{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KNSNYZQJFM3J6WCXLKONFA2EY4","short_pith_number":"pith:KNSNYZQJ","canonical_record":{"source":{"id":"1105.1143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-05T19:00:53Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3b5abd8a7324cfc9753967ec566a4471c870cf21f4fd7f839c785cf6a0029d0e","abstract_canon_sha256":"ecf6b208e0c283fefdbb7f0d0489a6e0fa8b8b99d590ca8a24fa67a72931486d"},"schema_version":"1.0"},"canonical_sha256":"5364dc66092b369f58575a9cd28344c7371ce7a9ace89477dd1acc0c0c1643b2","source":{"kind":"arxiv","id":"1105.1143","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1143","created_at":"2026-05-18T00:18:36Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1143v2","created_at":"2026-05-18T00:18:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1143","created_at":"2026-05-18T00:18:36Z"},{"alias_kind":"pith_short_12","alias_value":"KNSNYZQJFM3J","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KNSNYZQJFM3J6WCX","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KNSNYZQJ","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KNSNYZQJFM3J6WCXLKONFA2EY4","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-05T19:00:53Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3b5abd8a7324cfc9753967ec566a4471c870cf21f4fd7f839c785cf6a0029d0e","abstract_canon_sha256":"ecf6b208e0c283fefdbb7f0d0489a6e0fa8b8b99d590ca8a24fa67a72931486d"},"schema_version":"1.0"},"canonical_sha256":"5364dc66092b369f58575a9cd28344c7371ce7a9ace89477dd1acc0c0c1643b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:36.593055Z","signature_b64":"gf688YSxiqcgM18wGITqTFxK0yI7C/1MTBtPa+b0eCI8x799rIMMMA0L9HoNc9ERqXqIp8UEvZMIA4Wvpes8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5364dc66092b369f58575a9cd28344c7371ce7a9ace89477dd1acc0c0c1643b2","last_reissued_at":"2026-05-18T00:18:36.592396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:36.592396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1143","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":"2026-05-18T00:18:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WpJOmyhRHBW1Pftuw6oPRd15RZ6QXF6TuCDZgf8b5J2F7ONzwtq4vI97FCMbcbKbUW72EebQQ/4AnQD/5wB/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:47:48.931271Z"},"content_sha256":"ecfe87837fb25e6578101da45218f96187630fa33c17c1c784f4678ecfe16d8e","schema_version":"1.0","event_id":"sha256:ecfe87837fb25e6578101da45218f96187630fa33c17c1c784f4678ecfe16d8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KNSNYZQJFM3J6WCXLKONFA2EY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomological uniqueness, Massey products and the modular isomorphism problem for 2-groups of maximal nilpotency class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AT","authors_text":"Albert Ruiz, Antonio Viruel","submitted_at":"2011-05-05T19:00:53Z","abstract_excerpt":"Let $G$ be a finite 2-group of maximal nilpotency class, and let $BG$ be its classifying space. We prove that iterated Massey products in $H^*(BG;\\F_2)$ do characterize the homotopy type of $BG$ among 2-complete spaces with the same cohomological structure. As a consequence we get an alternative proof of the modular isomorphism problem for 2-groups of maximal nilpotency class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1143","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":"2026-05-18T00:18:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/UXxHh11sfriPNYqemmxv+jXAMxVZAlMU0+thOSTehyCLKz/eMP0Y82xVoWvhscxA0g5XNp1i+4MW+tHrNSdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:47:48.931996Z"},"content_sha256":"8551b98ed1a0131c6f50fe00977047272647227bf0dfd5912d09256deb948678","schema_version":"1.0","event_id":"sha256:8551b98ed1a0131c6f50fe00977047272647227bf0dfd5912d09256deb948678"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNSNYZQJFM3J6WCXLKONFA2EY4/bundle.json","state_url":"https://pith.science/pith/KNSNYZQJFM3J6WCXLKONFA2EY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNSNYZQJFM3J6WCXLKONFA2EY4/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":"2026-06-09T11:47:48Z","links":{"resolver":"https://pith.science/pith/KNSNYZQJFM3J6WCXLKONFA2EY4","bundle":"https://pith.science/pith/KNSNYZQJFM3J6WCXLKONFA2EY4/bundle.json","state":"https://pith.science/pith/KNSNYZQJFM3J6WCXLKONFA2EY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNSNYZQJFM3J6WCXLKONFA2EY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KNSNYZQJFM3J6WCXLKONFA2EY4","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":"ecf6b208e0c283fefdbb7f0d0489a6e0fa8b8b99d590ca8a24fa67a72931486d","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-05T19:00:53Z","title_canon_sha256":"3b5abd8a7324cfc9753967ec566a4471c870cf21f4fd7f839c785cf6a0029d0e"},"schema_version":"1.0","source":{"id":"1105.1143","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1143","created_at":"2026-05-18T00:18:36Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1143v2","created_at":"2026-05-18T00:18:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1143","created_at":"2026-05-18T00:18:36Z"},{"alias_kind":"pith_short_12","alias_value":"KNSNYZQJFM3J","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KNSNYZQJFM3J6WCX","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KNSNYZQJ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:8551b98ed1a0131c6f50fe00977047272647227bf0dfd5912d09256deb948678","target":"graph","created_at":"2026-05-18T00:18:36Z","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":"Let $G$ be a finite 2-group of maximal nilpotency class, and let $BG$ be its classifying space. We prove that iterated Massey products in $H^*(BG;\\F_2)$ do characterize the homotopy type of $BG$ among 2-complete spaces with the same cohomological structure. As a consequence we get an alternative proof of the modular isomorphism problem for 2-groups of maximal nilpotency class.","authors_text":"Albert Ruiz, Antonio Viruel","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-05T19:00:53Z","title":"Cohomological uniqueness, Massey products and the modular isomorphism problem for 2-groups of maximal nilpotency class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1143","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:ecfe87837fb25e6578101da45218f96187630fa33c17c1c784f4678ecfe16d8e","target":"record","created_at":"2026-05-18T00:18:36Z","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":"ecf6b208e0c283fefdbb7f0d0489a6e0fa8b8b99d590ca8a24fa67a72931486d","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-05T19:00:53Z","title_canon_sha256":"3b5abd8a7324cfc9753967ec566a4471c870cf21f4fd7f839c785cf6a0029d0e"},"schema_version":"1.0","source":{"id":"1105.1143","kind":"arxiv","version":2}},"canonical_sha256":"5364dc66092b369f58575a9cd28344c7371ce7a9ace89477dd1acc0c0c1643b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5364dc66092b369f58575a9cd28344c7371ce7a9ace89477dd1acc0c0c1643b2","first_computed_at":"2026-05-18T00:18:36.592396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:36.592396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gf688YSxiqcgM18wGITqTFxK0yI7C/1MTBtPa+b0eCI8x799rIMMMA0L9HoNc9ERqXqIp8UEvZMIA4Wvpes8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:36.593055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1143","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecfe87837fb25e6578101da45218f96187630fa33c17c1c784f4678ecfe16d8e","sha256:8551b98ed1a0131c6f50fe00977047272647227bf0dfd5912d09256deb948678"],"state_sha256":"4a39efd944f17f6459fb14ecb52f5cdb62669e52e416529ba46625f5ebad328c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g+4CW0LWsRoG85NYJYc8bpRIUAcyyUn78VrMdMJg5kzaUUwf3LaquhM5//O+xqHqyABjbXzAla3sYNeg4hvZAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:47:48.937164Z","bundle_sha256":"398c53588b02f5bbf818eb87b2bba61f63c509d4e0206351a52985a360cc4a1d"}}