{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:XXKR46IMS3NSFDI5WUD3NXPPO5","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":"c1d789fa53a6bc5cd1d02a7bf272b8e7ad2ccf88f9d6fba52ee7c4716b5d0cde","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AT","submitted_at":"2005-12-21T02:43:55Z","title_canon_sha256":"a46e324f5414d69cb2a56da936dd05bf61c0a6b6305b2d2c80ff7f7c0017ea60"},"schema_version":"1.0","source":{"id":"math/0512479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512479","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512479v1","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512479","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"XXKR46IMS3NS","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"XXKR46IMS3NSFDI5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"XXKR46IM","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:01f5f307ed0a58a392c555acb9e0f4a9452e73a41aa76e589dadfd9fae7b0cae","target":"graph","created_at":"2026-05-18T02:37:59Z","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":"We give a new approach to intersection theory. Our \"cycles\" are closed manifolds mapping into compact manifolds and our \"intersections\" are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn, but our proofs are fundamentally different.","authors_text":"E. Bruce Williams, John R. Klein","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2005-12-21T02:43:55Z","title":"Homotopical Intersection Theory, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512479","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":"sha256:9b66fb37069f96753d24c360330770f21d5b960c8e60a860e50916e480fccb26","target":"record","created_at":"2026-05-18T02:37:59Z","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":"c1d789fa53a6bc5cd1d02a7bf272b8e7ad2ccf88f9d6fba52ee7c4716b5d0cde","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.AT","submitted_at":"2005-12-21T02:43:55Z","title_canon_sha256":"a46e324f5414d69cb2a56da936dd05bf61c0a6b6305b2d2c80ff7f7c0017ea60"},"schema_version":"1.0","source":{"id":"math/0512479","kind":"arxiv","version":1}},"canonical_sha256":"bdd51e790c96db228d1db507b6ddef7765e63ecad5a67c45933cae63541f3fe4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdd51e790c96db228d1db507b6ddef7765e63ecad5a67c45933cae63541f3fe4","first_computed_at":"2026-05-18T02:37:59.659946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:59.659946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"04RS3EIgF1kZCI+g4LBps8DiFKmGzRlsj6xeThs0aYR8e95Fdy/9WD7PVb50YI/m6ppp+v/q3smy6/MEq2HjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:59.660334Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b66fb37069f96753d24c360330770f21d5b960c8e60a860e50916e480fccb26","sha256:01f5f307ed0a58a392c555acb9e0f4a9452e73a41aa76e589dadfd9fae7b0cae"],"state_sha256":"e089616d83ba7c40fe78786d359548e3bb11b77c7f5c47d33af3264149febfcf"}