{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2G2RZNL5Z7BH2GWLSHON365FBV","short_pith_number":"pith:2G2RZNL5","canonical_record":{"source":{"id":"1008.3959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-08-24T03:58:25Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"f2151732a3f883bfd8e19a4290ab3de3cdf2341f06c048eac56c3fb0ac0a2377","abstract_canon_sha256":"c30ae705a28ec06ad552ebc0f54f7d040c4a64a0882cc1682419ece090cc6c56"},"schema_version":"1.0"},"canonical_sha256":"d1b51cb57dcfc27d1acb91dcddfba50d53cd88dec1f79cc5a1badf09ed2fc894","source":{"kind":"arxiv","id":"1008.3959","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3959","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3959v1","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3959","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"2G2RZNL5Z7BH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2G2RZNL5Z7BH2GWL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2G2RZNL5","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2G2RZNL5Z7BH2GWLSHON365FBV","target":"record","payload":{"canonical_record":{"source":{"id":"1008.3959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-08-24T03:58:25Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"f2151732a3f883bfd8e19a4290ab3de3cdf2341f06c048eac56c3fb0ac0a2377","abstract_canon_sha256":"c30ae705a28ec06ad552ebc0f54f7d040c4a64a0882cc1682419ece090cc6c56"},"schema_version":"1.0"},"canonical_sha256":"d1b51cb57dcfc27d1acb91dcddfba50d53cd88dec1f79cc5a1badf09ed2fc894","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:54.415270Z","signature_b64":"I25tFvyzs28AmDgFxYM/W3ceMOUUacC4utyOTeR35OBLLXJjH1yvoN/LgJcCx1/1wuwH/goHgjNdY7kvsPvTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1b51cb57dcfc27d1acb91dcddfba50d53cd88dec1f79cc5a1badf09ed2fc894","last_reissued_at":"2026-05-18T04:41:54.414757Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:54.414757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.3959","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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7OETq3wxx8DuhUZf3pFCqEChQ92Uh4R0HN+qhzJTlgYjfTVkXPwPBY2Daqkd7UfY0tg1IV97R0U0vlcWt5iAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:53:38.743962Z"},"content_sha256":"da8ab6ff56a9970ed1bc4422e4c49a214dab363383b14abed5a0a4e4039b213e","schema_version":"1.0","event_id":"sha256:da8ab6ff56a9970ed1bc4422e4c49a214dab363383b14abed5a0a4e4039b213e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2G2RZNL5Z7BH2GWLSHON365FBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On classifying Hurewicz fibrations and fibre bundles over polyhedron bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Adem Kilicman, Amin Saif","submitted_at":"2010-08-24T03:58:25Z","abstract_excerpt":"Let $f:E\\longrightarrow O$ be a Hurewicz fibration with a fiber space $F_{r_{o}}$ and a lifting function $L_{f}$. The \\emph{$Lf-$function} $\\Theta_{L_{f}}$ of $f$ is defined by the restriction map of $L_{f}$ on the space $\\Omega(O,r_{o})\\times F_{r_{o}}\\times \\{1\\}$. The purpose of this paper is to give some results which show the role of $Lf-$functions in finding a fiber homotopically equivalent relation between two fibrations, over a common polyhedron base. Furthermore we will prove the equivalently between our results and Dold's theorem in fiber bundles, over a common suspension base of pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3959","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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82f0uZ7lSOAjE/rN/fOrRqOsg8Me0MsuALhhU6vhjXMd5cbryBpRlH+BsZ/bOMlAMKSc0Ov31T7ByutKZ/qBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T23:53:38.744677Z"},"content_sha256":"96f236d4057f6f0fbb3b6b9d5f86a7e5685b14536256f8323441c1eaff649530","schema_version":"1.0","event_id":"sha256:96f236d4057f6f0fbb3b6b9d5f86a7e5685b14536256f8323441c1eaff649530"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2G2RZNL5Z7BH2GWLSHON365FBV/bundle.json","state_url":"https://