{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6YAP7AKRQYCGQ2443GDZPYANJE","short_pith_number":"pith:6YAP7AKR","canonical_record":{"source":{"id":"1210.0995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-03T06:13:24Z","cross_cats_sorted":[],"title_canon_sha256":"647947792f65520c4318a1273adacfe579efa9a344a413549eb893bd85a1d180","abstract_canon_sha256":"60cbf855b2ed3f5ef992efb67d3cdba06c65c770ad9b1bee3f8167e9a7d871f6"},"schema_version":"1.0"},"canonical_sha256":"f600ff81518604686b9cd98797e00d49321e1d10d82393d91be428e41c0109b5","source":{"kind":"arxiv","id":"1210.0995","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0995","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0995v1","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0995","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"6YAP7AKRQYCG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6YAP7AKRQYCGQ244","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6YAP7AKR","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6YAP7AKRQYCGQ2443GDZPYANJE","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0995","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-03T06:13:24Z","cross_cats_sorted":[],"title_canon_sha256":"647947792f65520c4318a1273adacfe579efa9a344a413549eb893bd85a1d180","abstract_canon_sha256":"60cbf855b2ed3f5ef992efb67d3cdba06c65c770ad9b1bee3f8167e9a7d871f6"},"schema_version":"1.0"},"canonical_sha256":"f600ff81518604686b9cd98797e00d49321e1d10d82393d91be428e41c0109b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:13.137767Z","signature_b64":"kILUfQVYkk5FS9sfWXIJwsuTBRdIG6geX9cYc0j4z5+HQQt1yKoJ4QKtOnp+2r90SLMj3kYWyWsKkDxRSGM7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f600ff81518604686b9cd98797e00d49321e1d10d82393d91be428e41c0109b5","last_reissued_at":"2026-05-18T03:44:13.137218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:13.137218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0995","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"thn7OTeJW45KqyNSmMluxC0yyg4929kebQLHzMxYbb4nm4ERgFsh4Ya8fE/nvNxb+1KaNbfIEVmIYqnS0Jr4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:50:26.462334Z"},"content_sha256":"edb3eab3c1383cf1a539fdf97ca0a8de79ebe1e7eb67aaa7d8c97c676e0f49b5","schema_version":"1.0","event_id":"sha256:edb3eab3c1383cf1a539fdf97ca0a8de79ebe1e7eb67aaa7d8c97c676e0f49b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6YAP7AKRQYCGQ2443GDZPYANJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The 2-components of the 31-stem homotopy groups of the 9 and 10-spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Juno Mukai, Tomohisa Inoue","submitted_at":"2012-10-03T06:13:24Z","abstract_excerpt":"Group structures of the 2-primary components of the 31-stem homotopy groups of spheres were studied by Oda in 1979. There are, however, two incompletely determined groups. In this paper, our investigation with Toda's composition method gives structures of them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0995","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8CnbfxZ3VuGh9fMXq3H3MCNBF4dinaUAfGhjxqjLYJV86L2blnckqTgiAgU0672lyQyTeCsRoN7BniUzqdYZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T14:50:26.462684Z"},"content_sha256":"2026c2f8f4b929bf4016a4e3744b3b93008d1cced70d057fd6dc40175d54aa94","schema_version":"1.0","event_id":"sha256:2026c2f8f4b929bf4016a4e3744b3b93008d1cced70d057fd6dc40175d54aa94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YAP7AKRQYCGQ2443GDZPYANJE/bundle.json","state_url":"https://pith.science/pith/6YAP7AKRQYCGQ2443GDZPYANJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YAP7AKRQYCGQ2443GDZPYANJE/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":"2026-06-26T14:50:26Z","links":{"resolver":"https://pith.science/pith/6YAP7AKRQYCGQ2443GDZPYANJE","bundle":"https://pith.science/pith/6YAP7AKRQYCGQ2443GDZPYANJE/bundle.json","state":"https://pith.science/pith/6YAP7AKRQYCGQ2443GDZPYANJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YAP7AKRQYCGQ2443GDZPYANJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6YAP7AKRQYCGQ2443GDZPYANJE","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":"60cbf855b2ed3f5ef992efb67d3cdba06c65c770ad9b1bee3f8167e9a7d871f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-03T06:13:24Z","title_canon_sha256":"647947792f65520c4318a1273adacfe579efa9a344a413549eb893bd85a1d180"},"schema_version":"1.0","source":{"id":"1210.0995","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0995","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0995v1","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0995","created_at":"2026-05-18T03:44:13Z"},{"alias_kind":"pith_short_12","alias_value":"6YAP7AKRQYCG","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6YAP7AKRQYCGQ244","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6YAP7AKR","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:2026c2f8f4b929bf4016a4e3744b3b93008d1cced70d057fd6dc40175d54aa94","target":"graph","created_at":"2026-05-18T03:44:13Z","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":"Group structures of the 2-primary components of the 31-stem homotopy groups of spheres were studied by Oda in 1979. There are, however, two incompletely determined groups. In this paper, our investigation with Toda's composition method gives structures of them.","authors_text":"Juno Mukai, Tomohisa Inoue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-03T06:13:24Z","title":"The 2-components of the 31-stem homotopy groups of the 9 and 10-spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0995","kind":"arxiv","version":1},"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:edb3eab3c1383cf1a539fdf97ca0a8de79ebe1e7eb67aaa7d8c97c676e0f49b5","target":"record","created_at":"2026-05-18T03:44:13Z","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":"60cbf855b2ed3f5ef992efb67d3cdba06c65c770ad9b1bee3f8167e9a7d871f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-10-03T06:13:24Z","title_canon_sha256":"647947792f65520c4318a1273adacfe579efa9a344a413549eb893bd85a1d180"},"schema_version":"1.0","source":{"id":"1210.0995","kind":"arxiv","version":1}},"canonical_sha256":"f600ff81518604686b9cd98797e00d49321e1d10d82393d91be428e41c0109b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f600ff81518604686b9cd98797e00d49321e1d10d82393d91be428e41c0109b5","first_computed_at":"2026-05-18T03:44:13.137218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:13.137218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kILUfQVYkk5FS9sfWXIJwsuTBRdIG6geX9cYc0j4z5+HQQt1yKoJ4QKtOnp+2r90SLMj3kYWyWsKkDxRSGM7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:13.137767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edb3eab3c1383cf1a539fdf97ca0a8de79ebe1e7eb67aaa7d8c97c676e0f49b5","sha256:2026c2f8f4b929bf4016a4e3744b3b93008d1cced70d057fd6dc40175d54aa94"],"state_sha256":"fb8dcc3835b195342015d6d3deb114f2dcc64a0a50cfd4ecfde2b9e609e1f5bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fV6KQ6KaFygTMKQw78uA4cbFQla/VoQeWin5EZZ6skyWy2tl/IaA1Jh1dppUE/7HZ2Fjc+13qX9d8CgF0cjlCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T14:50:26.464565Z","bundle_sha256":"845a7ca1143a0a94ee327c541c78e42e35e2a7270e7c225a5f0f4863727cd3cc"}}