{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5VPGQ4WVIRM6MP6VAXMGFL4RZH","short_pith_number":"pith:5VPGQ4WV","canonical_record":{"source":{"id":"1208.2971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-14T20:31:26Z","cross_cats_sorted":[],"title_canon_sha256":"b507a22699cc8523b6e34ca66f27bf2c1a6e4e5568719040fdbaafc59ed0af21","abstract_canon_sha256":"c068a592f38e3f28700193bf5a753433889037cb355d17c6e7f32cdae0f7c6ef"},"schema_version":"1.0"},"canonical_sha256":"ed5e6872d54459e63fd505d862af91c9eb4fc9058f40fb6730bac1204071c833","source":{"kind":"arxiv","id":"1208.2971","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2971","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2971v1","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2971","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"5VPGQ4WVIRM6","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5VPGQ4WVIRM6MP6V","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5VPGQ4WV","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5VPGQ4WVIRM6MP6VAXMGFL4RZH","target":"record","payload":{"canonical_record":{"source":{"id":"1208.2971","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-14T20:31:26Z","cross_cats_sorted":[],"title_canon_sha256":"b507a22699cc8523b6e34ca66f27bf2c1a6e4e5568719040fdbaafc59ed0af21","abstract_canon_sha256":"c068a592f38e3f28700193bf5a753433889037cb355d17c6e7f32cdae0f7c6ef"},"schema_version":"1.0"},"canonical_sha256":"ed5e6872d54459e63fd505d862af91c9eb4fc9058f40fb6730bac1204071c833","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:45.887756Z","signature_b64":"YYrEa8b+VzJzzGo8PpE4pANLqF3bUFyRauFIT/vD0ConPeXHHc2CnjGn41tt2bBQyEaomb2HjOxb8x12Gw+GCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed5e6872d54459e63fd505d862af91c9eb4fc9058f40fb6730bac1204071c833","last_reissued_at":"2026-05-18T03:48:45.887075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:45.887075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.2971","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":"2026-05-18T03:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5iHyEz1YvIhH+wzwwT5GWMt0c1Iig6Jaa6/vZ7N7NCcOLXRP7Lt75cjx+ldwDR0Mq9UZxkDenb3qPATQjzQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:20:31.122503Z"},"content_sha256":"656b9fec4d08a2cffc58756cb42bdba840da8bc5a534862a668fa01717e0eb4e","schema_version":"1.0","event_id":"sha256:656b9fec4d08a2cffc58756cb42bdba840da8bc5a534862a668fa01717e0eb4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5VPGQ4WVIRM6MP6VAXMGFL4RZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intuitionistic logic with two Galois connections combined with Fischer Servi axioms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jouni J\\\"arvinen, Michiro Kondo, Wojciech Dzik","submitted_at":"2012-08-14T20:31:26Z","abstract_excerpt":"Earlier, the authors introduced the logic IntGC, which is an extension of intuitionistic propositional logic by two rules of inference mimicking the performance of Galois connections (Logic J. of the IGPL, 18:837-858, 2010). In this paper, the extensions Int2GC and Int2GC+FS of IntGC are studied. Int2GC can be seen as a fusion of two IntGC logics, and Int2GC+FS is obtained from Int2GC by adding instances of duality-like connections $\\Diamond(A \\to\\ B) \\to (\\Box A \\to \\Diamond B)$ and $(\\Diamond A \\to \\Box B) \\to \\Box(A \\to B)$, introduced by G. Fischer Servi (Rend. Sem. Mat. Univers. Politecn."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2971","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":"2026-05-18T03:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDK+YrUmauC/EEZe8/6HwAs3OwN/mM0aAyaLLKCxVZ/co1TphsJjPvTFuuwPBIFhF6JJHCcOQTi4J162c31TDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:20:31.122865Z"},"content_sha256":"64ee2da9ce32ddf45ef697bb4f8427161cc9a1daded24388e3607ce5aaff0653","schema_version":"1.0","event_id":"sha256:64ee2da9ce32ddf45ef697bb4f8427161cc9a1daded24388e3607ce5aaff0653"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VPGQ4WVIRM6MP6VAXMGFL4RZH/bundle.json","state_url":"https://pith.science/pith/