{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6SGPUIYUE4TCVZYMMZVGTQI5LV","short_pith_number":"pith:6SGPUIYU","canonical_record":{"source":{"id":"1803.06811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-03-19T06:14:55Z","cross_cats_sorted":[],"title_canon_sha256":"1739a17ca569d85c2cf1f0025ba37ddccfaf7410b3305a1a8641a4891cea688b","abstract_canon_sha256":"2f78c1abe869e3d3be7d7b4d0cebc50c6a8be7500040a40d508f162627eff7cf"},"schema_version":"1.0"},"canonical_sha256":"f48cfa231427262ae70c666a69c11d5d68e4a27a9cf85552126c039e322539c8","source":{"kind":"arxiv","id":"1803.06811","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06811","created_at":"2026-05-18T00:20:41Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06811v1","created_at":"2026-05-18T00:20:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06811","created_at":"2026-05-18T00:20:41Z"},{"alias_kind":"pith_short_12","alias_value":"6SGPUIYUE4TC","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6SGPUIYUE4TCVZYM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6SGPUIYU","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6SGPUIYUE4TCVZYMMZVGTQI5LV","target":"record","payload":{"canonical_record":{"source":{"id":"1803.06811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-03-19T06:14:55Z","cross_cats_sorted":[],"title_canon_sha256":"1739a17ca569d85c2cf1f0025ba37ddccfaf7410b3305a1a8641a4891cea688b","abstract_canon_sha256":"2f78c1abe869e3d3be7d7b4d0cebc50c6a8be7500040a40d508f162627eff7cf"},"schema_version":"1.0"},"canonical_sha256":"f48cfa231427262ae70c666a69c11d5d68e4a27a9cf85552126c039e322539c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:41.290722Z","signature_b64":"R9AWmbLlhSNJRQ5aICdGU/OlV8Lj0M7cWE12gLfcYExPgY3GPVrhnvpBJAw1yoPaC1gRHFzzli6HPmpn/PO5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f48cfa231427262ae70c666a69c11d5d68e4a27a9cf85552126c039e322539c8","last_reissued_at":"2026-05-18T00:20:41.290005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:41.290005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.06811","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":"2026-05-18T00:20:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/M2rau/wQhnzrg+oDSf3VEwLFfL6dn+vgSZG5iH064NDoWymEiBAO5d44z0f+8PrfXw25AAy9cILmI7Xl5y0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:35:09.216432Z"},"content_sha256":"1bb749d05b34fb07f11875665b76331f98d32dd46835f34f8099ad2734d9c90d","schema_version":"1.0","event_id":"sha256:1bb749d05b34fb07f11875665b76331f98d32dd46835f34f8099ad2734d9c90d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6SGPUIYUE4TCVZYMMZVGTQI5LV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorical Buechi and Parity Conditions via Alternating Fixed Points of Functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Ichiro Hasuo, Natsuki Urabe","submitted_at":"2018-03-19T06:14:55Z","abstract_excerpt":"Categorical studies of recursive data structures and their associated reasoning principles have mostly focused on two extremes: initial algebras and induction, and final coalgebras and coinduction. In this paper we study their in-betweens. We formalize notions of alternating fixed points of functors using constructions that are similar to that of free monads. We find their use in categorical modeling of accepting run trees under the Buechi and parity acceptance condition. This modeling abstracts away from states of an automaton; it can thus be thought of as the \"behaviors\" of systems with the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06811","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":"2026-05-18T00:20:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3bOZu2BedS0oVZLN5LGIDgPPBtaEMlHn1oXjTd5mL2pPC8ESX6rO0yaeW9hHvkR+SCj+3BeKPgiFd0qVkoofBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:35:09.217397Z"},"content_sha256":"15706b959be67f8aa5fcc2438e7de5f5a7dd8a49008fa60b909a4d083a12f39f","schema_version":"1.0","event_id":"sha256:15706b959be67f8aa5fcc2438e7de5f5a7dd8a49008fa60b909a4d083a12f39f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6SGPUIYUE4TCVZYMMZVGTQI5LV/bundle.json","state_url":"https://pith.science/pith/