{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:FISONX4EPICI7RYPYPXKGO6MJZ","short_pith_number":"pith:FISONX4E","canonical_record":{"source":{"id":"0907.0308","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T16:45:32Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"cd3b162a90ae2cb17b0614f7e3c4abe42b41e9b184f47c14e259401e7283ad37","abstract_canon_sha256":"a5a381137ae84d35b5d0a1e9c834def9367db7ef46655161dd92717015882b68"},"schema_version":"1.0"},"canonical_sha256":"2a24e6df847a048fc70fc3eea33bcc4e6d96d246228d217cf783b30110348d84","source":{"kind":"arxiv","id":"0907.0308","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0308","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0308v5","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0308","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"FISONX4EPICI","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FISONX4EPICI7RYP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FISONX4E","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:FISONX4EPICI7RYPYPXKGO6MJZ","target":"record","payload":{"canonical_record":{"source":{"id":"0907.0308","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T16:45:32Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"cd3b162a90ae2cb17b0614f7e3c4abe42b41e9b184f47c14e259401e7283ad37","abstract_canon_sha256":"a5a381137ae84d35b5d0a1e9c834def9367db7ef46655161dd92717015882b68"},"schema_version":"1.0"},"canonical_sha256":"2a24e6df847a048fc70fc3eea33bcc4e6d96d246228d217cf783b30110348d84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:23.491574Z","signature_b64":"qmnRgOAVrZKQt2I1ppAnvW4csd5qUb/mCTktFSoQNvO4EmtYG3mog0nausOLmzNZXSgaRqZsek6HlevsOq+KDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a24e6df847a048fc70fc3eea33bcc4e6d96d246228d217cf783b30110348d84","last_reissued_at":"2026-05-18T03:45:23.491057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:23.491057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.0308","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jwAGuWosuQloURjhHPlrar4a/uxeRr9OhN+tsi0mQ2D7of/HyT3icjhzGyFtP/td20yhcK8mz51DkTqAPJhnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:01:31.174409Z"},"content_sha256":"2020174aa2f7c5c326bd8120b45a3b2afe3fc0211928696cf62ee5e701f669f0","schema_version":"1.0","event_id":"sha256:2020174aa2f7c5c326bd8120b45a3b2afe3fc0211928696cf62ee5e701f669f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:FISONX4EPICI7RYPYPXKGO6MJZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy invariance of 4-manifold decompositions: connected sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Qayum Khan","submitted_at":"2009-07-02T16:45:32Z","abstract_excerpt":"We show, up to h-cobordism, that the existence and uniqueness of connected sum decompositions of oriented 4-dimensional manifolds is an invariant of homotopy equivalence, assuming that the fundamental group of each summand is \"good\" in the sense of Freedman and Quinn. On a separate note, we observe that the Borel Conjecture is true in dimension 4 up to s-cobordism, assuming that the fundamental group satisfies the Farrell--Jones Conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0308","kind":"arxiv","version":5},"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":"2026-05-18T03:45:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aOkq8jQyHqqDs9xpgdJ/tx6VO2PVEgilyoo/EAlmhXvhGScCg4Y+OCSjDQp9uH2WrSWDHAwyUkDzSWiszaMCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T13:01:31.174767Z"},"content_sha256":"a301cbde53a4bb254c202d8b366e8d7dff8069afe32cc4b78e689490a6950ef9","schema_version":"1.0","event_id":"sha256:a301cbde53a4bb254c202d8b366e8d7dff8069afe32cc4b78e689490a6950ef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FISONX4EPICI7RYPYPXKGO6MJZ/bundle.json","state_url":"https://pith.science/pith/FISONX4EPICI7RYPYPXKGO6MJZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FISONX4EPICI7RYPYPXKGO6MJZ/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":"2026-06-06T13:01:31Z","links":{"resolver":"https://pith.science/pith/FISONX4EPICI7RYPYPXKGO6MJZ","bundle":"https://pith.science/pith/FISONX4EPICI7RYPYPXKGO6MJZ/bundle.json","state":"https://pith.science/pith/FISONX4EPICI7RYPYPXKGO6MJZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FISONX4EPICI7RYPYPXKGO6MJZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FISONX4EPICI7RYPYPXKGO6MJZ","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":"a5a381137ae84d35b5d0a1e9c834def9367db7ef46655161dd92717015882b68","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T16:45:32Z","title_canon_sha256":"cd3b162a90ae2cb17b0614f7e3c4abe42b41e9b184f47c14e259401e7283ad37"},"schema_version":"1.0","source":{"id":"0907.0308","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.0308","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"arxiv_version","alias_value":"0907.0308v5","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.0308","created_at":"2026-05-18T03:45:23Z"},{"alias_kind":"pith_short_12","alias_value":"FISONX4EPICI","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FISONX4EPICI7RYP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FISONX4E","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:a301cbde53a4bb254c202d8b366e8d7dff8069afe32cc4b78e689490a6950ef9","target":"graph","created_at":"2026-05-18T03:45:23Z","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 show, up to h-cobordism, that the existence and uniqueness of connected sum decompositions of oriented 4-dimensional manifolds is an invariant of homotopy equivalence, assuming that the fundamental group of each summand is \"good\" in the sense of Freedman and Quinn. On a separate note, we observe that the Borel Conjecture is true in dimension 4 up to s-cobordism, assuming that the fundamental group satisfies the Farrell--Jones Conjecture.","authors_text":"Qayum Khan","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T16:45:32Z","title":"Homotopy invariance of 4-manifold decompositions: connected sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.0308","kind":"arxiv","version":5},"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":"sha256:2020174aa2f7c5c326bd8120b45a3b2afe3fc0211928696cf62ee5e701f669f0","target":"record","created_at":"2026-05-18T03:45:23Z","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":"a5a381137ae84d35b5d0a1e9c834def9367db7ef46655161dd92717015882b68","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-07-02T16:45:32Z","title_canon_sha256":"cd3b162a90ae2cb17b0614f7e3c4abe42b41e9b184f47c14e259401e7283ad37"},"schema_version":"1.0","source":{"id":"0907.0308","kind":"arxiv","version":5}},"canonical_sha256":"2a24e6df847a048fc70fc3eea33bcc4e6d96d246228d217cf783b30110348d84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a24e6df847a048fc70fc3eea33bcc4e6d96d246228d217cf783b30110348d84","first_computed_at":"2026-05-18T03:45:23.491057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:23.491057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qmnRgOAVrZKQt2I1ppAnvW4csd5qUb/mCTktFSoQNvO4EmtYG3mog0nausOLmzNZXSgaRqZsek6HlevsOq+KDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:23.491574Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.0308","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2020174aa2f7c5c326bd8120b45a3b2afe3fc0211928696cf62ee5e701f669f0","sha256:a301cbde53a4bb254c202d8b366e8d7dff8069afe32cc4b78e689490a6950ef9"],"state_sha256":"35516b71f34592778b30a55f88bd3823fc4ab7a4afd540cd1b0ecdff8f6c3cde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DiSZHZs1euF06V+1ZF579fAnzWm/VamQjEUoq+jMGgz9iDhQtoEwQqbeWBaKCbmadvX0A9odTNsvNxHnCEDbCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T13:01:31.177079Z","bundle_sha256":"1182bfa36a45e678f59261e17f4df75596265f772ac2a9c0a3bf78a88524ca06"}}