{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Z2TKFLMAPELZZPPBVFOHF6X2V2","short_pith_number":"pith:Z2TKFLMA","canonical_record":{"source":{"id":"1704.07248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-24T14:18:32Z","cross_cats_sorted":[],"title_canon_sha256":"2f15dda1c32613d0bb416802bdb117b6ca08d7c21b79e3b1540a4d1d8d0cf8ea","abstract_canon_sha256":"d2cd2e6f3166c955771721b316367ba5ab1697b2836a6ba92fff846ad254e125"},"schema_version":"1.0"},"canonical_sha256":"cea6a2ad8079179cbde1a95c72fafaae97e320270315445c40fece7cf7d9e37f","source":{"kind":"arxiv","id":"1704.07248","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07248","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07248v2","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07248","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z2TKFLMAPELZ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2TKFLMAPELZZPPB","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2TKFLMA","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Z2TKFLMAPELZZPPBVFOHF6X2V2","target":"record","payload":{"canonical_record":{"source":{"id":"1704.07248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-24T14:18:32Z","cross_cats_sorted":[],"title_canon_sha256":"2f15dda1c32613d0bb416802bdb117b6ca08d7c21b79e3b1540a4d1d8d0cf8ea","abstract_canon_sha256":"d2cd2e6f3166c955771721b316367ba5ab1697b2836a6ba92fff846ad254e125"},"schema_version":"1.0"},"canonical_sha256":"cea6a2ad8079179cbde1a95c72fafaae97e320270315445c40fece7cf7d9e37f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:56.723556Z","signature_b64":"CBLDb72b2gShH0TH/xKWrJ+M3TUHkREQXq2CWTWGAdgAAAKi9lnehRdz6klqj5ufrBQEfQlV/QjosTGD6iHYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cea6a2ad8079179cbde1a95c72fafaae97e320270315445c40fece7cf7d9e37f","last_reissued_at":"2026-05-17T23:41:56.722867Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:56.722867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.07248","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":"2026-05-17T23:41:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iT41LjjArERCd6+q73gicrT3KlqyRib3jGmHmd3m3Ds6KyZd7dkHcktq3YUVNFG9YuzcWy6ckIVv/o3sken6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:30:25.064539Z"},"content_sha256":"8958fa6b8728cff0caad38d1fbbd8011cbcf71dcba37b6b099581b7f25060f41","schema_version":"1.0","event_id":"sha256:8958fa6b8728cff0caad38d1fbbd8011cbcf71dcba37b6b099581b7f25060f41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Z2TKFLMAPELZZPPBVFOHF6X2V2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Homology of Connective Morava $E$-theory with coefficients in $\\mathbb{F}_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Lukas Katth\\\"an, Sean Tilson","submitted_at":"2017-04-24T14:18:32Z","abstract_excerpt":"Let $e_n$ be the connective cover of the Morava $E$-theory spectrum $E_n$ of height $n$. In this paper we compute its homology $H_*(e_n;\\mathbb{F}_p)$ for any prime $p$ and $n \\leq 4$ up to possible multiplicative extensions. In order to accomplish this we show that the K\\\"unneth spectral sequence based on an $E_3$-algebra $R$ is multiplicative when the $R$-modules in question are commutative $S$-algebras. We then apply this result by working over $BP$ which is known to be an $E_4$-algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07248","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":"2026-05-17T23:41:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9HuRQQ3TfytOgh4B9qL8fzhoiA6L9AwfxNX4IJ0bZ6A4+b4ehy0Qzj07wqzOjiPPc5QcUi5kyrfrbc0scLcRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:30:25.064992Z"},"content_sha256":"f1e94c87864df5d41b02217c1e1b83934719106fb4727075a7ff186c5aa8a6f4","schema_version":"1.0","event_id":"sha256:f1e94c87864df5d41b02217c1e1b83934719106fb4727075a7ff186c5aa8a6f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2TKFLMAPELZZPPBVFOHF6X2V2/bundle.json","state_url":"https://