{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WIS6LNNUP5NH6JQWGLZD3S4WRB","short_pith_number":"pith:WIS6LNNU","canonical_record":{"source":{"id":"1805.02409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-05-07T09:15:24Z","cross_cats_sorted":[],"title_canon_sha256":"63face2094027c14438df80ba66a8606f0a9512289e34e0c75339baefec76ce2","abstract_canon_sha256":"b41879a8a58a42e617f21b1a58de1ffaf1a10141283a3e8e2d6f30ad6f0d92f0"},"schema_version":"1.0"},"canonical_sha256":"b225e5b5b47f5a7f261632f23dcb96886cc7c1d88acbd8d14e969c4c868de111","source":{"kind":"arxiv","id":"1805.02409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02409","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02409v1","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02409","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"WIS6LNNUP5NH","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WIS6LNNUP5NH6JQW","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WIS6LNNU","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WIS6LNNUP5NH6JQWGLZD3S4WRB","target":"record","payload":{"canonical_record":{"source":{"id":"1805.02409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-05-07T09:15:24Z","cross_cats_sorted":[],"title_canon_sha256":"63face2094027c14438df80ba66a8606f0a9512289e34e0c75339baefec76ce2","abstract_canon_sha256":"b41879a8a58a42e617f21b1a58de1ffaf1a10141283a3e8e2d6f30ad6f0d92f0"},"schema_version":"1.0"},"canonical_sha256":"b225e5b5b47f5a7f261632f23dcb96886cc7c1d88acbd8d14e969c4c868de111","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:40.034966Z","signature_b64":"b2q+SLMQKXg9qlLRFB1IW626ktc8w1PE9yo6hgT5LUtxdSDThSp78owdhNGUUoAn3m1bJUc8KU0i4QkZuL4HCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b225e5b5b47f5a7f261632f23dcb96886cc7c1d88acbd8d14e969c4c868de111","last_reissued_at":"2026-05-18T00:16:40.034554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:40.034554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.02409","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":"2026-05-18T00:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+T4+PtWfXlhcDRjpGDx0nICAd9BB/mLF2I/w+oYZ9KGQI/na4DfH5nQR+wkDHs62wbZWhwYoWSmZhC8x7tBCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:50:55.115075Z"},"content_sha256":"ccd36aac83a3b57354b0c0d9289df000853079919e097ffec860b3a013e3dede","schema_version":"1.0","event_id":"sha256:ccd36aac83a3b57354b0c0d9289df000853079919e097ffec860b3a013e3dede"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WIS6LNNUP5NH6JQWGLZD3S4WRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A zoo of geometric homology theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Matthias Kreck","submitted_at":"2018-05-07T09:15:24Z","abstract_excerpt":"The theories in our zoo are all bordism groups, which generalize the case of smooth manifolds by allowing singularities. There are many concepts of manifolds with singularities one could use here. For our pupose the objects the author introduced some years ago, which are called stratifolds, work particularly well. The zoo comes from forcing certain strata indexed by the subset $A$ to be empty. Special cases are ordinary singular homology and singular bordism.\n  Despite their simple construction computations of these groups seem to be very complicated. We give a few simple examples. Thus there "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02409","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":"2026-05-18T00:16:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZnyXE5BIeFUvTFas8Zkbr+spIJBIVN5yGKa4aPoRfZPyPBnZc4r9KNPHiXuSb0scfgToYzo53Cj1GHU+iyYfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:50:55.115680Z"},"content_sha256":"e68cbe0c57b2ac5911eca544527f302fece4f14e2c3a7b75bf5920f7ac7f59e8","schema_version":"1.0","event_id":"sha256:e68cbe0c57b2ac5911eca544527f302fece4f14e2c3a7b75bf5920f7ac7f59e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WIS6LNNUP5NH6JQWGLZD3S4WRB/bundle.json","state_url":"https://pith.science/pith/WIS6LNNUP5NH6JQWGLZD3S4WRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WIS6LNNUP5NH6JQWGLZD3S4WRB/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":"2026-06-05T20:50:55Z","links":{"resolver":"https://pith.science/pith/WIS6LNNUP5NH6JQWGLZD3S4WRB","bundle":"https://pith.science/pith/WIS6LNNUP5NH6JQWGLZD3S4WRB/bundle.json","state":"https://pith.science/pith/WIS6LNNUP5NH6JQWGLZD3S4WRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WIS6LNNUP5NH6JQWGLZD3S4WRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WIS6LNNUP5NH6JQWGLZD3S4WRB","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":"b41879a8a58a42e617f21b1a58de1ffaf1a10141283a3e8e2d6f30ad6f0d92f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-05-07T09:15:24Z","title_canon_sha256":"63face2094027c14438df80ba66a8606f0a9512289e34e0c75339baefec76ce2"},"schema_version":"1.0","source":{"id":"1805.02409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.02409","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1805.02409v1","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.02409","created_at":"2026-05-18T00:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"WIS6LNNUP5NH","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WIS6LNNUP5NH6JQW","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WIS6LNNU","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:e68cbe0c57b2ac5911eca544527f302fece4f14e2c3a7b75bf5920f7ac7f59e8","target":"graph","created_at":"2026-05-18T00:16:40Z","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 theories in our zoo are all bordism groups, which generalize the case of smooth manifolds by allowing singularities. There are many concepts of manifolds with singularities one could use here. For our pupose the objects the author introduced some years ago, which are called stratifolds, work particularly well. The zoo comes from forcing certain strata indexed by the subset $A$ to be empty. Special cases are ordinary singular homology and singular bordism.\n  Despite their simple construction computations of these groups seem to be very complicated. We give a few simple examples. Thus there ","authors_text":"Matthias Kreck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-05-07T09:15:24Z","title":"A zoo of geometric homology theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02409","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:ccd36aac83a3b57354b0c0d9289df000853079919e097ffec860b3a013e3dede","target":"record","created_at":"2026-05-18T00:16:40Z","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":"b41879a8a58a42e617f21b1a58de1ffaf1a10141283a3e8e2d6f30ad6f0d92f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-05-07T09:15:24Z","title_canon_sha256":"63face2094027c14438df80ba66a8606f0a9512289e34e0c75339baefec76ce2"},"schema_version":"1.0","source":{"id":"1805.02409","kind":"arxiv","version":1}},"canonical_sha256":"b225e5b5b47f5a7f261632f23dcb96886cc7c1d88acbd8d14e969c4c868de111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b225e5b5b47f5a7f261632f23dcb96886cc7c1d88acbd8d14e969c4c868de111","first_computed_at":"2026-05-18T00:16:40.034554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:40.034554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b2q+SLMQKXg9qlLRFB1IW626ktc8w1PE9yo6hgT5LUtxdSDThSp78owdhNGUUoAn3m1bJUc8KU0i4QkZuL4HCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:40.034966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.02409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccd36aac83a3b57354b0c0d9289df000853079919e097ffec860b3a013e3dede","sha256:e68cbe0c57b2ac5911eca544527f302fece4f14e2c3a7b75bf5920f7ac7f59e8"],"state_sha256":"adca060889ddd6346bc5172027c54517e9cee220dc884867618602fd2bb6f8f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nj0c4UHIxsAEtQ6ncnpM027hvUGZecIydi32hvDg7a6ep9HOKk1Aa+SdYP9WlbKFjC+RGMTbyG3OtzlmVRS2Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:50:55.118871Z","bundle_sha256":"c674b6de1fbf68734abe14d38a5a83c2d4b36c4f7cb20ead6fae006cf9801a0c"}}