{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7TZWUTAM5JJDKN7PFKNXXB5NRL","short_pith_number":"pith:7TZWUTAM","canonical_record":{"source":{"id":"1401.7150","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-01-28T12:05:28Z","cross_cats_sorted":[],"title_canon_sha256":"09bcd2b17f12b589b4b0c1b83d8a65372da0d368f49d836af1bc33f659c6a08b","abstract_canon_sha256":"bdb2cc4e8248c05eacdbb9a0bdcb33086cf063603a1284cd59ade6562f43305c"},"schema_version":"1.0"},"canonical_sha256":"fcf36a4c0cea523537ef2a9b7b87ad8ace8967b225205d67ba6d4a9f5bca0068","source":{"kind":"arxiv","id":"1401.7150","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7150","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7150v4","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7150","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"7TZWUTAM5JJD","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7TZWUTAM5JJDKN7P","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7TZWUTAM","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7TZWUTAM5JJDKN7PFKNXXB5NRL","target":"record","payload":{"canonical_record":{"source":{"id":"1401.7150","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-01-28T12:05:28Z","cross_cats_sorted":[],"title_canon_sha256":"09bcd2b17f12b589b4b0c1b83d8a65372da0d368f49d836af1bc33f659c6a08b","abstract_canon_sha256":"bdb2cc4e8248c05eacdbb9a0bdcb33086cf063603a1284cd59ade6562f43305c"},"schema_version":"1.0"},"canonical_sha256":"fcf36a4c0cea523537ef2a9b7b87ad8ace8967b225205d67ba6d4a9f5bca0068","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:14.949332Z","signature_b64":"HiSAlSWjf9QEj7GZzZ5ntnHngZuRSD+li4fKE7dCAJMgsbfkx+d2GLvX/DSa+yFK9VsZaxF5XTXexAi2DDuiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcf36a4c0cea523537ef2a9b7b87ad8ace8967b225205d67ba6d4a9f5bca0068","last_reissued_at":"2026-05-18T01:04:14.948878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:14.948878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.7150","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8xQqo0/1KUWSyGnBQ/h/8uZcEYUDJhN5OaVeHL9iNcgJhN1m8efLmzimCJgNgefvnPLvuzR6x3b8acSmzi+bDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:59:46.081830Z"},"content_sha256":"6d35e8a9b825a8b26ffc84201390ea327cb3ca5138d5f1752b2e74b27c35abc7","schema_version":"1.0","event_id":"sha256:6d35e8a9b825a8b26ffc84201390ea327cb3ca5138d5f1752b2e74b27c35abc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7TZWUTAM5JJDKN7PFKNXXB5NRL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Profinite and discrete G-spectra and iterated homotopy fixed points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Daniel G. Davis, Gereon Quick","submitted_at":"2014-01-28T12:05:28Z","abstract_excerpt":"For a profinite group $G$, let $(\\text{-})^{hG}$, $(\\text{-})^{h_dG}$, and $(\\text{-})^{h'G}$ denote continuous homotopy fixed points for profinite $G$-spectra, discrete $G$-spectra, and continuous $G$-spectra (coming from towers of discrete $G$-spectra), respectively. We establish some connections between the first two notions, and by using Postnikov towers, for $K \\vartriangleleft_c G$ (a closed normal subgroup), give various conditions for when the iterated homotopy fixed points $(X^{hK})^{hG/K}$ exist and are $X^{hG}$. For the Lubin-Tate spectrum $E_n$ and $G <_c G_n$, the extended Morava "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7150","kind":"arxiv","version":4},"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":"2026-05-18T01:04:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aILhjK1WYqa+Bv16mgDK4YJXfLUcRBDrWyTA8WWbsbJ61ANleOO7gNx5yrPeaD+9Nj93A7bB7Yy5xv7f4t8PAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:59:46.082582Z"},"content_sha256":"2f7d09f7ce4c14b1ef7f415d78db1089c671d2c33be4ebc2094cc463f39c08fd","schema_version":"1.0","event_id":"sha256:2f7d09f7ce4c14b1ef7f415d78db1089c671d2c33be4ebc2094cc463f39c08fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7TZWUTAM5JJDKN7PFKNXXB5NRL/bundle.json","state_url":"https://pith.science/pith/7TZWUTAM5JJDKN7PFKNXXB5NRL