{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SXBXGSTWIS5ZRLHQN5NJF4GDPW","short_pith_number":"pith:SXBXGSTW","canonical_record":{"source":{"id":"1607.03354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-07-12T13:46:52Z","cross_cats_sorted":["cs.AI","cs.LO"],"title_canon_sha256":"a3d3538670ff4f30edbd20477e79392c725b6b6dc62f8b782de0cfe8294d38a9","abstract_canon_sha256":"227f4bc8cc2d16b2fb88b09831089ae4f62deac2c61a93ce2b8884036aba3c2a"},"schema_version":"1.0"},"canonical_sha256":"95c3734a7644bb98acf06f5a92f0c37db5bb484ba7dee53f26b7c9a0ebf4a769","source":{"kind":"arxiv","id":"1607.03354","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03354","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03354v1","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03354","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"SXBXGSTWIS5Z","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SXBXGSTWIS5ZRLHQ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SXBXGSTW","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SXBXGSTWIS5ZRLHQN5NJF4GDPW","target":"record","payload":{"canonical_record":{"source":{"id":"1607.03354","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-07-12T13:46:52Z","cross_cats_sorted":["cs.AI","cs.LO"],"title_canon_sha256":"a3d3538670ff4f30edbd20477e79392c725b6b6dc62f8b782de0cfe8294d38a9","abstract_canon_sha256":"227f4bc8cc2d16b2fb88b09831089ae4f62deac2c61a93ce2b8884036aba3c2a"},"schema_version":"1.0"},"canonical_sha256":"95c3734a7644bb98acf06f5a92f0c37db5bb484ba7dee53f26b7c9a0ebf4a769","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:08.880704Z","signature_b64":"oT0Tw4M48nYtP5B7sUwPCYacNvPUPuw1NQ5eJWiuzGZX2yfh7WaBkoMsY6Jn3BjmToAuQok7tX1GuAESZshHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95c3734a7644bb98acf06f5a92f0c37db5bb484ba7dee53f26b7c9a0ebf4a769","last_reissued_at":"2026-05-18T01:11:08.880246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:08.880246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.03354","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":"2026-05-18T01:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HU5IuuVoHkEw8cOzHdAu/+F9XIzKZlj8AxHBGyopL26+17bT7MxGD5+OWyFHPelvbb4Oe0o4fUHQzVVQVLLuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:25:56.639961Z"},"content_sha256":"9d128fdaee0521363ebbbbe6c5bb481a464959d9e0ccb76728f4a25e8f2c43c4","schema_version":"1.0","event_id":"sha256:9d128fdaee0521363ebbbbe6c5bb481a464959d9e0ccb76728f4a25e8f2c43c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SXBXGSTWIS5ZRLHQN5NJF4GDPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extended Graded Modalities in Strategy Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LO"],"primary_cat":"cs.GT","authors_text":"Aniello Murano (Universit\\`a degli Studi di Napoli Federico II, Austria), Benjamin Aminof (Technische Universitat Wien, Italy), Sasha Rubin (Universit\\`a degli Studi di Napoli Federico II, Vadim Malvone (Universit\\`a degli Studi di Napoli Federico II","submitted_at":"2016-07-12T13:46:52Z","abstract_excerpt":"Strategy Logic (SL) is a logical formalism for strategic reasoning in multi-agent systems. Its main feature is that it has variables for strategies that are associated to specific agents with a binding operator. We introduce Graded Strategy Logic (GradedSL), an extension of SL by graded quantifiers over tuples of strategy variables, i.e., \"there exist at least g different tuples (x_1,...,x_n) of strategies\" where g is a cardinal from the set N union {aleph_0, aleph_1, 2^aleph_0}. We prove that the model-checking problem of GradedSL is decidable. We then turn to the complexity of fragments of G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03354","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":"2026-05-18T01:11:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQoU2Sx8Vf3OInfzpbR6+89ZGThjwaH2fK0uiTViflb8+v49FWBnUKf8XUDwLf7wukp73sqBHf2XDuQeoLUuDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:25:56.640326Z"},"content_sha256":"089681e154bf91ab268c5ccae7b0fb0017307b1a7d053178ceb956cd06268f3a","schema_version":"1.0","event_id":"sha256:089681e154bf91ab268c5ccae7b0fb0017307b1a7d053178ceb956cd06268f3a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SXBXGSTWIS5ZRLHQN5NJF4GDPW/bundle.json","state_url":"https://pith.science/pith/SXBXGSTWIS5ZRLHQN5NJF4GDPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SXBXGSTWIS5ZRLHQN5NJF4GDPW/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":"2026-06-05T14:25:56Z","links":{"resolver":"https://pith.science/pith/SXBXGSTWIS5ZRLHQN5NJF4GDPW","bundle":"https://pith.science/pith/SXBXGSTWIS5ZRLHQN5NJF4GDPW/bundle.json","state":"https://pith.science/pith/SXBXGSTWIS5ZRLHQN5NJF4GDPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SXBXGSTWIS5ZRLHQN5NJF4GDPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SXBXGSTWIS5ZRLHQN5NJF4GDPW","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":"227f4bc8cc2d16b2fb88b09831089ae4f62deac2c61a93ce2b8884036aba3c2a","cross_cats_sorted":["cs.AI","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-07-12T13:46:52Z","title_canon_sha256":"a3d3538670ff4f30edbd20477e79392c725b6b6dc62f8b782de0cfe8294d38a9"},"schema_version":"1.0","source":{"id":"1607.03354","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03354","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03354v1","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03354","created_at":"2026-05-18T01:11:08Z"},{"alias_kind":"pith_short_12","alias_value":"SXBXGSTWIS5Z","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SXBXGSTWIS5ZRLHQ","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SXBXGSTW","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:089681e154bf91ab268c5ccae7b0fb0017307b1a7d053178ceb956cd06268f3a","target":"graph","created_at":"2026-05-18T01:11:08Z","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":"Strategy Logic (SL) is a logical formalism for strategic reasoning in multi-agent systems. Its main feature is that it has variables for strategies that are associated to specific agents with a binding operator. We introduce Graded Strategy Logic (GradedSL), an extension of SL by graded quantifiers over tuples of strategy variables, i.e., \"there exist at least g different tuples (x_1,...,x_n) of strategies\" where g is a cardinal from the set N union {aleph_0, aleph_1, 2^aleph_0}. We prove that the model-checking problem of GradedSL is decidable. We then turn to the complexity of fragments of G","authors_text":"Aniello Murano (Universit\\`a degli Studi di Napoli Federico II, Austria), Benjamin Aminof (Technische Universitat Wien, Italy), Sasha Rubin (Universit\\`a degli Studi di Napoli Federico II, Vadim Malvone (Universit\\`a degli Studi di Napoli Federico II","cross_cats":["cs.AI","cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-07-12T13:46:52Z","title":"Extended Graded Modalities in Strategy Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03354","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":"sha256:9d128fdaee0521363ebbbbe6c5bb481a464959d9e0ccb76728f4a25e8f2c43c4","target":"record","created_at":"2026-05-18T01:11:08Z","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":"227f4bc8cc2d16b2fb88b09831089ae4f62deac2c61a93ce2b8884036aba3c2a","cross_cats_sorted":["cs.AI","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2016-07-12T13:46:52Z","title_canon_sha256":"a3d3538670ff4f30edbd20477e79392c725b6b6dc62f8b782de0cfe8294d38a9"},"schema_version":"1.0","source":{"id":"1607.03354","kind":"arxiv","version":1}},"canonical_sha256":"95c3734a7644bb98acf06f5a92f0c37db5bb484ba7dee53f26b7c9a0ebf4a769","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95c3734a7644bb98acf06f5a92f0c37db5bb484ba7dee53f26b7c9a0ebf4a769","first_computed_at":"2026-05-18T01:11:08.880246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:08.880246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oT0Tw4M48nYtP5B7sUwPCYacNvPUPuw1NQ5eJWiuzGZX2yfh7WaBkoMsY6Jn3BjmToAuQok7tX1GuAESZshHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:08.880704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03354","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d128fdaee0521363ebbbbe6c5bb481a464959d9e0ccb76728f4a25e8f2c43c4","sha256:089681e154bf91ab268c5ccae7b0fb0017307b1a7d053178ceb956cd06268f3a"],"state_sha256":"c398a4395dd67b2d36b43db1c1405ea11068336c68d9af33d1bf709d557753d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSvnLAfspuyjSe8o3qzIB3hMTP/jAhlJxTCBNgWsxWAffFCh749ftTKnMMm55DRMN4CcR6sMhn5z6zsbBRdeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:25:56.642270Z","bundle_sha256":"e3607ac4a569ff0fe540124df46ac44a53d6388670641f81d9ca6881158d9f00"}}