5VPGQ4WVIRM6MP6VAXMGFL4RZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VPGQ4WVIRM6MP6VAXMGFL4RZH/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":"2026-06-22T22:20:31Z","links":{"resolver":"https://pith.science/pith/5VPGQ4WVIRM6MP6VAXMGFL4RZH","bundle":"https://pith.science/pith/5VPGQ4WVIRM6MP6VAXMGFL4RZH/bundle.json","state":"https://pith.science/pith/5VPGQ4WVIRM6MP6VAXMGFL4RZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VPGQ4WVIRM6MP6VAXMGFL4RZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5VPGQ4WVIRM6MP6VAXMGFL4RZH","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":"c068a592f38e3f28700193bf5a753433889037cb355d17c6e7f32cdae0f7c6ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-14T20:31:26Z","title_canon_sha256":"b507a22699cc8523b6e34ca66f27bf2c1a6e4e5568719040fdbaafc59ed0af21"},"schema_version":"1.0","source":{"id":"1208.2971","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.2971","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1208.2971v1","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2971","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"5VPGQ4WVIRM6","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5VPGQ4WVIRM6MP6V","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5VPGQ4WV","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:64ee2da9ce32ddf45ef697bb4f8427161cc9a1daded24388e3607ce5aaff0653","target":"graph","created_at":"2026-05-18T03:48:45Z","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":"Earlier, the authors introduced the logic IntGC, which is an extension of intuitionistic propositional logic by two rules of inference mimicking the performance of Galois connections (Logic J. of the IGPL, 18:837-858, 2010). In this paper, the extensions Int2GC and Int2GC+FS of IntGC are studied. Int2GC can be seen as a fusion of two IntGC logics, and Int2GC+FS is obtained from Int2GC by adding instances of duality-like connections $\\Diamond(A \\to\\ B) \\to (\\Box A \\to \\Diamond B)$ and $(\\Diamond A \\to \\Box B) \\to \\Box(A \\to B)$, introduced by G. Fischer Servi (Rend. Sem. Mat. Univers. Politecn.","authors_text":"Jouni J\\\"arvinen, Michiro Kondo, Wojciech Dzik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-14T20:31:26Z","title":"Intuitionistic logic with two Galois connections combined with Fischer Servi axioms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2971","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":"sha256:656b9fec4d08a2cffc58756cb42bdba840da8bc5a534862a668fa01717e0eb4e","target":"record","created_at":"2026-05-18T03:48:45Z","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":"c068a592f38e3f28700193bf5a753433889037cb355d17c6e7f32cdae0f7c6ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-08-14T20:31:26Z","title_canon_sha256":"b507a22699cc8523b6e34ca66f27bf2c1a6e4e5568719040fdbaafc59ed0af21"},"schema_version":"1.0","source":{"id":"1208.2971","kind":"arxiv","version":1}},"canonical_sha256":"ed5e6872d54459e63fd505d862af91c9eb4fc9058f40fb6730bac1204071c833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed5e6872d54459e63fd505d862af91c9eb4fc9058f40fb6730bac1204071c833","first_computed_at":"2026-05-18T03:48:45.887075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:45.887075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YYrEa8b+VzJzzGo8PpE4pANLqF3bUFyRauFIT/vD0ConPeXHHc2CnjGn41tt2bBQyEaomb2HjOxb8x12Gw+GCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:45.887756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.2971","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:656b9fec4d08a2cffc58756cb42bdba840da8bc5a534862a668fa01717e0eb4e","sha256:64ee2da9ce32ddf45ef697bb4f8427161cc9a1daded24388e3607ce5aaff0653"],"state_sha256":"7ceb1f79ea770cf9988aa041d5efbb2fc087ab6ea425bab83b5efc5a1754a336"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kISqMAYqmYPjiKiG0PZ5fGpM7gaJ5VYYZ1eaX9Z3ycmaV//t1bXnpJfi5Ymb+qaMU4ACgfcR6NkjkhqdEv4pCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:20:31.124751Z","bundle_sha256":"238c14de9fda24b0eddf26117ce53928735112bd570b8811a161b5c3695b076f"}}