{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:F74XNB74WXYBZNEYUR4ONZNYOQ","short_pith_number":"pith:F74XNB74","canonical_record":{"source":{"id":"1502.05001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-02-17T18:58:23Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"38ced51bf7cd384d580e2cb6ca41889eba39ac758d4dee48a4269fd5621c26c4","abstract_canon_sha256":"0dc45abe46e9822cf669afdac681aec1b3a54a6ae80dc29a91d953d83513ad9d"},"schema_version":"1.0"},"canonical_sha256":"2ff97687fcb5f01cb498a478e6e5b8740390e0a0e719f4b255d31b82a6e3c1ee","source":{"kind":"arxiv","id":"1502.05001","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05001","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05001v2","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05001","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"F74XNB74WXYB","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F74XNB74WXYBZNEY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F74XNB74","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:F74XNB74WXYBZNEYUR4ONZNYOQ","target":"record","payload":{"canonical_record":{"source":{"id":"1502.05001","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-02-17T18:58:23Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"38ced51bf7cd384d580e2cb6ca41889eba39ac758d4dee48a4269fd5621c26c4","abstract_canon_sha256":"0dc45abe46e9822cf669afdac681aec1b3a54a6ae80dc29a91d953d83513ad9d"},"schema_version":"1.0"},"canonical_sha256":"2ff97687fcb5f01cb498a478e6e5b8740390e0a0e719f4b255d31b82a6e3c1ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:47.407544Z","signature_b64":"w0/5TwjpjdwOK/VB+Yoo3gmlsFa437QqeJBO2ShZ5UTZASqM3kIzwqw6UwZIuOzY8/AWZDG5DU4fkIT7d3HEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ff97687fcb5f01cb498a478e6e5b8740390e0a0e719f4b255d31b82a6e3c1ee","last_reissued_at":"2026-05-18T00:27:47.407124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:47.407124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.05001","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":"2026-05-18T00:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mY+teW4nQhYlx+9J1uE0DhU83a444Z4TbouUJ87H2E1nwknY7nhV4oQ+PwM0Y5rHmEF4nk3LxQSmKbO6X9OtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:44:33.223745Z"},"content_sha256":"320e8e628765a17c1101deb84e64134223a06f7a7a49e0c8017fefb64977a31d","schema_version":"1.0","event_id":"sha256:320e8e628765a17c1101deb84e64134223a06f7a7a49e0c8017fefb64977a31d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:F74XNB74WXYBZNEYUR4ONZNYOQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long and thin covers for flow spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Daniel Kasprowski, Henrik Rueping","submitted_at":"2015-02-17T18:58:23Z","abstract_excerpt":"Long and thin covers of flow spaces are important ingredients in the proof of the Farrell--Jones conjecture for certain classes of groups, like hyperbolic and CAT(0)-groups. In this paper we provide an alternative construction of such covers which holds in a more general setting and simplifies some of the arguments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05001","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":"2026-05-18T00:27:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1L11vjnhRx6A8+Rn5CfXDPyGLXup9v5UbhTlat6QtduevzllfjZcYmSKAFzW2BbWmFRPrGP61JWBfYz84T3/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:44:33.224082Z"},"content_sha256":"46d8208c623c859d5ff9a41644f239441d386e4477877cd60eb02943ed8ec562","schema_version":"1.0","event_id":"sha256:46d8208c623c859d5ff9a41644f239441d386e4477877cd60eb02943ed8ec562"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F74XNB74WXYBZNEYUR4ONZNYOQ/bundle.json","state_url":"https://pith.science/pith/F74XNB74WXYBZNEYUR4ONZNYOQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F74XNB74WXYBZNEYUR4ONZNYOQ/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":"2026-05-28T08:44:33Z","links":{"resolver":"https://pith.science/pith/F74XNB74WXYBZNEYUR4ONZNYOQ","bundle":"https://pith.science/pith/F74XNB74WXYBZNEYUR4ONZNYOQ/bundle.json","state":"https://pith.science/pith/F74XNB74WXYBZNEYUR4ONZNYOQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F74XNB74WXYBZNEYUR4ONZNYOQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:F74XNB74WXYBZNEYUR4ONZNYOQ","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":"0dc45abe46e9822cf669afdac681aec1b3a54a6ae80dc29a91d953d83513ad9d","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-02-17T18:58:23Z","title_canon_sha256":"38ced51bf7cd384d580e2cb6ca41889eba39ac758d4dee48a4269fd5621c26c4"},"schema_version":"1.0","source":{"id":"1502.05001","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05001","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05001v2","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05001","created_at":"2026-05-18T00:27:47Z"},{"alias_kind":"pith_short_12","alias_value":"F74XNB74WXYB","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"F74XNB74WXYBZNEY","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"F74XNB74","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:46d8208c623c859d5ff9a41644f239441d386e4477877cd60eb02943ed8ec562","target":"graph","created_at":"2026-05-18T00:27:47Z","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":"Long and thin covers of flow spaces are important ingredients in the proof of the Farrell--Jones conjecture for certain classes of groups, like hyperbolic and CAT(0)-groups. In this paper we provide an alternative construction of such covers which holds in a more general setting and simplifies some of the arguments.","authors_text":"Daniel Kasprowski, Henrik Rueping","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-02-17T18:58:23Z","title":"Long and thin covers for flow spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05001","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":"sha256:320e8e628765a17c1101deb84e64134223a06f7a7a49e0c8017fefb64977a31d","target":"record","created_at":"2026-05-18T00:27:47Z","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":"0dc45abe46e9822cf669afdac681aec1b3a54a6ae80dc29a91d953d83513ad9d","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-02-17T18:58:23Z","title_canon_sha256":"38ced51bf7cd384d580e2cb6ca41889eba39ac758d4dee48a4269fd5621c26c4"},"schema_version":"1.0","source":{"id":"1502.05001","kind":"arxiv","version":2}},"canonical_sha256":"2ff97687fcb5f01cb498a478e6e5b8740390e0a0e719f4b255d31b82a6e3c1ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ff97687fcb5f01cb498a478e6e5b8740390e0a0e719f4b255d31b82a6e3c1ee","first_computed_at":"2026-05-18T00:27:47.407124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:47.407124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w0/5TwjpjdwOK/VB+Yoo3gmlsFa437QqeJBO2ShZ5UTZASqM3kIzwqw6UwZIuOzY8/AWZDG5DU4fkIT7d3HEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:47.407544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05001","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:320e8e628765a17c1101deb84e64134223a06f7a7a49e0c8017fefb64977a31d","sha256:46d8208c623c859d5ff9a41644f239441d386e4477877cd60eb02943ed8ec562"],"state_sha256":"21fc39086479646d96f73ff8922fa1b3d223917b882a894effdb2aa67547abc9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A7kW3YPczgVkngnXFrD3GYmkjIvHaSkm9eazQRbpUn0sZZNITIdUaFmEsxNDpQASwETMGZLkbN9RdAEjBve2Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:44:33.226107Z","bundle_sha256":"bc3e61aa223e934aa673823156f8f4f7479e5f6b67a40d2470fd5e256308b219"}}