{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BTHY4Z6PCELFWVYRGCLWW6W4D7","short_pith_number":"pith:BTHY4Z6P","schema_version":"1.0","canonical_sha256":"0ccf8e67cf11165b571130976b7adc1fed47a5082197ff54063ea569aeb11172","source":{"kind":"arxiv","id":"1707.01620","version":2},"attestation_state":"computed","paper":{"title":"Some extensions in the Adams spectral sequence and the 51-stem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Guozhen Wang, Zhouli Xu","submitted_at":"2017-07-06T02:58:59Z","abstract_excerpt":"We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of $\\pi_{51}$ is $\\mathbb{Z}/8\\oplus\\mathbb{Z}/8\\oplus\\mathbb{Z}/2$. This was the last unsolved 2-extension problem left by the recent works of Isaksen and the authors (\\cite{Isa1}, \\cite{IX}, \\cite{WX1}) through the 61-stem.\n  The proof of this result uses the $RP^\\infty$ technique, which was introduced by the authors in \\cite{WX1} to prove $\\pi_{61}=0$. This paper advertises this method through examples that have simpler proofs than in \\cite{WX1}."},"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":"1707.01620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-07-06T02:58:59Z","cross_cats_sorted":[],"title_canon_sha256":"e759a57f3435a0b432979f93ae6f18f909a50313313f2e51cdc897fce199da34","abstract_canon_sha256":"4c7340bfe4a287f57144768bcc1a9a8e473c777329808e5efbdf5d11c5e98857"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:05.468159Z","signature_b64":"39uqwApydXpJ/pgvPWyQenIGa0dqf7cwBabqbmExnufAcgpRADQKOvULrKxi6TTBauD6lbUU9VutEU9f51UYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ccf8e67cf11165b571130976b7adc1fed47a5082197ff54063ea569aeb11172","last_reissued_at":"2026-05-17T23:58:05.467606Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:05.467606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some extensions in the Adams spectral sequence and the 51-stem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Guozhen Wang, Zhouli Xu","submitted_at":"2017-07-06T02:58:59Z","abstract_excerpt":"We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of $\\pi_{51}$ is $\\mathbb{Z}/8\\oplus\\mathbb{Z}/8\\oplus\\mathbb{Z}/2$. This was the last unsolved 2-extension problem left by the recent works of Isaksen and the authors (\\cite{Isa1}, \\cite{IX}, \\cite{WX1}) through the 61-stem.\n  The proof of this result uses the $RP^\\infty$ technique, which was introduced by the authors in \\cite{WX1} to prove $\\pi_{61}=0$. This paper advertises this method through examples that have simpler proofs than in \\cite{WX1}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01620","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.01620","created_at":"2026-05-17T23:58:05.467690+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.01620v2","created_at":"2026-05-17T23:58:05.467690+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01620","created_at":"2026-05-17T23:58:05.467690+00:00"},{"alias_kind":"pith_short_12","alias_value":"BTHY4Z6PCELF","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BTHY4Z6PCELFWVYR","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BTHY4Z6P","created_at":"2026-05-18T12:31:08.081275+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/BTHY4Z6PCELFWVYRGCLWW6W4D7","json":"https://pith.science/pith/BTHY4Z6PCELFWVYRGCLWW6W4D7.json","graph_json":"https://pith.science/api/pith-number/BTHY4Z6PCELFWVYRGCLWW6W4D7/graph.json","events_json":"https://pith.science/api/pith-number/BTHY4Z6PCELFWVYRGCLWW6W4D7/events.json","paper":"https://pith.science/paper/BTHY4Z6P"},"agent_actions":{"view_html":"https://pith.science/pith/BTHY4Z6PCELFWVYRGCLWW6W4D7","download_json":"https://pith.science/pith/BTHY4Z6PCELFWVYRGCLWW6W4D7.json","view_paper":"https://pith.science/paper/BTHY4Z6P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.01620&json=true","fetch_graph":"https://pith.science/api/pith-number/BTHY4Z6PCELFWVYRGCLWW6W4D7/graph.json","fetch_events":"https://pith.science/api/pith-number/BTHY4Z6PCELFWVYRGCLWW6W4D7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BTHY4Z6PCELFWVYRGCLWW6W4D7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BTHY4Z6PCELFWVYRGCLWW6W4D7/action/storage_attestation","attest_author":"https://pith.science/pith/BTHY4Z6PCELFWVYRGCLWW6W4D7/action/author_attestation","sign_citation":"https://pith.science/pith/BTHY4Z6PCELFWVYRGCLWW6W4D7/action/citation_signature","submit_replication":"https://pith.science/pith/BTHY4Z6PCELFWVYRGCLWW6W4D7/action/replication_record"}},"created_at":"2026-05-17T23:58:05.467690+00:00","updated_at":"2026-05-17T23:58:05.467690+00:00"}