{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XRNLCNSBINVO437TN4RY5CBKXT","short_pith_number":"pith:XRNLCNSB","canonical_record":{"source":{"id":"1810.07103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-16T16:04:25Z","cross_cats_sorted":[],"title_canon_sha256":"12ac9b4a9046e4a85110126feef0d0f7538ccc3bf61e510d4ffdf14db6fe2d3a","abstract_canon_sha256":"4276d3e0cb3cf1d0b22f3753f9a40584802f28dd6bd5439ba462ea115060bbb3"},"schema_version":"1.0"},"canonical_sha256":"bc5ab13641436aee6ff36f238e882abce417471479bf81c1b60a01b01a4e3fbc","source":{"kind":"arxiv","id":"1810.07103","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07103","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07103v1","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07103","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"XRNLCNSBINVO","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XRNLCNSBINVO437T","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XRNLCNSB","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XRNLCNSBINVO437TN4RY5CBKXT","target":"record","payload":{"canonical_record":{"source":{"id":"1810.07103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-16T16:04:25Z","cross_cats_sorted":[],"title_canon_sha256":"12ac9b4a9046e4a85110126feef0d0f7538ccc3bf61e510d4ffdf14db6fe2d3a","abstract_canon_sha256":"4276d3e0cb3cf1d0b22f3753f9a40584802f28dd6bd5439ba462ea115060bbb3"},"schema_version":"1.0"},"canonical_sha256":"bc5ab13641436aee6ff36f238e882abce417471479bf81c1b60a01b01a4e3fbc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:10.412543Z","signature_b64":"T+YLIrnqZszI71A0YcUW/pkMYj3d/TbY1pD6fs6ltLm9e6v86OIfTEBsKDJRFg1WLobwk8VknVHUdPr8WzPzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc5ab13641436aee6ff36f238e882abce417471479bf81c1b60a01b01a4e3fbc","last_reissued_at":"2026-05-18T00:03:10.411824Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:10.411824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.07103","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":"2026-05-18T00:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qc/UxYSW8YetGaVC/2xQSqFimlAe9Ki/LM046ugMdD70RjFdskNWo7/4IgjjgKsCI4nWSSZBMHivThwcvTrhCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:41:13.418772Z"},"content_sha256":"638c21c3305f4802be244cf9a48ca2d3556300fdefeedf185e30148f96d54cde","schema_version":"1.0","event_id":"sha256:638c21c3305f4802be244cf9a48ca2d3556300fdefeedf185e30148f96d54cde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XRNLCNSBINVO437TN4RY5CBKXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trial and error mathematics: Dialectical systems and completions of theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrea Sorbi, Duccio Pianigiani, Jacopo Amidei, Luca San Mauro, Uri Andrews","submitted_at":"2018-10-16T16:04:25Z","abstract_excerpt":"This paper is part of a project that is based on the notion of dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In previous work, we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasidialectical systems, that enrich Magari's systems with a natural mechanism of revision. In the present paper we consider a third class of systems, that of $p$-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about $p$-dialect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07103","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":"2026-05-18T00:03:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6JzieHGWB+LEgbAxwVUpM0Ib9WYuAuLbRxyAD948bPOCkb1BW6ZVITllJFKxEXNpI+ihtvE7XZKcZQJ/Xa/FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T12:41:13.419442Z"},"content_sha256":"27a1810095f5cc7d59189eba911622a64e3e274113822009518d1b9b56235209","schema_version":"1.0","event_id":"sha256:27a1810095f5cc7d59189eba911622a64e3e274113822009518d1b9b56235209"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRNLCNSBINVO437TN4RY5CBKXT/bundle.json","state_url":"https://pith.science/pith/XRNLCNSBINVO437TN4RY5CBKXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRNLCNSBINVO437TN4RY5CBKXT/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":"2026-05-25T12:41:13Z","links":{"resolver":"https://pith.science/pith/XRNLCNSBINVO437TN4RY5CBKXT","bundle":"https://pith.science/pith/XRNLCNSBINVO437TN4RY5CBKXT/bundle.json","state":"https://pith.science/pith/XRNLCNSBINVO437TN4RY5CBKXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRNLCNSBINVO437TN4RY5CBKXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XRNLCNSBINVO437TN4RY5CBKXT","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":"4276d3e0cb3cf1d0b22f3753f9a40584802f28dd6bd5439ba462ea115060bbb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-16T16:04:25Z","title_canon_sha256":"12ac9b4a9046e4a85110126feef0d0f7538ccc3bf61e510d4ffdf14db6fe2d3a"},"schema_version":"1.0","source":{"id":"1810.07103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07103","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07103v1","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07103","created_at":"2026-05-18T00:03:10Z"},{"alias_kind":"pith_short_12","alias_value":"XRNLCNSBINVO","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XRNLCNSBINVO437T","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XRNLCNSB","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:27a1810095f5cc7d59189eba911622a64e3e274113822009518d1b9b56235209","target":"graph","created_at":"2026-05-18T00:03:10Z","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":"This paper is part of a project that is based on the notion of dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In previous work, we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasidialectical systems, that enrich Magari's systems with a natural mechanism of revision. In the present paper we consider a third class of systems, that of $p$-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about $p$-dialect","authors_text":"Andrea Sorbi, Duccio Pianigiani, Jacopo Amidei, Luca San Mauro, Uri Andrews","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-16T16:04:25Z","title":"Trial and error mathematics: Dialectical systems and completions of theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07103","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":"sha256:638c21c3305f4802be244cf9a48ca2d3556300fdefeedf185e30148f96d54cde","target":"record","created_at":"2026-05-18T00:03:10Z","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":"4276d3e0cb3cf1d0b22f3753f9a40584802f28dd6bd5439ba462ea115060bbb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-16T16:04:25Z","title_canon_sha256":"12ac9b4a9046e4a85110126feef0d0f7538ccc3bf61e510d4ffdf14db6fe2d3a"},"schema_version":"1.0","source":{"id":"1810.07103","kind":"arxiv","version":1}},"canonical_sha256":"bc5ab13641436aee6ff36f238e882abce417471479bf81c1b60a01b01a4e3fbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc5ab13641436aee6ff36f238e882abce417471479bf81c1b60a01b01a4e3fbc","first_computed_at":"2026-05-18T00:03:10.411824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:10.411824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T+YLIrnqZszI71A0YcUW/pkMYj3d/TbY1pD6fs6ltLm9e6v86OIfTEBsKDJRFg1WLobwk8VknVHUdPr8WzPzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:10.412543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:638c21c3305f4802be244cf9a48ca2d3556300fdefeedf185e30148f96d54cde","sha256:27a1810095f5cc7d59189eba911622a64e3e274113822009518d1b9b56235209"],"state_sha256":"ad90a87a2ded836224906c1984ea36bed9f2eeba593211c36cbd78a31562860d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wakFDEaN1Qd4GK84blfokT7xrzLqmP+bCKLG/xv4HLMYYR5Mcr/Hvyca0HW7U+Y0e6n6rF7x4HRuy9TFcRViCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T12:41:13.423084Z","bundle_sha256":"ee2d202079ead7a2c085279464b2fac719cca1df5d62d859edf48ee8ee153cc9"}}