{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BSA53SKPBJKY7FU5A4NX3XWPSX","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":"8d5d2aafa2474018e8719d54dae6f126b9ef97b0f671ba003ea9f142f0e5fe09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-12-11T14:05:18Z","title_canon_sha256":"961f0596e52eb80eeb6a57110a80b2e3489532ba4d647dd4111491a62611b040"},"schema_version":"1.0","source":{"id":"1412.3652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3652","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3652v2","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3652","created_at":"2026-05-18T02:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"BSA53SKPBJKY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BSA53SKPBJKY7FU5","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BSA53SKP","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:349e16ff33b8c31a52385380421da32155cce06d8761e741368510de3fa751c8","target":"graph","created_at":"2026-05-18T02:30:33Z","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":"These notes are extracted from the lectures on forcing axioms and applications held by professor Matteo Viale at the University of Turin in the academic year 2011-2012. Our purpose is to give a brief account on forcing axioms with a special focus on some consequences of them (SRP, OCA, PID). These principles were first isolated by Todor\\v cevi\\'c and interpolate most consequences of MM and PFA, thus providing a useful insight on the combinatorial structure of the theory of forcing axioms.\n  In the first part of this notes we will give a brief account on forcing axioms, introducing some equival","authors_text":"Gemma Carotenuto, Giorgio Audrito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-12-11T14:05:18Z","title":"An introduction to forcing axioms, SRP and OCA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3652","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:e162b5bb2cb09d7d43adb06a15ebc385e82bff9edcd9c65dc4641dba8a4c2463","target":"record","created_at":"2026-05-18T02:30:33Z","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":"8d5d2aafa2474018e8719d54dae6f126b9ef97b0f671ba003ea9f142f0e5fe09","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-12-11T14:05:18Z","title_canon_sha256":"961f0596e52eb80eeb6a57110a80b2e3489532ba4d647dd4111491a62611b040"},"schema_version":"1.0","source":{"id":"1412.3652","kind":"arxiv","version":2}},"canonical_sha256":"0c81ddc94f0a558f969d071b7ddecf95ece5943da703604f56ca8ac5006cf10c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c81ddc94f0a558f969d071b7ddecf95ece5943da703604f56ca8ac5006cf10c","first_computed_at":"2026-05-18T02:30:33.636584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:33.636584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sEfW7VYzZERNLs6Mzccr6khMSoLpS71Ah9PSCU3nBVsxmvl535dkoEy/mT8w8hMUy74tsa1KpkLGKScxWF3uDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:33.636962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e162b5bb2cb09d7d43adb06a15ebc385e82bff9edcd9c65dc4641dba8a4c2463","sha256:349e16ff33b8c31a52385380421da32155cce06d8761e741368510de3fa751c8"],"state_sha256":"49bed7fd0c15025570e035e8a1a0a79a045464fc581e1aac3b6c98b8ced6c4c1"}