. Then a coarse map $f:X\\to Y$ between metric spaces is mapped to a continuous map $\\nu' f:\\nu' X\\to \\nu' Y$ between coronas. Sheaf cohomology on coarse spaces has been introduced in arXiv:1710.06725. We show the functor $\\nu'$ preserves and reflects sheaf cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00380","kind":"arxiv","version":1},"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":"2026-05-17T23:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yw9AkiEXEc1/eF1GWNrFUMnUIGrhWkSOsgYy3UK66e98qY66deRiSJODNmNciFNdu7Jkv9+j4G0Od6jkD9/DBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:25:59.836859Z"},"content_sha256":"0b93a3249ab8c62f752200d0e1cab73ec1cae91faff60d8dafe881f37979558d","schema_version":"1.0","event_id":"sha256:0b93a3249ab8c62f752200d0e1cab73ec1cae91faff60d8dafe881f37979558d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DBEDJBMQFZS2VMCPA6AVTZI4K/bundle.json","state_url":"https://pith.science/pith/3DBEDJBMQFZS2VMCPA6AVTZI4K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DBEDJBMQFZS2VMCPA6AVTZI4K/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":"2026-05-25T13:25:59Z","links":{"resolver":"https://pith.science/pith/3DBEDJBMQFZS2VMCPA6AVTZI4K","bundle":"https://pith.science/pith/3DBEDJBMQFZS2VMCPA6AVTZI4K/bundle.json","state":"https://pith.science/pith/3DBEDJBMQFZS2VMCPA6AVTZI4K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DBEDJBMQFZS2VMCPA6AVTZI4K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3DBEDJBMQFZS2VMCPA6AVTZI4K","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":"6a5e649d119d83bce8d7ba5d74999a0b63f6cebe768e0371c1e2146ab465759b","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-03-31T11:07:46Z","title_canon_sha256":"2748b2c9d08f9b76e3b27003c1d2929404bdafdc63adfdfaea3ff0c65ced633e"},"schema_version":"1.0","source":{"id":"1904.00380","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00380","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00380v1","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00380","created_at":"2026-05-17T23:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"3DBEDJBMQFZS","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3DBEDJBMQFZS2VMC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3DBEDJBM","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:0b93a3249ab8c62f752200d0e1cab73ec1cae91faff60d8dafe881f37979558d","target":"graph","created_at":"2026-05-17T23:49:48Z","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":"To a metric space $X$ we associate a compact topological space $\\nu' X$ called the corona of $X$. Then a coarse map $f:X\\to Y$ between metric spaces is mapped to a continuous map $\\nu' f:\\nu' X\\to \\nu' Y$ between coronas. Sheaf cohomology on coarse spaces has been introduced in arXiv:1710.06725. We show the functor $\\nu'$ preserves and reflects sheaf cohomology.","authors_text":"Elisa Hartmann","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-03-31T11:07:46Z","title":"Twisted Coefficients on coarse Spaces and their Corona"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00380","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:f118515a32f5ef2f715fdde6d4ab3cd554e5b3a10ad2687e598d08b3dd90cb9a","target":"record","created_at":"2026-05-17T23:49:48Z","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":"6a5e649d119d83bce8d7ba5d74999a0b63f6cebe768e0371c1e2146ab465759b","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2019-03-31T11:07:46Z","title_canon_sha256":"2748b2c9d08f9b76e3b27003c1d2929404bdafdc63adfdfaea3ff0c65ced633e"},"schema_version":"1.0","source":{"id":"1904.00380","kind":"arxiv","version":1}},"canonical_sha256":"d8c241a42c81732d5582783c0acf28e29b9167a097201dd6d13ecf6be34145b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8c241a42c81732d5582783c0acf28e29b9167a097201dd6d13ecf6be34145b5","first_computed_at":"2026-05-17T23:49:48.533204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:48.533204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qlAWtfC6QSez9sJDuiSjsBNyywvqTFEirlbUc2YwLp4TIH7wCnFISH/wlGPYRt3jJk+4x2xNufdkMOJaeaq5DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:48.533861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.00380","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f118515a32f5ef2f715fdde6d4ab3cd554e5b3a10ad2687e598d08b3dd90cb9a","sha256:0b93a3249ab8c62f752200d0e1cab73ec1cae91faff60d8dafe881f37979558d"],"state_sha256":"dabd44cb76b6c267396e1cf8cc998e2ae37ba937634c6af9c03effad68168a4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+A0hzAsmCcrPnc3q+n4CjNcItja43fMlYTmasG+nOrWgeY00a8KmktXZwnUCN7HA67gGlCk83XwceAwnMNG5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T13:25:59.839672Z","bundle_sha256":"e906298206060ddf5955090a68ecf793a494345b575362e9d81034082186111b"}}