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There are a sequence of Ext groups $E_1^{s,t}(n-s)$ for non-negative integers $n$ with $E_1^{s,t}(0)=E_1^{s,t}$, and Bockstein spectral sequences computing a module $E_1^{s,*}(n-s)$ from $E_1^{s-1,*}(n-s+1)$. So far, a small number of the $E_1$-terms are determined. Here, we determine the $E_1^{1,1}(n-1)=\\e^1M^1_{n-1}$ for $p>2$ and $n>3$ by computing"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1202.2517","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-02-12T11:18:59Z","cross_cats_sorted":[],"title_canon_sha256":"ba5b94f8476a25d5157aeac34359a88be8f687e5de84ca47073d62f4eb1cfe50","abstract_canon_sha256":"ad47f4690928dcab01ef68b0b203cdde70bb04b270141fd63349c4134d8fabd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:26.317283Z","signature_b64":"AAMS8sWKqlrA1t7F25dxQ2rgW67EqUtDIX8E9Ugxelt7HeXDz1ZiWIghko0akxvRIEA3iDlSLGtoDCSGKruQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dbd0813ed7abbbebfd228ca78ccc2fb6ba2e37f45b3071bb4a254d860601ffc","last_reissued_at":"2026-05-18T04:02:26.316814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:26.316814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Katsumi Shimomura, Ryo Kato","submitted_at":"2012-02-12T11:18:59Z","abstract_excerpt":"The chromatic spectral sequence is introduced in \\cite{mrw} to compute the $E_2$-term of the \\ANSS\\ for computing the stable homotopy groups of spheres. The $E_1$-term $E_1^{s,t}(k)$ of the spectral sequence is an Ext group of $BP_*BP$-comodules. There are a sequence of Ext groups $E_1^{s,t}(n-s)$ for non-negative integers $n$ with $E_1^{s,t}(0)=E_1^{s,t}$, and Bockstein spectral sequences computing a module $E_1^{s,*}(n-s)$ from $E_1^{s-1,*}(n-s+1)$. So far, a small number of the $E_1$-terms are determined. Here, we determine the $E_1^{1,1}(n-1)=\\e^1M^1_{n-1}$ for $p>2$ and $n>3$ by computing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2517","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.2517","created_at":"2026-05-18T04:02:26.316880+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.2517v1","created_at":"2026-05-18T04:02:26.316880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2517","created_at":"2026-05-18T04:02:26.316880+00:00"},{"alias_kind":"pith_short_12","alias_value":"NW6QQE7NPK53","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NW6QQE7NPK535P6S","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NW6QQE7N","created_at":"2026-05-18T12:27:16.716162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N","json":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N.json","graph_json":"https://pith.science/api/pith-number/NW6QQE7NPK535P6SFDFHRTGC7N/graph.json","events_json":"https://pith.science/api/pith-number/NW6QQE7NPK535P6SFDFHRTGC7N/events.json","paper":"https://pith.science/paper/NW6QQE7N"},"agent_actions":{"view_html":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N","download_json":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N.json","view_paper":"https://pith.science/paper/NW6QQE7N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.2517&json=true","fetch_graph":"https://pith.science/api/pith-number/NW6QQE7NPK535P6SFDFHRTGC7N/graph.json","fetch_events":"https://pith.science/api/pith-number/NW6QQE7NPK535P6SFDFHRTGC7N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N/action/storage_attestation","attest_author":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N/action/author_attestation","sign_citation":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N/action/citation_signature","submit_replication":"https://pith.science/pith/NW6QQE7NPK535P6SFDFHRTGC7N/action/replication_record"}},"created_at":"2026-05-18T04:02:26.316880+00:00","updated_at":"2026-05-18T04:02:26.316880+00:00"}