pith.science/pith/2G2RZNL5Z7BH2GWLSHON365FBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2G2RZNL5Z7BH2GWLSHON365FBV/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":"2026-06-07T23:53:38Z","links":{"resolver":"https://pith.science/pith/2G2RZNL5Z7BH2GWLSHON365FBV","bundle":"https://pith.science/pith/2G2RZNL5Z7BH2GWLSHON365FBV/bundle.json","state":"https://pith.science/pith/2G2RZNL5Z7BH2GWLSHON365FBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2G2RZNL5Z7BH2GWLSHON365FBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2G2RZNL5Z7BH2GWLSHON365FBV","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":"c30ae705a28ec06ad552ebc0f54f7d040c4a64a0882cc1682419ece090cc6c56","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-08-24T03:58:25Z","title_canon_sha256":"f2151732a3f883bfd8e19a4290ab3de3cdf2341f06c048eac56c3fb0ac0a2377"},"schema_version":"1.0","source":{"id":"1008.3959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3959","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3959v1","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3959","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"2G2RZNL5Z7BH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2G2RZNL5Z7BH2GWL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2G2RZNL5","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:96f236d4057f6f0fbb3b6b9d5f86a7e5685b14536256f8323441c1eaff649530","target":"graph","created_at":"2026-05-18T04:41:54Z","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":"Let $f:E\\longrightarrow O$ be a Hurewicz fibration with a fiber space $F_{r_{o}}$ and a lifting function $L_{f}$. The \\emph{$Lf-$function} $\\Theta_{L_{f}}$ of $f$ is defined by the restriction map of $L_{f}$ on the space $\\Omega(O,r_{o})\\times F_{r_{o}}\\times \\{1\\}$. The purpose of this paper is to give some results which show the role of $Lf-$functions in finding a fiber homotopically equivalent relation between two fibrations, over a common polyhedron base. Furthermore we will prove the equivalently between our results and Dold's theorem in fiber bundles, over a common suspension base of pol","authors_text":"Adem Kilicman, Amin Saif","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-08-24T03:58:25Z","title":"On classifying Hurewicz fibrations and fibre bundles over polyhedron bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3959","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:da8ab6ff56a9970ed1bc4422e4c49a214dab363383b14abed5a0a4e4039b213e","target":"record","created_at":"2026-05-18T04:41:54Z","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":"c30ae705a28ec06ad552ebc0f54f7d040c4a64a0882cc1682419ece090cc6c56","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-08-24T03:58:25Z","title_canon_sha256":"f2151732a3f883bfd8e19a4290ab3de3cdf2341f06c048eac56c3fb0ac0a2377"},"schema_version":"1.0","source":{"id":"1008.3959","kind":"arxiv","version":1}},"canonical_sha256":"d1b51cb57dcfc27d1acb91dcddfba50d53cd88dec1f79cc5a1badf09ed2fc894","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1b51cb57dcfc27d1acb91dcddfba50d53cd88dec1f79cc5a1badf09ed2fc894","first_computed_at":"2026-05-18T04:41:54.414757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:54.414757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I25tFvyzs28AmDgFxYM/W3ceMOUUacC4utyOTeR35OBLLXJjH1yvoN/LgJcCx1/1wuwH/goHgjNdY7kvsPvTCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:54.415270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da8ab6ff56a9970ed1bc4422e4c49a214dab363383b14abed5a0a4e4039b213e","sha256:96f236d4057f6f0fbb3b6b9d5f86a7e5685b14536256f8323441c1eaff649530"],"state_sha256":"4c9cf670b336c39526ba6116fd42662f6dc437e672ad044d6f2f9b9d66a29888"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xWW5XhgyOyTtlvQc3gSbLSyCgk3y4boKKWeJSkyS/9rVk1CU2KJ9aAf2pzqCPox1kRBaZYjFkWh9XhB4bhWvAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T23:53:38.748673Z","bundle_sha256":"0e6f11e80a8dd1367ec32f35f0c315d93b5107d6c53b5048b618e239521adb9c"}}