{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:J7E36DAQPEJXBEC6RQZDTH6WXH","short_pith_number":"pith:J7E36DAQ","canonical_record":{"source":{"id":"math/0406081","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-06-04T12:05:21Z","cross_cats_sorted":[],"title_canon_sha256":"d607f8cc2b85b46c7ea9f4883ebfdffac7cf505c4770429ab08532753045e321","abstract_canon_sha256":"679eefe2d472757cde421ba6b1d7343efdc27636d7ae8feda7eb4a3b5f8eac5a"},"schema_version":"1.0"},"canonical_sha256":"4fc9bf0c10791370905e8c32399fd6b9c7fe7e67f6b98ca20d50fa8e7a8da521","source":{"kind":"arxiv","id":"math/0406081","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406081","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406081v2","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406081","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"J7E36DAQPEJX","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"J7E36DAQPEJXBEC6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"J7E36DAQ","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:J7E36DAQPEJXBEC6RQZDTH6WXH","target":"record","payload":{"canonical_record":{"source":{"id":"math/0406081","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AT","submitted_at":"2004-06-04T12:05:21Z","cross_cats_sorted":[],"title_canon_sha256":"d607f8cc2b85b46c7ea9f4883ebfdffac7cf505c4770429ab08532753045e321","abstract_canon_sha256":"679eefe2d472757cde421ba6b1d7343efdc27636d7ae8feda7eb4a3b5f8eac5a"},"schema_version":"1.0"},"canonical_sha256":"4fc9bf0c10791370905e8c32399fd6b9c7fe7e67f6b98ca20d50fa8e7a8da521","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:32.409500Z","signature_b64":"ZLG41oY93PVoB3ehBJJfw/F6qRczkmx9Wz33y9DmVatmG7aTpFkmov6W+xRJozKy/vtIurWHKGCLj3vzual4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fc9bf0c10791370905e8c32399fd6b9c7fe7e67f6b98ca20d50fa8e7a8da521","last_reissued_at":"2026-05-18T02:41:32.409120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:32.409120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0406081","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":"2026-05-18T02:41:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y8iQ0JSh08Tu6667B4T77TAsbn4tytScYVJ5yniwpmYc/EYpchIdVBpdzxg9AE09vhW4tdRJPT1OFximRYJPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:39:28.084366Z"},"content_sha256":"554c6d7a427293f0e6027eb1b1f8c2aac58635ddc113d38fa4b297f459a1df95","schema_version":"1.0","event_id":"sha256:554c6d7a427293f0e6027eb1b1f8c2aac58635ddc113d38fa4b297f459a1df95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:J7E36DAQPEJXBEC6RQZDTH6WXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentials in the homological homotopy fixed point spectral sequence","license":"","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"John Rognes, Robert R. Bruner","submitted_at":"2004-06-04T12:05:21Z","abstract_excerpt":"We analyze in homological terms the homotopy fixed point spectrum of a T-equivariant commutative S-algebra R. There is a homological homotopy fixed point spectral sequence with E^2_{s,t} = H^{-s}_{gp}(T; H_t(R; F_p)), converging conditionally to the continuous homology H^c_{s+t}(R^{hT}; F_p) of the homotopy fixed point spectrum. We show that there are Dyer-Lashof operations beta^epsilon Q^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the $^{2r}-term "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406081","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":"2026-05-18T02:41:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xC3OgFd51FegLGrbmQp3Vgdx7nycUvaDH5N58A38Fad+7ipdWL71VD7og6fAXyPd3x2frrZACfiONgLqGYZtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:39:28.084727Z"},"content_sha256":"09cc1864ce4c57e041ce307a6ca22b500187926a94884c489f98ec0dea44482b","schema_version":"1.0","event_id":"sha256:09cc1864ce4c57e041ce307a6ca22b500187926a94884c489f98ec0dea44482b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7E36DAQPEJXBEC6RQZDTH6WXH/bundle.json","state_url":"https://pith.science/pith/J7E36DAQPEJXBEC6RQZDTH6WXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7E36DAQPEJXBEC6RQZDTH6WXH/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":"2026-06-05T09:39:28Z","links":{"resolver":"https://pith.science/pith/J7E36DAQPEJXBEC6RQZDTH6WXH","bundle":"https://pith.science/pith/J7E36DAQPEJXBEC6RQZDTH6WXH/bundle.json","state":"https://pith.science/pith/J7E36DAQPEJXBEC6RQZDTH6WXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7E36DAQPEJXBEC6RQZDTH6WXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:J7E36DAQPEJXBEC6RQZDTH6WXH","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":"679eefe2d472757cde421ba6b1d7343efdc27636d7ae8feda7eb4a3b5f8eac5a","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2004-06-04T12:05:21Z","title_canon_sha256":"d607f8cc2b85b46c7ea9f4883ebfdffac7cf505c4770429ab08532753045e321"},"schema_version":"1.0","source":{"id":"math/0406081","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406081","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406081v2","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406081","created_at":"2026-05-18T02:41:32Z"},{"alias_kind":"pith_short_12","alias_value":"J7E36DAQPEJX","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"J7E36DAQPEJXBEC6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"J7E36DAQ","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:09cc1864ce4c57e041ce307a6ca22b500187926a94884c489f98ec0dea44482b","target":"graph","created_at":"2026-05-18T02:41:32Z","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 analyze in homological terms the homotopy fixed point spectrum of a T-equivariant commutative S-algebra R. There is a homological homotopy fixed point spectral sequence with E^2_{s,t} = H^{-s}_{gp}(T; H_t(R; F_p)), converging conditionally to the continuous homology H^c_{s+t}(R^{hT}; F_p) of the homotopy fixed point spectrum. We show that there are Dyer-Lashof operations beta^epsilon Q^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the $^{2r}-term ","authors_text":"John Rognes, Robert R. Bruner","cross_cats":[],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2004-06-04T12:05:21Z","title":"Differentials in the homological homotopy fixed point spectral sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406081","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":"sha256:554c6d7a427293f0e6027eb1b1f8c2aac58635ddc113d38fa4b297f459a1df95","target":"record","created_at":"2026-05-18T02:41:32Z","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":"679eefe2d472757cde421ba6b1d7343efdc27636d7ae8feda7eb4a3b5f8eac5a","cross_cats_sorted":[],"license":"","primary_cat":"math.AT","submitted_at":"2004-06-04T12:05:21Z","title_canon_sha256":"d607f8cc2b85b46c7ea9f4883ebfdffac7cf505c4770429ab08532753045e321"},"schema_version":"1.0","source":{"id":"math/0406081","kind":"arxiv","version":2}},"canonical_sha256":"4fc9bf0c10791370905e8c32399fd6b9c7fe7e67f6b98ca20d50fa8e7a8da521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fc9bf0c10791370905e8c32399fd6b9c7fe7e67f6b98ca20d50fa8e7a8da521","first_computed_at":"2026-05-18T02:41:32.409120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:32.409120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZLG41oY93PVoB3ehBJJfw/F6qRczkmx9Wz33y9DmVatmG7aTpFkmov6W+xRJozKy/vtIurWHKGCLj3vzual4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:32.409500Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0406081","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:554c6d7a427293f0e6027eb1b1f8c2aac58635ddc113d38fa4b297f459a1df95","sha256:09cc1864ce4c57e041ce307a6ca22b500187926a94884c489f98ec0dea44482b"],"state_sha256":"a0a3fb7f7aa8de12268890df72ab8cd285b283c6ce2f7169a59eb241826ef061"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6oEIKHi8O9sfHj5WdiXoYR9pT4Cs7iXuIQBGuSEcgIdIYq7f8RSoQFq7xlRSwY5RRj7J8FsCB1v6uMlkAdyEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:39:28.086754Z","bundle_sha256":"029a5312bd9af6ae6e73bf228da58550b46e37ff1a799889d831422261ab2389"}}