6SGPUIYUE4TCVZYMMZVGTQI5LV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6SGPUIYUE4TCVZYMMZVGTQI5LV/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":"2026-05-30T22:35:09Z","links":{"resolver":"https://pith.science/pith/6SGPUIYUE4TCVZYMMZVGTQI5LV","bundle":"https://pith.science/pith/6SGPUIYUE4TCVZYMMZVGTQI5LV/bundle.json","state":"https://pith.science/pith/6SGPUIYUE4TCVZYMMZVGTQI5LV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6SGPUIYUE4TCVZYMMZVGTQI5LV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6SGPUIYUE4TCVZYMMZVGTQI5LV","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":"2f78c1abe869e3d3be7d7b4d0cebc50c6a8be7500040a40d508f162627eff7cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-03-19T06:14:55Z","title_canon_sha256":"1739a17ca569d85c2cf1f0025ba37ddccfaf7410b3305a1a8641a4891cea688b"},"schema_version":"1.0","source":{"id":"1803.06811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.06811","created_at":"2026-05-18T00:20:41Z"},{"alias_kind":"arxiv_version","alias_value":"1803.06811v1","created_at":"2026-05-18T00:20:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.06811","created_at":"2026-05-18T00:20:41Z"},{"alias_kind":"pith_short_12","alias_value":"6SGPUIYUE4TC","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6SGPUIYUE4TCVZYM","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6SGPUIYU","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:15706b959be67f8aa5fcc2438e7de5f5a7dd8a49008fa60b909a4d083a12f39f","target":"graph","created_at":"2026-05-18T00:20:41Z","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":"Categorical studies of recursive data structures and their associated reasoning principles have mostly focused on two extremes: initial algebras and induction, and final coalgebras and coinduction. In this paper we study their in-betweens. We formalize notions of alternating fixed points of functors using constructions that are similar to that of free monads. We find their use in categorical modeling of accepting run trees under the Buechi and parity acceptance condition. This modeling abstracts away from states of an automaton; it can thus be thought of as the \"behaviors\" of systems with the ","authors_text":"Ichiro Hasuo, Natsuki Urabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-03-19T06:14:55Z","title":"Categorical Buechi and Parity Conditions via Alternating Fixed Points of Functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.06811","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":"sha256:1bb749d05b34fb07f11875665b76331f98d32dd46835f34f8099ad2734d9c90d","target":"record","created_at":"2026-05-18T00:20:41Z","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":"2f78c1abe869e3d3be7d7b4d0cebc50c6a8be7500040a40d508f162627eff7cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-03-19T06:14:55Z","title_canon_sha256":"1739a17ca569d85c2cf1f0025ba37ddccfaf7410b3305a1a8641a4891cea688b"},"schema_version":"1.0","source":{"id":"1803.06811","kind":"arxiv","version":1}},"canonical_sha256":"f48cfa231427262ae70c666a69c11d5d68e4a27a9cf85552126c039e322539c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f48cfa231427262ae70c666a69c11d5d68e4a27a9cf85552126c039e322539c8","first_computed_at":"2026-05-18T00:20:41.290005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:41.290005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R9AWmbLlhSNJRQ5aICdGU/OlV8Lj0M7cWE12gLfcYExPgY3GPVrhnvpBJAw1yoPaC1gRHFzzli6HPmpn/PO5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:41.290722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.06811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bb749d05b34fb07f11875665b76331f98d32dd46835f34f8099ad2734d9c90d","sha256:15706b959be67f8aa5fcc2438e7de5f5a7dd8a49008fa60b909a4d083a12f39f"],"state_sha256":"bbfbc98171563a37414c9426a5b628e83cd6d567c35343dc4cec016cc5622120"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S8ExJJEVq2EVT43yAygWH49omiDyh7N2BsJMJYVrUZ14TbZdFaKYxYvW0xAD3SRi9Ostba4I2TCdwDL62eE6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:35:09.221873Z","bundle_sha256":"c29a48bb445f95f346138ef6e5e855569ae81d4e170cd66051d847b077e56c37"}}