pith.science/pith/Z2TKFLMAPELZZPPBVFOHF6X2V2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2TKFLMAPELZZPPBVFOHF6X2V2/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":"2026-05-31T23:30:25Z","links":{"resolver":"https://pith.science/pith/Z2TKFLMAPELZZPPBVFOHF6X2V2","bundle":"https://pith.science/pith/Z2TKFLMAPELZZPPBVFOHF6X2V2/bundle.json","state":"https://pith.science/pith/Z2TKFLMAPELZZPPBVFOHF6X2V2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2TKFLMAPELZZPPBVFOHF6X2V2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z2TKFLMAPELZZPPBVFOHF6X2V2","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":"d2cd2e6f3166c955771721b316367ba5ab1697b2836a6ba92fff846ad254e125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-24T14:18:32Z","title_canon_sha256":"2f15dda1c32613d0bb416802bdb117b6ca08d7c21b79e3b1540a4d1d8d0cf8ea"},"schema_version":"1.0","source":{"id":"1704.07248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07248","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07248v2","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07248","created_at":"2026-05-17T23:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z2TKFLMAPELZ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z2TKFLMAPELZZPPB","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z2TKFLMA","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:f1e94c87864df5d41b02217c1e1b83934719106fb4727075a7ff186c5aa8a6f4","target":"graph","created_at":"2026-05-17T23:41:56Z","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 $e_n$ be the connective cover of the Morava $E$-theory spectrum $E_n$ of height $n$. In this paper we compute its homology $H_*(e_n;\\mathbb{F}_p)$ for any prime $p$ and $n \\leq 4$ up to possible multiplicative extensions. In order to accomplish this we show that the K\\\"unneth spectral sequence based on an $E_3$-algebra $R$ is multiplicative when the $R$-modules in question are commutative $S$-algebras. We then apply this result by working over $BP$ which is known to be an $E_4$-algebra.","authors_text":"Lukas Katth\\\"an, Sean Tilson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-24T14:18:32Z","title":"The Homology of Connective Morava $E$-theory with coefficients in $\\mathbb{F}_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07248","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":"sha256:8958fa6b8728cff0caad38d1fbbd8011cbcf71dcba37b6b099581b7f25060f41","target":"record","created_at":"2026-05-17T23:41:56Z","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":"d2cd2e6f3166c955771721b316367ba5ab1697b2836a6ba92fff846ad254e125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-04-24T14:18:32Z","title_canon_sha256":"2f15dda1c32613d0bb416802bdb117b6ca08d7c21b79e3b1540a4d1d8d0cf8ea"},"schema_version":"1.0","source":{"id":"1704.07248","kind":"arxiv","version":2}},"canonical_sha256":"cea6a2ad8079179cbde1a95c72fafaae97e320270315445c40fece7cf7d9e37f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea6a2ad8079179cbde1a95c72fafaae97e320270315445c40fece7cf7d9e37f","first_computed_at":"2026-05-17T23:41:56.722867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:56.722867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CBLDb72b2gShH0TH/xKWrJ+M3TUHkREQXq2CWTWGAdgAAAKi9lnehRdz6klqj5ufrBQEfQlV/QjosTGD6iHYBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:56.723556Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8958fa6b8728cff0caad38d1fbbd8011cbcf71dcba37b6b099581b7f25060f41","sha256:f1e94c87864df5d41b02217c1e1b83934719106fb4727075a7ff186c5aa8a6f4"],"state_sha256":"c00c0d41a2569a2a440cba6a4cfa73d1cab2dae14474f2f0913530b9912985ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7A1gpU1dok9yMjya+/Tc8iLSUXlxCIxvI3+W3AXJYrIVJVL5ZRbjV3iuPHya1PUWJvX0QU+ooLCBpaIDPAGABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:30:25.068552Z","bundle_sha256":"f4b9f44319e39af32f46b2c8ef2e2475f35b7198091a518c57f7a86402020758"}}