{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TWK5USYHJEM3J435IALT4FLEMP","short_pith_number":"pith:TWK5USYH","schema_version":"1.0","canonical_sha256":"9d95da4b074919b4f37d40173e156463f0cb7c1395247418c5dfd99dd1becf6e","source":{"kind":"arxiv","id":"1605.00250","version":2},"attestation_state":"computed","paper":{"title":"Shadows of 4-manifolds with complexity zero and polyhedral collapsing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hironobu Naoe","submitted_at":"2016-05-01T13:16:43Z","abstract_excerpt":"Our purpose is to classify acyclic 4-manifolds having shadow complexity zero. In this paper, we focus on simple polyhedra and discuss this problem combinatorially. We consider a shadowed polyhedron $X$ and a simple polyhedron $X_0$ that is obtained by collapsing from $X$. Then we prove that there exists a canonical way to equip internal regions of $X_0$ with gleams so that two 4-manifolds reconstructed from $X_0$ and $X$ are diffeomorphic. We also show that any acyclic simple polyhedron whose singular set is a union of circles can collapse onto a disk. As a consequence of these results, we pro"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.00250","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-05-01T13:16:43Z","cross_cats_sorted":[],"title_canon_sha256":"31026e75a3dd7f9de696a0648fee0e50f091a30553897a9f13859af6db8eb6b6","abstract_canon_sha256":"1b5175fd1696f8b16f5979d87f4d91d67a2584fd967e7ab3cb9407bfa4050aec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:23.390927Z","signature_b64":"5Tmz30d97YV49G9rhGPLjUGTduQrpDWI2cnWYNpXtnMfNpCqU5VrzuF692dwmiXibRtvXjRqC0wNbIplLGaRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d95da4b074919b4f37d40173e156463f0cb7c1395247418c5dfd99dd1becf6e","last_reissued_at":"2026-05-18T00:52:23.390292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:23.390292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shadows of 4-manifolds with complexity zero and polyhedral collapsing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hironobu Naoe","submitted_at":"2016-05-01T13:16:43Z","abstract_excerpt":"Our purpose is to classify acyclic 4-manifolds having shadow complexity zero. In this paper, we focus on simple polyhedra and discuss this problem combinatorially. We consider a shadowed polyhedron $X$ and a simple polyhedron $X_0$ that is obtained by collapsing from $X$. Then we prove that there exists a canonical way to equip internal regions of $X_0$ with gleams so that two 4-manifolds reconstructed from $X_0$ and $X$ are diffeomorphic. We also show that any acyclic simple polyhedron whose singular set is a union of circles can collapse onto a disk. As a consequence of these results, we pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00250","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.00250","created_at":"2026-05-18T00:52:23.390406+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.00250v2","created_at":"2026-05-18T00:52:23.390406+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00250","created_at":"2026-05-18T00:52:23.390406+00:00"},{"alias_kind":"pith_short_12","alias_value":"TWK5USYHJEM3","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"TWK5USYHJEM3J435","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"TWK5USYH","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP","json":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP.json","graph_json":"https://pith.science/api/pith-number/TWK5USYHJEM3J435IALT4FLEMP/graph.json","events_json":"https://pith.science/api/pith-number/TWK5USYHJEM3J435IALT4FLEMP/events.json","paper":"https://pith.science/paper/TWK5USYH"},"agent_actions":{"view_html":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP","download_json":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP.json","view_paper":"https://pith.science/paper/TWK5USYH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.00250&json=true","fetch_graph":"https://pith.science/api/pith-number/TWK5USYHJEM3J435IALT4FLEMP/graph.json","fetch_events":"https://pith.science/api/pith-number/TWK5USYHJEM3J435IALT4FLEMP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP/action/storage_attestation","attest_author":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP/action/author_attestation","sign_citation":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP/action/citation_signature","submit_replication":"https://pith.science/pith/TWK5USYHJEM3J435IALT4FLEMP/action/replication_record"}},"created_at":"2026-05-18T00:52:23.390406+00:00","updated_at":"2026-05-18T00:52:23.390406+00:00"}