{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AFITJC7ZAFQ2ND5ZYZXFUJOY2X","short_pith_number":"pith:AFITJC7Z","canonical_record":{"source":{"id":"1204.2703","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-04-12T12:32:57Z","cross_cats_sorted":[],"title_canon_sha256":"5c60740d84bb4682f333465127eb57f6de5ca521b3a8bd1b07ddaaf6c541e211","abstract_canon_sha256":"11dfcd5139461a57ceda4fc7adbce9386357e2ba224b79ce08bc2b70ef5ee4b1"},"schema_version":"1.0"},"canonical_sha256":"0151348bf90161a68fb9c66e5a25d8d5c2941c7f77cf1dab45a977e44dc61347","source":{"kind":"arxiv","id":"1204.2703","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2703","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2703v2","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2703","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"AFITJC7ZAFQ2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AFITJC7ZAFQ2ND5Z","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AFITJC7Z","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AFITJC7ZAFQ2ND5ZYZXFUJOY2X","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2703","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-04-12T12:32:57Z","cross_cats_sorted":[],"title_canon_sha256":"5c60740d84bb4682f333465127eb57f6de5ca521b3a8bd1b07ddaaf6c541e211","abstract_canon_sha256":"11dfcd5139461a57ceda4fc7adbce9386357e2ba224b79ce08bc2b70ef5ee4b1"},"schema_version":"1.0"},"canonical_sha256":"0151348bf90161a68fb9c66e5a25d8d5c2941c7f77cf1dab45a977e44dc61347","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:18.802873Z","signature_b64":"YscBJ6S860/7msHvK9bfvo6haeX+v0qsW1GjEVJjaw3J0fcxbkcK696cdQZi/UgUH314qWkct8mhs2VeKFZpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0151348bf90161a68fb9c66e5a25d8d5c2941c7f77cf1dab45a977e44dc61347","last_reissued_at":"2026-05-17T23:53:18.802251Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:18.802251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2703","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pRaooC5toTyFZBeyRObRWVOK44ZR5MoOhyJ/usZyE2oUSncdm7Auu9Tu61w89W660K2cWa87RdEn6lsGN5hyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:17:24.689649Z"},"content_sha256":"e44ce7d3d87facd8f9da2b4afe6ba82f5021e8963224c6fd99b5af1988301321","schema_version":"1.0","event_id":"sha256:e44ce7d3d87facd8f9da2b4afe6ba82f5021e8963224c6fd99b5af1988301321"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AFITJC7ZAFQ2ND5ZYZXFUJOY2X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theories of analytic monads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Marek Zawadowski, Stanis{\\l}aw Szawiel","submitted_at":"2012-04-12T12:32:57Z","abstract_excerpt":"We characterize the equational theories and Lawvere theories that correspond to the categories of analytic and polynomial monads on Set, and hence also the categories of the symmetric and rigid operads in Set. We show that the category of analytic monads is equivalent to the category of regular-linear theories. The category of polynomial monads is equivalent to the category of rigid theories, i.e. regular-linear theories satisfying an additional global condition. This solves a problem A. Carboni and P. T. Johnstone. The Lawvere theories corresponding to these monads are identified via some fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2703","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WIce82o6kBcofQTWkLhqg2yXD5p3D0JkWJH1GKW6JSATZ9VxgtZylfe0hJslxSy0ydBL+vjwUErv4YfDgH8pDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:17:24.690087Z"},"content_sha256":"fdb054c3438d94624e36df5395069fc466db08ef283f40742d77795436655c96","schema_version":"1.0","event_id":"sha256:fdb054c3438d94624e36df5395069fc466db08ef283f40742d77795436655c96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AFITJC7ZAFQ2ND5ZYZXFUJOY2X/bundle.json","state_url":"https://pith.science/pith/AFITJC7ZAFQ2ND5ZYZXFUJOY2X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AFITJC7ZAFQ2ND5ZYZXFUJOY2X/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":"2026-05-25T13:17:24Z","links":{"resolver":"https://pith.science/pith/AFITJC7ZAFQ2ND5ZYZXFUJOY2X","bundle":"https://pith.science/pith/AFITJC7ZAFQ2ND5ZYZXFUJOY2X/bundle.json","state":"https://pith.science/pith/AFITJC7ZAFQ2ND5ZYZXFUJOY2X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AFITJC7ZAFQ2ND5ZYZXFUJOY2X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AFITJC7ZAFQ2ND5ZYZXFUJOY2X","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":"11dfcd5139461a57ceda4fc7adbce9386357e2ba224b79ce08bc2b70ef5ee4b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-04-12T12:32:57Z","title_canon_sha256":"5c60740d84bb4682f333465127eb57f6de5ca521b3a8bd1b07ddaaf6c541e211"},"schema_version":"1.0","source":{"id":"1204.2703","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2703","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2703v2","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2703","created_at":"2026-05-17T23:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"AFITJC7ZAFQ2","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AFITJC7ZAFQ2ND5Z","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AFITJC7Z","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:fdb054c3438d94624e36df5395069fc466db08ef283f40742d77795436655c96","target":"graph","created_at":"2026-05-17T23:53:18Z","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 characterize the equational theories and Lawvere theories that correspond to the categories of analytic and polynomial monads on Set, and hence also the categories of the symmetric and rigid operads in Set. We show that the category of analytic monads is equivalent to the category of regular-linear theories. The category of polynomial monads is equivalent to the category of rigid theories, i.e. regular-linear theories satisfying an additional global condition. This solves a problem A. Carboni and P. T. Johnstone. The Lawvere theories corresponding to these monads are identified via some fac","authors_text":"Marek Zawadowski, Stanis{\\l}aw Szawiel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-04-12T12:32:57Z","title":"Theories of analytic monads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2703","kind":"arxiv","version":2},"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:e44ce7d3d87facd8f9da2b4afe6ba82f5021e8963224c6fd99b5af1988301321","target":"record","created_at":"2026-05-17T23:53:18Z","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":"11dfcd5139461a57ceda4fc7adbce9386357e2ba224b79ce08bc2b70ef5ee4b1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2012-04-12T12:32:57Z","title_canon_sha256":"5c60740d84bb4682f333465127eb57f6de5ca521b3a8bd1b07ddaaf6c541e211"},"schema_version":"1.0","source":{"id":"1204.2703","kind":"arxiv","version":2}},"canonical_sha256":"0151348bf90161a68fb9c66e5a25d8d5c2941c7f77cf1dab45a977e44dc61347","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0151348bf90161a68fb9c66e5a25d8d5c2941c7f77cf1dab45a977e44dc61347","first_computed_at":"2026-05-17T23:53:18.802251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:18.802251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YscBJ6S860/7msHvK9bfvo6haeX+v0qsW1GjEVJjaw3J0fcxbkcK696cdQZi/UgUH314qWkct8mhs2VeKFZpBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:18.802873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2703","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e44ce7d3d87facd8f9da2b4afe6ba82f5021e8963224c6fd99b5af1988301321","sha256:fdb054c3438d94624e36df5395069fc466db08ef283f40742d77795436655c96"],"state_sha256":"482d9b2b2a224f67aefae60a9211eef4eb84e1d2fa816ca6067d18fc752bc0c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FPd2xdwXng1D+62xCKjjvTo0wg+gR0Xib60AqlmPEektiDfDKACprmqxN3bnG0BhJfM3kiFJPfPF/g1Gk+OkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T13:17:24.693465Z","bundle_sha256":"30d609a7fefb1d3c9ccc10fb6cf29af1ef6ea808f1dc3cadecfc1b5be8cee042"}}