{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VQGKGNBPPUTDN2QD4CKFCS7G7D","short_pith_number":"pith:VQGKGNBP","canonical_record":{"source":{"id":"2607.01110","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-07-01T16:01:42Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2f37e3a3a4a4f53238f17c2b4aba7d9fd927b1fe887bb2929f0ce289c8878d4e","abstract_canon_sha256":"441dafb4a1b4c657637567cc5db2797795f284381c707f5d7d18278ca2a1faab"},"schema_version":"1.0"},"canonical_sha256":"ac0ca3342f7d2636ea03e094514be6f8f3a56c72a327971e1f5857eaa844dc0e","source":{"kind":"arxiv","id":"2607.01110","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01110","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01110v1","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01110","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_12","alias_value":"VQGKGNBPPUTD","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_16","alias_value":"VQGKGNBPPUTDN2QD","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_8","alias_value":"VQGKGNBP","created_at":"2026-07-02T01:18:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VQGKGNBPPUTDN2QD4CKFCS7G7D","target":"record","payload":{"canonical_record":{"source":{"id":"2607.01110","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-07-01T16:01:42Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2f37e3a3a4a4f53238f17c2b4aba7d9fd927b1fe887bb2929f0ce289c8878d4e","abstract_canon_sha256":"441dafb4a1b4c657637567cc5db2797795f284381c707f5d7d18278ca2a1faab"},"schema_version":"1.0"},"canonical_sha256":"ac0ca3342f7d2636ea03e094514be6f8f3a56c72a327971e1f5857eaa844dc0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-02T01:18:29.328878Z","signature_b64":"SWE8xWnd1kJ6LZtxFG/TigYKY9rOt13G6vdNAnuJfoPmB9pFjj+U3AtsFyMMDKEfpNN8pPRFm9aklqHpxZ8PDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac0ca3342f7d2636ea03e094514be6f8f3a56c72a327971e1f5857eaa844dc0e","last_reissued_at":"2026-07-02T01:18:29.328482Z","signature_status":"signed_v1","first_computed_at":"2026-07-02T01:18:29.328482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.01110","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":"2026-07-02T01:18:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PibKL7z0Jy9ubGU8lI/nnH5y3Gfs4/zqOX34PKQeXIubO67ZXDpdaFmzvYIqNAQFr1/Sd2pTu6KMx8N3A9G5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:07:22.314606Z"},"content_sha256":"3a88746d36d075d60bf742a5462aa0d4b4def8e150099b15b4cf7e71b8bcd879","schema_version":"1.0","event_id":"sha256:3a88746d36d075d60bf742a5462aa0d4b4def8e150099b15b4cf7e71b8bcd879"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VQGKGNBPPUTDN2QD4CKFCS7G7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Definability of Functional Properties in the Basic Modal-Temporal Language over Ordered Frames","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Alfredo Burrieza","submitted_at":"2026-07-01T16:01:42Z","abstract_excerpt":"We study the expressive power of the simplest modal-temporal language, obtained by adding Prior's temporal operators \\(G\\) and \\(H\\) to the basic modal language with \\(\\Box\\). This language is the standard bimodal combination of modal and tense logic; under its functional interpretation it is denoted \\(L_{T\\times W}\\). To analyse its definability across five order types, we consider two semantic readings of the temporal operators: the standard reading (\\(G,H\\)), which includes the current instant, and the strict reading (\\(G^{\\ast},H^{\\ast}\\)), which always excludes it.\n  We examine nine funct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01110","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01110/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":"2026-07-02T01:18:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eAfchMOquie9dlYZN+avolt7Dx9B9oLi7FprMtvbiP6nwkwDiZIoVvJrTUUF7HkEkbDi5QQ2C50oPDfmfK97Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:07:22.314960Z"},"content_sha256":"2debb90821e8d238255bc623d403f4e75db0775a85252900461b2f3487997eb2","schema_version":"1.0","event_id":"sha256:2debb90821e8d238255bc623d403f4e75db0775a85252900461b2f3487997eb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQGKGNBPPUTDN2QD4CKFCS7G7D/bundle.json","state_url":"https://pith.science/pith/VQGKGNBPPUTDN