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7TZWUTAM5JJDKN7PFKNXXB5NRL/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":"2026-06-12T03:59:46Z","links":{"resolver":"https://pith.science/pith/7TZWUTAM5JJDKN7PFKNXXB5NRL","bundle":"https://pith.science/pith/7TZWUTAM5JJDKN7PFKNXXB5NRL/bundle.json","state":"https://pith.science/pith/7TZWUTAM5JJDKN7PFKNXXB5NRL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7TZWUTAM5JJDKN7PFKNXXB5NRL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7TZWUTAM5JJDKN7PFKNXXB5NRL","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":"bdb2cc4e8248c05eacdbb9a0bdcb33086cf063603a1284cd59ade6562f43305c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-01-28T12:05:28Z","title_canon_sha256":"09bcd2b17f12b589b4b0c1b83d8a65372da0d368f49d836af1bc33f659c6a08b"},"schema_version":"1.0","source":{"id":"1401.7150","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.7150","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1401.7150v4","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7150","created_at":"2026-05-18T01:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"7TZWUTAM5JJD","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7TZWUTAM5JJDKN7P","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7TZWUTAM","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:2f7d09f7ce4c14b1ef7f415d78db1089c671d2c33be4ebc2094cc463f39c08fd","target":"graph","created_at":"2026-05-18T01:04:14Z","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":"For a profinite group $G$, let $(\\text{-})^{hG}$, $(\\text{-})^{h_dG}$, and $(\\text{-})^{h'G}$ denote continuous homotopy fixed points for profinite $G$-spectra, discrete $G$-spectra, and continuous $G$-spectra (coming from towers of discrete $G$-spectra), respectively. We establish some connections between the first two notions, and by using Postnikov towers, for $K \\vartriangleleft_c G$ (a closed normal subgroup), give various conditions for when the iterated homotopy fixed points $(X^{hK})^{hG/K}$ exist and are $X^{hG}$. For the Lubin-Tate spectrum $E_n$ and $G <_c G_n$, the extended Morava ","authors_text":"Daniel G. Davis, Gereon Quick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-01-28T12:05:28Z","title":"Profinite and discrete G-spectra and iterated homotopy fixed points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7150","kind":"arxiv","version":4},"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":"sha256:6d35e8a9b825a8b26ffc84201390ea327cb3ca5138d5f1752b2e74b27c35abc7","target":"record","created_at":"2026-05-18T01:04:14Z","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":"bdb2cc4e8248c05eacdbb9a0bdcb33086cf063603a1284cd59ade6562f43305c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-01-28T12:05:28Z","title_canon_sha256":"09bcd2b17f12b589b4b0c1b83d8a65372da0d368f49d836af1bc33f659c6a08b"},"schema_version":"1.0","source":{"id":"1401.7150","kind":"arxiv","version":4}},"canonical_sha256":"fcf36a4c0cea523537ef2a9b7b87ad8ace8967b225205d67ba6d4a9f5bca0068","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcf36a4c0cea523537ef2a9b7b87ad8ace8967b225205d67ba6d4a9f5bca0068","first_computed_at":"2026-05-18T01:04:14.948878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:14.948878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HiSAlSWjf9QEj7GZzZ5ntnHngZuRSD+li4fKE7dCAJMgsbfkx+d2GLvX/DSa+yFK9VsZaxF5XTXexAi2DDuiCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:14.949332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.7150","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d35e8a9b825a8b26ffc84201390ea327cb3ca5138d5f1752b2e74b27c35abc7","sha256:2f7d09f7ce4c14b1ef7f415d78db1089c671d2c33be4ebc2094cc463f39c08fd"],"state_sha256":"4bf7f0d8de9d356905ad6f99168eb2ea6a057a67413f0a428ba11eb239d82725"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AAKBoYMdjkiWomizeaENAMx10t8OaVyl/Txh+RRoCGKr901kBSziptckNvRAs5QftHvHlwh7UBcz2VCrZ74pCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:59:46.086805Z","bundle_sha256":"0349623e9c9b86db9e4f08d007140a52638fc67d37be8392c08ec0d31f1953b1"}}