{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EYLHARUCZ2YGIVG56WCVZVRPMZ","short_pith_number":"pith:EYLHARUC","canonical_record":{"source":{"id":"1505.04561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-18T09:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"9264bc2034476a31acc915b1007554e377ccc0d94a922904609c8b2364797d7b","abstract_canon_sha256":"6aa52866504a0841c604abe441bbb93b487aa64d47b110a7ec0fe83cfe64caee"},"schema_version":"1.0"},"canonical_sha256":"2616704682ceb06454ddf5855cd62f6671a7078986d83f45fcebd5305c676b21","source":{"kind":"arxiv","id":"1505.04561","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04561","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04561v1","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04561","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"pith_short_12","alias_value":"EYLHARUCZ2YG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EYLHARUCZ2YGIVG5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EYLHARUC","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EYLHARUCZ2YGIVG56WCVZVRPMZ","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-18T09:10:56Z","cross_cats_sorted":[],"title_canon_sha256":"9264bc2034476a31acc915b1007554e377ccc0d94a922904609c8b2364797d7b","abstract_canon_sha256":"6aa52866504a0841c604abe441bbb93b487aa64d47b110a7ec0fe83cfe64caee"},"schema_version":"1.0"},"canonical_sha256":"2616704682ceb06454ddf5855cd62f6671a7078986d83f45fcebd5305c676b21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:46.754878Z","signature_b64":"g3hXiVnBIW5zWrW7H2L+FGNksZXPOXj3SVmknuZzmuLUa45ze2xGOm0u/pKuLtBIQtAgMFhiDU3pVG6JMTzmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2616704682ceb06454ddf5855cd62f6671a7078986d83f45fcebd5305c676b21","last_reissued_at":"2026-05-18T01:15:46.754248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:46.754248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04561","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":"2026-05-18T01:15:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YflYKCTPUQSAioN+Rpi3QLjIwQ2NH6hN5xAYje/KbpP5SSmGOwe+8bGAokp/SeXsmO1cmF72rANV3zR4218Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:33:37.793037Z"},"content_sha256":"8f53c34c63f055371f34a42ef294bcb6cd1b48a2a4afc64dd080375eb65150cb","schema_version":"1.0","event_id":"sha256:8f53c34c63f055371f34a42ef294bcb6cd1b48a2a4afc64dd080375eb65150cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EYLHARUCZ2YGIVG56WCVZVRPMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants and structures of the homology cobordism group of homology cylinders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Minkyoung Song","submitted_at":"2015-05-18T09:10:56Z","abstract_excerpt":"The homology cobordism group of homology cylinders is a generalization of the mapping class group and the string link concordance group. We study this group and its filtrations by subgroups by developing new homomorphisms. First, we define extended Milnor invariants by combining the ideas of Milnor's link invariants and Johnson homomorphisms. They give rise to a descending filtration of the homology cobordism group of homology cylinders. We show that each successive quotient of the filtration is free abelian of finite rank. Second, we define Hirzebruch-type intersection form defect invariants "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04561","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":"2026-05-18T01:15:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7MNm8ZSu24cLIh/dFptWh2yKiQj1Gh4aag3EBFgOBCnTr5nKtPV9QoulIKN+1xxsb9w5GCFbENKGbk76n6SFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:33:37.793435Z"},"content_sha256":"dd002d05cc8a709144d6034881a8da6304dedc63326dd31033fd41f028f8174a","schema_version":"1.0","event_id":"sha256:dd002d05cc8a709144d6034881a8da6304dedc63326dd31033fd41f028f8174a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYLHARUCZ2YGIVG56WCVZVRPMZ/bundle.json","state_url":"https://pith.science/pith/EYLHARUCZ2YGIVG56WCVZVRPMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYLHARUCZ2YGIVG56WCVZVRPMZ/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":"2026-07-02T10:33:37Z","links":{"resolver":"https://pith.science/pith/EYLHARUCZ2YGIVG56WCVZVRPMZ","bundle":"https://pith.science/pith/EYLHARUCZ2YGIVG56WCVZVRPMZ/bundle.json","state":"https://pith.science/pith/EYLHARUCZ2YGIVG56WCVZVRPMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYLHARUCZ2YGIVG56WCVZVRPMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EYLHARUCZ2YGIVG56WCVZVRPMZ","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":"6aa52866504a0841c604abe441bbb93b487aa64d47b110a7ec0fe83cfe64caee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-18T09:10:56Z","title_canon_sha256":"9264bc2034476a31acc915b1007554e377ccc0d94a922904609c8b2364797d7b"},"schema_version":"1.0","source":{"id":"1505.04561","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04561","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04561v1","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04561","created_at":"2026-05-18T01:15:46Z"},{"alias_kind":"pith_short_12","alias_value":"EYLHARUCZ2YG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EYLHARUCZ2YGIVG5","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EYLHARUC","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:dd002d05cc8a709144d6034881a8da6304dedc63326dd31033fd41f028f8174a","target":"graph","created_at":"2026-05-18T01:15:46Z","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 homology cobordism group of homology cylinders is a generalization of the mapping class group and the string link concordance group. We study this group and its filtrations by subgroups by developing new homomorphisms. First, we define extended Milnor invariants by combining the ideas of Milnor's link invariants and Johnson homomorphisms. They give rise to a descending filtration of the homology cobordism group of homology cylinders. We show that each successive quotient of the filtration is free abelian of finite rank. Second, we define Hirzebruch-type intersection form defect invariants ","authors_text":"Minkyoung Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-18T09:10:56Z","title":"Invariants and structures of the homology cobordism group of homology cylinders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04561","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":"sha256:8f53c34c63f055371f34a42ef294bcb6cd1b48a2a4afc64dd080375eb65150cb","target":"record","created_at":"2026-05-18T01:15:46Z","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":"6aa52866504a0841c604abe441bbb93b487aa64d47b110a7ec0fe83cfe64caee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-05-18T09:10:56Z","title_canon_sha256":"9264bc2034476a31acc915b1007554e377ccc0d94a922904609c8b2364797d7b"},"schema_version":"1.0","source":{"id":"1505.04561","kind":"arxiv","version":1}},"canonical_sha256":"2616704682ceb06454ddf5855cd62f6671a7078986d83f45fcebd5305c676b21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2616704682ceb06454ddf5855cd62f6671a7078986d83f45fcebd5305c676b21","first_computed_at":"2026-05-18T01:15:46.754248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:46.754248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g3hXiVnBIW5zWrW7H2L+FGNksZXPOXj3SVmknuZzmuLUa45ze2xGOm0u/pKuLtBIQtAgMFhiDU3pVG6JMTzmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:46.754878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04561","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f53c34c63f055371f34a42ef294bcb6cd1b48a2a4afc64dd080375eb65150cb","sha256:dd002d05cc8a709144d6034881a8da6304dedc63326dd31033fd41f028f8174a"],"state_sha256":"4b8cbd9ef8bf935b22d0ef4505f75485723134080858b1eb02027fda3fa9fbb1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nhpFQO0odv9UmqbJYAqhDEgdd9ibj2Al6+hZLv6XTbTUFP9oqf/yqbZChPSOhTEcgS8XulD2OTEt/HKG/vTNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T10:33:37.795399Z","bundle_sha256":"cc12b7e213a769dbb61638d8aea5753b289ffbe60d8f99b53375c05750697896"}}