2QD4CKFCS7G7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQGKGNBPPUTDN2QD4CKFCS7G7D/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":"2026-07-03T11:07:22Z","links":{"resolver":"https://pith.science/pith/VQGKGNBPPUTDN2QD4CKFCS7G7D","bundle":"https://pith.science/pith/VQGKGNBPPUTDN2QD4CKFCS7G7D/bundle.json","state":"https://pith.science/pith/VQGKGNBPPUTDN2QD4CKFCS7G7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQGKGNBPPUTDN2QD4CKFCS7G7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VQGKGNBPPUTDN2QD4CKFCS7G7D","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":"441dafb4a1b4c657637567cc5db2797795f284381c707f5d7d18278ca2a1faab","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-07-01T16:01:42Z","title_canon_sha256":"2f37e3a3a4a4f53238f17c2b4aba7d9fd927b1fe887bb2929f0ce289c8878d4e"},"schema_version":"1.0","source":{"id":"2607.01110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.01110","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"arxiv_version","alias_value":"2607.01110v1","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01110","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_12","alias_value":"VQGKGNBPPUTD","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_16","alias_value":"VQGKGNBPPUTDN2QD","created_at":"2026-07-02T01:18:29Z"},{"alias_kind":"pith_short_8","alias_value":"VQGKGNBP","created_at":"2026-07-02T01:18:29Z"}],"graph_snapshots":[{"event_id":"sha256:2debb90821e8d238255bc623d403f4e75db0775a85252900461b2f3487997eb2","target":"graph","created_at":"2026-07-02T01:18:29Z","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/2607.01110/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the expressive power of the simplest modal-temporal language, obtained by adding Prior's temporal operators \\(G\\) and \\(H\\) to the basic modal language with \\(\\Box\\). This language is the standard bimodal combination of modal and tense logic; under its functional interpretation it is denoted \\(L_{T\\times W}\\). To analyse its definability across five order types, we consider two semantic readings of the temporal operators: the standard reading (\\(G,H\\)), which includes the current instant, and the strict reading (\\(G^{\\ast},H^{\\ast}\\)), which always excludes it.\n  We examine nine funct","authors_text":"Alfredo Burrieza","cross_cats":["math.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-07-01T16:01:42Z","title":"Definability of Functional Properties in the Basic Modal-Temporal Language over Ordered Frames"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01110","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":"sha256:3a88746d36d075d60bf742a5462aa0d4b4def8e150099b15b4cf7e71b8bcd879","target":"record","created_at":"2026-07-02T01:18:29Z","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":"441dafb4a1b4c657637567cc5db2797795f284381c707f5d7d18278ca2a1faab","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-07-01T16:01:42Z","title_canon_sha256":"2f37e3a3a4a4f53238f17c2b4aba7d9fd927b1fe887bb2929f0ce289c8878d4e"},"schema_version":"1.0","source":{"id":"2607.01110","kind":"arxiv","version":1}},"canonical_sha256":"ac0ca3342f7d2636ea03e094514be6f8f3a56c72a327971e1f5857eaa844dc0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac0ca3342f7d2636ea03e094514be6f8f3a56c72a327971e1f5857eaa844dc0e","first_computed_at":"2026-07-02T01:18:29.328482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-02T01:18:29.328482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SWE8xWnd1kJ6LZtxFG/TigYKY9rOt13G6vdNAnuJfoPmB9pFjj+U3AtsFyMMDKEfpNN8pPRFm9aklqHpxZ8PDw==","signature_status":"signed_v1","signed_at":"2026-07-02T01:18:29.328878Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.01110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a88746d36d075d60bf742a5462aa0d4b4def8e150099b15b4cf7e71b8bcd879","sha256:2debb90821e8d238255bc623d403f4e75db0775a85252900461b2f3487997eb2"],"state_sha256":"2c3995712bd210e6a23e21ab29780904ef0be684ecb504f0d6ab6ba6446a3202"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J5tT8TiHn/++ERPuQSkky/kvSVFJqJaLgg567iIenq+ywTjQdWk26+i6vmxLWA2n7RXRcBonI8iUOI8tmQ7KCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T11:07:22.316898Z","bundle_sha256":"2129abd77532bbbaff6abc2e6eeb45cae795aa059adbbf6486457bd02fb187f7"}}