{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:5FMBV7DKFQLYX5TQEHYIAF2XJG","short_pith_number":"pith:5FMBV7DK","canonical_record":{"source":{"id":"2002.05255","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-02-12T21:58:13Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"f8506e0631a5ea4ff5c262d870e7b7721de5d4c070d34dfc2033415dc4f8fa52","abstract_canon_sha256":"f4b39ea025a9cfae645ca06d14b0e5f43f9fcb80a4cd7bc9f164ffb0cc1f99fe"},"schema_version":"1.0"},"canonical_sha256":"e9581afc6a2c178bf67021f0801757498d6b09031479c0ee24514cb592e80370","source":{"kind":"arxiv","id":"2002.05255","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.05255","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"2002.05255v2","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.05255","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"5FMBV7DKFQLY","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_16","alias_value":"5FMBV7DKFQLYX5TQ","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_8","alias_value":"5FMBV7DK","created_at":"2026-07-05T03:55:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:5FMBV7DKFQLYX5TQEHYIAF2XJG","target":"record","payload":{"canonical_record":{"source":{"id":"2002.05255","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-02-12T21:58:13Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"f8506e0631a5ea4ff5c262d870e7b7721de5d4c070d34dfc2033415dc4f8fa52","abstract_canon_sha256":"f4b39ea025a9cfae645ca06d14b0e5f43f9fcb80a4cd7bc9f164ffb0cc1f99fe"},"schema_version":"1.0"},"canonical_sha256":"e9581afc6a2c178bf67021f0801757498d6b09031479c0ee24514cb592e80370","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:55:24.347880Z","signature_b64":"A2Ckw0bGCqD0KU35zuqVJJUt3TL23ldsl/HP8lrQUKjqTBniGCr0lP4qK4yL+wQEmpZfjo5+32jz8aNQR6CQBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9581afc6a2c178bf67021f0801757498d6b09031479c0ee24514cb592e80370","last_reissued_at":"2026-07-05T03:55:24.347405Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:55:24.347405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.05255","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":"2026-07-05T03:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OAVI+9CiyiYqRpO5eT5TDvPUMCw/TH06Y7xzV7HIY+BFFrCTvSJeNDehuZWqgNY8yryEE74NL0p4z+6BSoOYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-27T11:03:42.051263Z"},"content_sha256":"ea5135557003ff3ca1ce072442829c15032a03badac6c6177d6c0e532407d492","schema_version":"1.0","event_id":"sha256:ea5135557003ff3ca1ce072442829c15032a03badac6c6177d6c0e532407d492"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:5FMBV7DKFQLYX5TQEHYIAF2XJG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Hermitian K-groups via geometric topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Alexander Kupers, Manuel Krannich","submitted_at":"2020-02-12T21:58:13Z","abstract_excerpt":"We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable homology groups of the group of symplectic integral matrices preserving the standard quadratic refinement. The main novelty in our calculation lies in its method, which is based on high-dimensional manifold theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.05255","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.05255/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:55:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGbMHT7r6gZwyT92Y6+6HWQtKfXlVs0TwFRrcPivFmIY7EirhXMTTUYCDbMJAV4Go+e8xQhks+gfnV2W3g8QDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-27T11:03:42.051646Z"},"content_sha256":"d7a6f27a0e2201b713885ccb3f8f8f19cca7c82fab0e8ee75d5a577914520e41","schema_version":"1.0","event_id":"sha256:d7a6f27a0e2201b713885ccb3f8f8f19cca7c82fab0e8ee75d5a577914520e41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FMBV7DKFQLYX5TQEHYIAF2XJG/bundle.json","state_url":"https://pith.science/pith/5FMBV7DKFQLYX5TQEHYIAF2XJG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FMBV7DKFQLYX5TQEHYIAF2XJG/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":"2026-07-27T11:03:42Z","links":{"resolver":"https://pith.science/pith/5FMBV7DKFQLYX5TQEHYIAF2XJG","bundle":"https://pith.science/pith/5FMBV7DKFQLYX5TQEHYIAF2XJG/bundle.json","state":"https://pith.science/pith/5FMBV7DKFQLYX5TQEHYIAF2XJG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FMBV7DKFQLYX5TQEHYIAF2XJG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:5FMBV7DKFQLYX5TQEHYIAF2XJG","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":"f4b39ea025a9cfae645ca06d14b0e5f43f9fcb80a4cd7bc9f164ffb0cc1f99fe","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-02-12T21:58:13Z","title_canon_sha256":"f8506e0631a5ea4ff5c262d870e7b7721de5d4c070d34dfc2033415dc4f8fa52"},"schema_version":"1.0","source":{"id":"2002.05255","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.05255","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"arxiv_version","alias_value":"2002.05255v2","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.05255","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_12","alias_value":"5FMBV7DKFQLY","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_16","alias_value":"5FMBV7DKFQLYX5TQ","created_at":"2026-07-05T03:55:24Z"},{"alias_kind":"pith_short_8","alias_value":"5FMBV7DK","created_at":"2026-07-05T03:55:24Z"}],"graph_snapshots":[{"event_id":"sha256:d7a6f27a0e2201b713885ccb3f8f8f19cca7c82fab0e8ee75d5a577914520e41","target":"graph","created_at":"2026-07-05T03:55:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2002.05255/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable homology groups of the group of symplectic integral matrices preserving the standard quadratic refinement. The main novelty in our calculation lies in its method, which is based on high-dimensional manifold theory.","authors_text":"Alexander Kupers, Manuel Krannich","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-02-12T21:58:13Z","title":"Some Hermitian K-groups via geometric topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.05255","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:ea5135557003ff3ca1ce072442829c15032a03badac6c6177d6c0e532407d492","target":"record","created_at":"2026-07-05T03:55:24Z","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":"f4b39ea025a9cfae645ca06d14b0e5f43f9fcb80a4cd7bc9f164ffb0cc1f99fe","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2020-02-12T21:58:13Z","title_canon_sha256":"f8506e0631a5ea4ff5c262d870e7b7721de5d4c070d34dfc2033415dc4f8fa52"},"schema_version":"1.0","source":{"id":"2002.05255","kind":"arxiv","version":2}},"canonical_sha256":"e9581afc6a2c178bf67021f0801757498d6b09031479c0ee24514cb592e80370","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9581afc6a2c178bf67021f0801757498d6b09031479c0ee24514cb592e80370","first_computed_at":"2026-07-05T03:55:24.347405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:55:24.347405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A2Ckw0bGCqD0KU35zuqVJJUt3TL23ldsl/HP8lrQUKjqTBniGCr0lP4qK4yL+wQEmpZfjo5+32jz8aNQR6CQBA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:55:24.347880Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.05255","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea5135557003ff3ca1ce072442829c15032a03badac6c6177d6c0e532407d492","sha256:d7a6f27a0e2201b713885ccb3f8f8f19cca7c82fab0e8ee75d5a577914520e41"],"state_sha256":"d79eedee4917359c7594a09d063238294854b87e3d1923360a4649a3ad8208f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Q7FpYvRGzWWbIo0nu6uxBtY5rl8Mc5kgFTgj/uNhyhthSBpvMF6MFGejJfzS9iWJfr0flppMtiHpE4vO+evBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-27T11:03:42.054098Z","bundle_sha256":"05960c2fe31e5d0ebeb32957584897bc1e7b3c80bd4823f10d5a6621850a1963"}}