{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TRLG64KN4DN5SJUYZFEUL5PHZL","short_pith_number":"pith:TRLG64KN","canonical_record":{"source":{"id":"1703.00935","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-02T20:11:54Z","cross_cats_sorted":[],"title_canon_sha256":"9c38fe3e1f3e58a53d52dda10c520daf7af4ba7eda35e4dea0543fca2a4fcc63","abstract_canon_sha256":"3b63e55557ee9d18ff4d49c76a6fd2981234c02cf7e527502b4fe3ab7c69f247"},"schema_version":"1.0"},"canonical_sha256":"9c566f714de0dbd92698c94945f5e7cad765737062e3a74ee21a33ee61713d4b","source":{"kind":"arxiv","id":"1703.00935","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00935","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00935v2","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00935","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"pith_short_12","alias_value":"TRLG64KN4DN5","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TRLG64KN4DN5SJUY","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TRLG64KN","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TRLG64KN4DN5SJUYZFEUL5PHZL","target":"record","payload":{"canonical_record":{"source":{"id":"1703.00935","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-02T20:11:54Z","cross_cats_sorted":[],"title_canon_sha256":"9c38fe3e1f3e58a53d52dda10c520daf7af4ba7eda35e4dea0543fca2a4fcc63","abstract_canon_sha256":"3b63e55557ee9d18ff4d49c76a6fd2981234c02cf7e527502b4fe3ab7c69f247"},"schema_version":"1.0"},"canonical_sha256":"9c566f714de0dbd92698c94945f5e7cad765737062e3a74ee21a33ee61713d4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:56.574518Z","signature_b64":"qQ2VxWQuqzVex+5EGrx72nfb7Fiu7iZcWMAt++83ZU6UOKqDAqHZE9MIwPTUhHoOedKM9vtuuPc5+vJnd1WZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c566f714de0dbd92698c94945f5e7cad765737062e3a74ee21a33ee61713d4b","last_reissued_at":"2026-05-18T00:16:56.573870Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:56.573870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.00935","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":"2026-05-18T00:16:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+gnCZhwSGP5av1VMH16k9oqesqQhExpaKKgQgeYLhutXPrg+nT6arXlWlaAh4Jm2O1qhxtRL1E456US2dnCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:19:32.045175Z"},"content_sha256":"fab62b077b3734190f24dbe8d05449bb24a3a176506219b8c957c2864a35d080","schema_version":"1.0","event_id":"sha256:fab62b077b3734190f24dbe8d05449bb24a3a176506219b8c957c2864a35d080"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TRLG64KN4DN5SJUYZFEUL5PHZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secondary power operations and the Brown-Peterson spectrum at the prime 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Tyler Lawson","submitted_at":"2017-03-02T20:11:54Z","abstract_excerpt":"The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown-Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us to conclude that the 2-primary Brown-Peterson spectrum does not admit the structure of an E_n-algebra for any n greater than or equal to 12, answering a question of May in the negative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00935","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":"2026-05-18T00:16:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kp+t4En/5ca77teG3Hvn59jhjJYFQJDFKTtGUlSZtjK1y/tKdQk85G8kVuwUX3CWeOV2kp+Wlr4u5wrufU60DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:19:32.045548Z"},"content_sha256":"3c0527200a3469d25fad59ec75bec36bd5463288bf11dc059bdff59fe931025b","schema_version":"1.0","event_id":"sha256:3c0527200a3469d25fad59ec75bec36bd5463288bf11dc059bdff59fe931025b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRLG64KN4DN5SJUYZFEUL5PHZL/bundle.json","state_url":"https://pith.science/pith/TRLG64KN4DN5SJUYZFEUL5PHZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRLG64KN4DN5SJUYZFEUL5PHZL/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":"2026-06-12T09:19:32Z","links":{"resolver":"https://pith.science/pith/TRLG64KN4DN5SJUYZFEUL5PHZL","bundle":"https://pith.science/pith/TRLG64KN4DN5SJUYZFEUL5PHZL/bundle.json","state":"https://pith.science/pith/TRLG64KN4DN5SJUYZFEUL5PHZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRLG64KN4DN5SJUYZFEUL5PHZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TRLG64KN4DN5SJUYZFEUL5PHZL","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":"3b63e55557ee9d18ff4d49c76a6fd2981234c02cf7e527502b4fe3ab7c69f247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-02T20:11:54Z","title_canon_sha256":"9c38fe3e1f3e58a53d52dda10c520daf7af4ba7eda35e4dea0543fca2a4fcc63"},"schema_version":"1.0","source":{"id":"1703.00935","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00935","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00935v2","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00935","created_at":"2026-05-18T00:16:56Z"},{"alias_kind":"pith_short_12","alias_value":"TRLG64KN4DN5","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TRLG64KN4DN5SJUY","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TRLG64KN","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:3c0527200a3469d25fad59ec75bec36bd5463288bf11dc059bdff59fe931025b","target":"graph","created_at":"2026-05-18T00:16:56Z","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":"The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown-Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us to conclude that the 2-primary Brown-Peterson spectrum does not admit the structure of an E_n-algebra for any n greater than or equal to 12, answering a question of May in the negative.","authors_text":"Tyler Lawson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-02T20:11:54Z","title":"Secondary power operations and the Brown-Peterson spectrum at the prime 2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00935","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:fab62b077b3734190f24dbe8d05449bb24a3a176506219b8c957c2864a35d080","target":"record","created_at":"2026-05-18T00:16:56Z","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":"3b63e55557ee9d18ff4d49c76a6fd2981234c02cf7e527502b4fe3ab7c69f247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-03-02T20:11:54Z","title_canon_sha256":"9c38fe3e1f3e58a53d52dda10c520daf7af4ba7eda35e4dea0543fca2a4fcc63"},"schema_version":"1.0","source":{"id":"1703.00935","kind":"arxiv","version":2}},"canonical_sha256":"9c566f714de0dbd92698c94945f5e7cad765737062e3a74ee21a33ee61713d4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c566f714de0dbd92698c94945f5e7cad765737062e3a74ee21a33ee61713d4b","first_computed_at":"2026-05-18T00:16:56.573870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:56.573870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qQ2VxWQuqzVex+5EGrx72nfb7Fiu7iZcWMAt++83ZU6UOKqDAqHZE9MIwPTUhHoOedKM9vtuuPc5+vJnd1WZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:56.574518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00935","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fab62b077b3734190f24dbe8d05449bb24a3a176506219b8c957c2864a35d080","sha256:3c0527200a3469d25fad59ec75bec36bd5463288bf11dc059bdff59fe931025b"],"state_sha256":"da5cc8c69d058a1968b9719b54b68816cba019561c761b3c1f792e5904f00f12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cIIHTVYYNh2MuWx1gUUKlX3er/sfcjfmQBILiaeDYHgUDgl/PfrI9Tq03bnzrNCT5b+DgTF6vPMxOP1S/9KtAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:19:32.047699Z","bundle_sha256":"6de3d501f0b5789434a2749b35adfc609ef61ffb6eae14d7c7270377fc43ac4c"}}