{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5C2JVHQVOXP2Y75W5OJFX5HNIO","short_pith_number":"pith:5C2JVHQV","canonical_record":{"source":{"id":"1710.10408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-28T07:29:16Z","cross_cats_sorted":[],"title_canon_sha256":"81efce27db553a80eea8a4eb509167e6ab402df0fc14172c37836609671de056","abstract_canon_sha256":"b07fcc93a987b3ee6d5b5603b0f9d2e22b325b7eec31774ec212a713910e618f"},"schema_version":"1.0"},"canonical_sha256":"e8b49a9e1575dfac7fb6eb925bf4ed43a98ec4db799579681d9fe74e884462a3","source":{"kind":"arxiv","id":"1710.10408","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10408","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10408v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10408","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"5C2JVHQVOXP2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5C2JVHQVOXP2Y75W","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5C2JVHQV","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5C2JVHQVOXP2Y75W5OJFX5HNIO","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-28T07:29:16Z","cross_cats_sorted":[],"title_canon_sha256":"81efce27db553a80eea8a4eb509167e6ab402df0fc14172c37836609671de056","abstract_canon_sha256":"b07fcc93a987b3ee6d5b5603b0f9d2e22b325b7eec31774ec212a713910e618f"},"schema_version":"1.0"},"canonical_sha256":"e8b49a9e1575dfac7fb6eb925bf4ed43a98ec4db799579681d9fe74e884462a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:49.614140Z","signature_b64":"PZTTcw1vXZ2AtSV5XMsoAK2k+wgE0ybb5Y8Rgho/Fg8pCOwxnqny0tTlLb1Os6E1aejtrZhjFeZl4/zetxENCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8b49a9e1575dfac7fb6eb925bf4ed43a98ec4db799579681d9fe74e884462a3","last_reissued_at":"2026-05-18T00:31:49.613423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:49.613423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10408","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":"2026-05-18T00:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q6ud4PkhLdigBiWdGV91/hJZKD5pMR5WuKhKTM/saAjoo/uOm57lVtn+GTgRMecgW+DlhYoSTe4Af0vR7oxtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:09:17.179954Z"},"content_sha256":"c85d847e879a925e4374b5d9b2442e86940d65a62336729e0280635f3b62fa59","schema_version":"1.0","event_id":"sha256:c85d847e879a925e4374b5d9b2442e86940d65a62336729e0280635f3b62fa59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5C2JVHQVOXP2Y75W5OJFX5HNIO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric Implication Zroupoids and Weak Associative Laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Hanamantagouda P. Sankappanavar, Juan M. Cornejo","submitted_at":"2017-10-28T07:29:16Z","abstract_excerpt":"An algebra $\\mathbf A = \\langle A, \\to, 0 \\rangle$, where $\\to$ is binary and $0$ is a constant, is called an implication zroupoid ($\\mathcal I$-zroupoid, for short) if $\\mathbf A$ satisfies the identities: $(x \\to y) \\to z \\approx ((z' \\to x) \\to (y \\to z)')'$ and $0'' \\approx 0$, where $x' : = x \\to 0$. An implication zroupoid is symmetric if it satisfies $x'' \\approx x$ and $(x \\to y')' \\approx (y \\to x')'$. The variety of symmetric $\\mathcal I$-zroupoids is denoted by $\\mathcal S$. We began a systematic analysis of weak associative laws of length $\\leq 4$ in [CS16e], by examining the ident"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10408","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":"2026-05-18T00:31:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DAtwjQ4E4IyyuZmVBNXXBC7QShw0cdUp5vKa7My+Qo+YVUkXSU6666abfEwsi335WsrfQ0Yw4PNNietO628/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:09:17.182716Z"},"content_sha256":"2bfb9997f730688244d436c465a2e035b5bb1e2ebc4765bdf704397072c10a50","schema_version":"1.0","event_id":"sha256:2bfb9997f730688244d436c465a2e035b5bb1e2ebc4765bdf704397072c10a50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5C2JVHQVOXP2Y75W5OJFX5HNIO/bundle.json","state_url":"https://pith.science/pith/5C2JVHQVOXP2Y75W5OJFX5HNIO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5C2JVHQVOXP2Y75W5OJFX5HNIO/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":"2026-06-01T02:09:17Z","links":{"resolver":"https://pith.science/pith/5C2JVHQVOXP2Y75W5OJFX5HNIO","bundle":"https://pith.science/pith/5C2JVHQVOXP2Y75W5OJFX5HNIO/bundle.json","state":"https://pith.science/pith/5C2JVHQVOXP2Y75W5OJFX5HNIO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5C2JVHQVOXP2Y75W5OJFX5HNIO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5C2JVHQVOXP2Y75W5OJFX5HNIO","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":"b07fcc93a987b3ee6d5b5603b0f9d2e22b325b7eec31774ec212a713910e618f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-28T07:29:16Z","title_canon_sha256":"81efce27db553a80eea8a4eb509167e6ab402df0fc14172c37836609671de056"},"schema_version":"1.0","source":{"id":"1710.10408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10408","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10408v1","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10408","created_at":"2026-05-18T00:31:49Z"},{"alias_kind":"pith_short_12","alias_value":"5C2JVHQVOXP2","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5C2JVHQVOXP2Y75W","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5C2JVHQV","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:2bfb9997f730688244d436c465a2e035b5bb1e2ebc4765bdf704397072c10a50","target":"graph","created_at":"2026-05-18T00:31:49Z","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":"An algebra $\\mathbf A = \\langle A, \\to, 0 \\rangle$, where $\\to$ is binary and $0$ is a constant, is called an implication zroupoid ($\\mathcal I$-zroupoid, for short) if $\\mathbf A$ satisfies the identities: $(x \\to y) \\to z \\approx ((z' \\to x) \\to (y \\to z)')'$ and $0'' \\approx 0$, where $x' : = x \\to 0$. An implication zroupoid is symmetric if it satisfies $x'' \\approx x$ and $(x \\to y')' \\approx (y \\to x')'$. The variety of symmetric $\\mathcal I$-zroupoids is denoted by $\\mathcal S$. We began a systematic analysis of weak associative laws of length $\\leq 4$ in [CS16e], by examining the ident","authors_text":"Hanamantagouda P. Sankappanavar, Juan M. Cornejo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-28T07:29:16Z","title":"Symmetric Implication Zroupoids and Weak Associative Laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10408","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:c85d847e879a925e4374b5d9b2442e86940d65a62336729e0280635f3b62fa59","target":"record","created_at":"2026-05-18T00:31:49Z","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":"b07fcc93a987b3ee6d5b5603b0f9d2e22b325b7eec31774ec212a713910e618f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-10-28T07:29:16Z","title_canon_sha256":"81efce27db553a80eea8a4eb509167e6ab402df0fc14172c37836609671de056"},"schema_version":"1.0","source":{"id":"1710.10408","kind":"arxiv","version":1}},"canonical_sha256":"e8b49a9e1575dfac7fb6eb925bf4ed43a98ec4db799579681d9fe74e884462a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8b49a9e1575dfac7fb6eb925bf4ed43a98ec4db799579681d9fe74e884462a3","first_computed_at":"2026-05-18T00:31:49.613423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:49.613423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZTTcw1vXZ2AtSV5XMsoAK2k+wgE0ybb5Y8Rgho/Fg8pCOwxnqny0tTlLb1Os6E1aejtrZhjFeZl4/zetxENCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:49.614140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c85d847e879a925e4374b5d9b2442e86940d65a62336729e0280635f3b62fa59","sha256:2bfb9997f730688244d436c465a2e035b5bb1e2ebc4765bdf704397072c10a50"],"state_sha256":"1ebceb881299e0bb5abd3187fa35026a55402e54ed27803aeb700a75a5a3e910"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJZvYXEklGYxJVXmRTBX9gvLI1+stXpdyPmFNx6BV8oeB5KdkHE1cxE3y7E+Pf3sFC6bECyVUfSfopeXSuKlDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:09:17.186127Z","bundle_sha256":"7ec4678c9e5dc9c5437deaba0a64db5f7f549efd8af23ab57841dde2f2a7c5fc"}}