{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C3OU2XCTG62YG5JNA6RSFHI5WD","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":"5ebe72ba51cf08134234671ac7755b04d82d4151629df05462ccb5a1dcf993fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-22T13:40:26Z","title_canon_sha256":"5f6fa793bfb5caad1b87abec4579dd22dcc7fca2e90763baa335f9c7beef1204"},"schema_version":"1.0","source":{"id":"1401.5665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5665","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5665v1","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5665","created_at":"2026-05-18T03:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"C3OU2XCTG62Y","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C3OU2XCTG62YG5JN","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C3OU2XCT","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:1c2561a5353f4445261b81a5f00c94b97808fc1ff3b7dbfab438d89366b97eef","target":"graph","created_at":"2026-05-18T03:01:25Z","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 following result has been shown recently in the form of a dichotomy: For every total clone $C$ on $\\mathbf{2} := \\{0,1\\}$, the set $\\mathcal{I}(C)$ of all partial clones on $\\mathbf{2}$ whose total component is $C$, is either finite or of continuum cardinality. In this paper we show that the dichotomy holds, even if only strong partial clones are considered, i.e., partial clones which are closed under taking subfunctions: For every total clone $C$ on $\\mathbf{2}$, the set $\\mathcal{I}_{\\mathrm{Str}}(C)$ of all strong partial clones on $\\mathbf{2}$ whose total component is $C$, is either fi","authors_text":"Karsten Sch\\\"olzel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-22T13:40:26Z","title":"Dichotomy on intervals of strong partial Boolean clones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5665","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":"sha256:8c571d1d91031dbb08235d195912b1f162efef621168226bacf7d7cee8a8362d","target":"record","created_at":"2026-05-18T03:01:25Z","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":"5ebe72ba51cf08134234671ac7755b04d82d4151629df05462ccb5a1dcf993fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-22T13:40:26Z","title_canon_sha256":"5f6fa793bfb5caad1b87abec4579dd22dcc7fca2e90763baa335f9c7beef1204"},"schema_version":"1.0","source":{"id":"1401.5665","kind":"arxiv","version":1}},"canonical_sha256":"16dd4d5c5337b583752d07a3229d1db0c73b51ae8835870dbc3db5a268c6112c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16dd4d5c5337b583752d07a3229d1db0c73b51ae8835870dbc3db5a268c6112c","first_computed_at":"2026-05-18T03:01:25.039592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:25.039592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dA0fEQkOneTFFrLMAQcbFRp5smokKJEfDA/QSLIBzHq0rOvZ7au5FC4KjgSLP7fy/iJTCUPkrrjhEhFBv4S0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:25.040241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c571d1d91031dbb08235d195912b1f162efef621168226bacf7d7cee8a8362d","sha256:1c2561a5353f4445261b81a5f00c94b97808fc1ff3b7dbfab438d89366b97eef"],"state_sha256":"62aead78651af3f2602352169b1697918ed88f64a65d0ae73f250796e2170160"}