{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JVFAGIJ7QU3YGU66N7YKZG3RDT","short_pith_number":"pith:JVFAGIJ7","canonical_record":{"source":{"id":"2409.19236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-09-28T04:50:01Z","cross_cats_sorted":[],"title_canon_sha256":"45afd4a3aa0ef48210801460375fab40fe4f6d5c560a036c27631e18d23be964","abstract_canon_sha256":"3412c0f235a9297b64e8cbeeb47ff05b71c5082a24012ab7f57e538317dc41e3"},"schema_version":"1.0"},"canonical_sha256":"4d4a03213f85378353de6ff0ac9b711cebfa20fe7ef0f8e5b4c04c06356f3c5f","source":{"kind":"arxiv","id":"2409.19236","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.19236","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"2409.19236v2","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.19236","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"JVFAGIJ7QU3Y","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"pith_short_16","alias_value":"JVFAGIJ7QU3YGU66","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"pith_short_8","alias_value":"JVFAGIJ7","created_at":"2026-07-05T11:32:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JVFAGIJ7QU3YGU66N7YKZG3RDT","target":"record","payload":{"canonical_record":{"source":{"id":"2409.19236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-09-28T04:50:01Z","cross_cats_sorted":[],"title_canon_sha256":"45afd4a3aa0ef48210801460375fab40fe4f6d5c560a036c27631e18d23be964","abstract_canon_sha256":"3412c0f235a9297b64e8cbeeb47ff05b71c5082a24012ab7f57e538317dc41e3"},"schema_version":"1.0"},"canonical_sha256":"4d4a03213f85378353de6ff0ac9b711cebfa20fe7ef0f8e5b4c04c06356f3c5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:18.185029Z","signature_b64":"/nQtAZBbUs8VgmKCrwxHN/ROnrU4bA0l5EfrMQtJTOVfW4ZbU/A3Vh4l6KAlQRXFgPjw4O/l5/qINqyCJbBeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d4a03213f85378353de6ff0ac9b711cebfa20fe7ef0f8e5b4c04c06356f3c5f","last_reissued_at":"2026-07-05T11:32:18.184554Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:18.184554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.19236","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":"2026-07-05T11:32:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQ9MRzLJD7Mwoan7/L1PkwlfPdtTkTiNGlmdj2hE7tZOgXbuoQYO37/KUAItuGA11OXPkCw83GRLDfkna6chCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T16:02:16.408965Z"},"content_sha256":"659f00d3c9d832e446798851aab8d518356006db2a276bfbfd9484aee7b9a531","schema_version":"1.0","event_id":"sha256:659f00d3c9d832e446798851aab8d518356006db2a276bfbfd9484aee7b9a531"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JVFAGIJ7QU3YGU66N7YKZG3RDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Walk on the Wild Side: Notions of maximality in first-order theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Michele Bailetti","submitted_at":"2024-09-28T04:50:01Z","abstract_excerpt":"In the classification of complete first-order theories, many dividing lines have been defined in order to understand the complexity and the behavior of some classes of theories. In this paper, using the concept of patterns of consistency and inconsistency, we describe a general framework to study dividing lines and we introduce a notion of maximal complexity by requesting the presence of all the exhibitable patterns of definable sets. Weakening this notion, we define new properties (Positive Maximality and the $\\mathrm{PM}^{(k)}$ hierarchy) and prove some results about them. In particular, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.19236","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.19236/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:32:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bSi5UXeY1pf+SI1oGv8hOjjNZpUBydYADX8XE27ENmr7vBjaEw7JGZjQH9dFufv+08rXVUQ7gbDMZW+a9O/9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T16:02:16.409920Z"},"content_sha256":"c7dbe75c5705fb652bdff4583ce0fd9c9d2d0a0027f1d5f69cc389c971ac2101","schema_version":"1.0","event_id":"sha256:c7dbe75c5705fb652bdff4583ce0fd9c9d2d0a0027f1d5f69cc389c971ac2101"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVFAGIJ7QU3YGU66N7YKZG3RDT/bundle.json","state_url":"https://pith.science/pith/JVFAGIJ7QU3YGU66N7YKZG3RDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVFAGIJ7QU3YGU66N7YKZG3RDT/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":"2026-08-20T16:02:16Z","links":{"resolver":"https://pith.science/pith/JVFAGIJ7QU3YGU66N7YKZG3RDT","bundle":"https://pith.science/pith/JVFAGIJ7QU3YGU66N7YKZG3RDT/bundle.json","state":"https://pith.science/pith/JVFAGIJ7QU3YGU66N7YKZG3RDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVFAGIJ7QU3YGU66N7YKZG3RDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JVFAGIJ7QU3YGU66N7YKZG3RDT","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":"3412c0f235a9297b64e8cbeeb47ff05b71c5082a24012ab7f57e538317dc41e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-09-28T04:50:01Z","title_canon_sha256":"45afd4a3aa0ef48210801460375fab40fe4f6d5c560a036c27631e18d23be964"},"schema_version":"1.0","source":{"id":"2409.19236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.19236","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"arxiv_version","alias_value":"2409.19236v2","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.19236","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"pith_short_12","alias_value":"JVFAGIJ7QU3Y","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"pith_short_16","alias_value":"JVFAGIJ7QU3YGU66","created_at":"2026-07-05T11:32:18Z"},{"alias_kind":"pith_short_8","alias_value":"JVFAGIJ7","created_at":"2026-07-05T11:32:18Z"}],"graph_snapshots":[{"event_id":"sha256:c7dbe75c5705fb652bdff4583ce0fd9c9d2d0a0027f1d5f69cc389c971ac2101","target":"graph","created_at":"2026-07-05T11:32:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.19236/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the classification of complete first-order theories, many dividing lines have been defined in order to understand the complexity and the behavior of some classes of theories. In this paper, using the concept of patterns of consistency and inconsistency, we describe a general framework to study dividing lines and we introduce a notion of maximal complexity by requesting the presence of all the exhibitable patterns of definable sets. Weakening this notion, we define new properties (Positive Maximality and the $\\mathrm{PM}^{(k)}$ hierarchy) and prove some results about them. In particular, we ","authors_text":"Michele Bailetti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-09-28T04:50:01Z","title":"A Walk on the Wild Side: Notions of maximality in first-order theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.19236","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":"sha256:659f00d3c9d832e446798851aab8d518356006db2a276bfbfd9484aee7b9a531","target":"record","created_at":"2026-07-05T11:32:18Z","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":"3412c0f235a9297b64e8cbeeb47ff05b71c5082a24012ab7f57e538317dc41e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-09-28T04:50:01Z","title_canon_sha256":"45afd4a3aa0ef48210801460375fab40fe4f6d5c560a036c27631e18d23be964"},"schema_version":"1.0","source":{"id":"2409.19236","kind":"arxiv","version":2}},"canonical_sha256":"4d4a03213f85378353de6ff0ac9b711cebfa20fe7ef0f8e5b4c04c06356f3c5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d4a03213f85378353de6ff0ac9b711cebfa20fe7ef0f8e5b4c04c06356f3c5f","first_computed_at":"2026-07-05T11:32:18.184554Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:32:18.184554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/nQtAZBbUs8VgmKCrwxHN/ROnrU4bA0l5EfrMQtJTOVfW4ZbU/A3Vh4l6KAlQRXFgPjw4O/l5/qINqyCJbBeCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:32:18.185029Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.19236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:659f00d3c9d832e446798851aab8d518356006db2a276bfbfd9484aee7b9a531","sha256:c7dbe75c5705fb652bdff4583ce0fd9c9d2d0a0027f1d5f69cc389c971ac2101"],"state_sha256":"8de83ed44051c0fb703c31be80e16e5deb1d95b394e672ce165707030839bfeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3Eh1j+A7iCMSTF3NpjbxwGUr7sOpiTCYt4CWZpQLYWXcadpGlS6uygSlfqbkBnJlTE4fDQz3J7aTEnw5JLhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T16:02:16.414410Z","bundle_sha256":"da3241e9777357686c42a9ad894e229ce344c9c57a40c49282a986b90e507eb8"}}