{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FZ3WKIHFQ7ATTHTCF47VAQ3UUF","short_pith_number":"pith:FZ3WKIHF","canonical_record":{"source":{"id":"2604.10669","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-04-12T14:52:24Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"de24c33b866885162a84c836c7270138a5a2d8fe7514ab5cfefa0711ed61b284","abstract_canon_sha256":"a655e2f47481437073b0199e059bc55da2221c058471f62d3bcf6e3704685344"},"schema_version":"1.0"},"canonical_sha256":"2e776520e587c1399e622f3f504374a162aa91c5e039850a4bdce22e6b5cbde8","source":{"kind":"arxiv","id":"2604.10669","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.10669","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"2604.10669v2","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.10669","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"FZ3WKIHFQ7AT","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"pith_short_16","alias_value":"FZ3WKIHFQ7ATTHTC","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"pith_short_8","alias_value":"FZ3WKIHF","created_at":"2026-05-29T02:05:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FZ3WKIHFQ7ATTHTCF47VAQ3UUF","target":"record","payload":{"canonical_record":{"source":{"id":"2604.10669","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-04-12T14:52:24Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"de24c33b866885162a84c836c7270138a5a2d8fe7514ab5cfefa0711ed61b284","abstract_canon_sha256":"a655e2f47481437073b0199e059bc55da2221c058471f62d3bcf6e3704685344"},"schema_version":"1.0"},"canonical_sha256":"2e776520e587c1399e622f3f504374a162aa91c5e039850a4bdce22e6b5cbde8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:05:44.774857Z","signature_b64":"0fEo2WxUgxW49DXZoPsW9ySDEIeePe1gcBlbfDV6TgR+/wur16PvDV+/qljZTgatDTz3f7Qs6xhreif8u9HJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e776520e587c1399e622f3f504374a162aa91c5e039850a4bdce22e6b5cbde8","last_reissued_at":"2026-05-29T02:05:44.774144Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:05:44.774144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.10669","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ndJq4Gj9x1/CEzo0PGY8JECdaghULgB2cH/5nFDns3D5VuLQercD+Eo5j+0D8bLz+1cQZMoyJiIjWNbIgyXwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:35:46.298531Z"},"content_sha256":"4f82779ad38b8fe4076fcdadd47320f0f91240482f43cae80a586fa0eab34679","schema_version":"1.0","event_id":"sha256:4f82779ad38b8fe4076fcdadd47320f0f91240482f43cae80a586fa0eab34679"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FZ3WKIHFQ7ATTHTCF47VAQ3UUF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Linear Temporal Logic of Frequencies on Series of Events","license":"http://creativecommons.org/licenses/by/4.0/","headline":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system.","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Alessandro Giuseppe Buda, Giuseppe Primiero, Leonardo Ceragioli, Melissa Antonelli","submitted_at":"2026-04-12T14:52:24Z","abstract_excerpt":"This paper introduces LTLF, a temporal logic designed to express the frequency properties of event series in a natural but rigorous manner. By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers. The core novelty lies in the introduction of original modal quantifiers associated with a standard Kripke-style semantics. These quantifiers enable the explicit formalization of event series properties an"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the proposed Kripke-style semantics with added modal quantifiers can be defined consistently to capture both actual observed frequencies and ideal distributions without internal contradictions or loss of useful logical properties.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"LTLF adds measure-sensitive modal quantifiers to temporal logic for formalizing frequencies in event series and relating observed to ideal distributions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5154656f5cd9b59879abacfd14b86dcf3adedcdfed8b41cf3cba7be750093d9b"},"source":{"id":"2604.10669","kind":"arxiv","version":2},"verdict":{"id":"d3bcff64-88a2-4654-b37b-0d0273a8eb3c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:50:06.604723Z","strongest_claim":"By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers.","one_line_summary":"LTLF adds measure-sensitive modal quantifiers to temporal logic for formalizing frequencies in event series and relating observed to ideal distributions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the proposed Kripke-style semantics with added modal quantifiers can be defined consistently to capture both actual observed frequencies and ideal distributions without internal contradictions or loss of useful logical properties.","pith_extraction_headline":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.10669/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":"d3bcff64-88a2-4654-b37b-0d0273a8eb3c"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T02:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6C4X3sxtn4ikL/P55UmOo10F9gL+Zdz3gUGxGxy0OEhc5lp8w+XvzGoR2LcZQsZzz/Td6i3ONeP5hoT/bYbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:35:46.299417Z"},"content_sha256":"97a7f6b7892bec53cbbde588ead3db3c71016cf493c6f775113fb2524206f1c4","schema_version":"1.0","event_id":"sha256:97a7f6b7892bec53cbbde588ead3db3c71016cf493c6f775113fb2524206f1c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZ3WKIHFQ7ATTHTCF47VAQ3UUF/bundle.json","state_url":"https://pith.science/pith/FZ3WKIHFQ7ATTHTCF47VAQ3UUF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZ3WKIHFQ7ATTHTCF47VAQ3UUF/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":"2026-06-09T02:35:46Z","links":{"resolver":"https://pith.science/pith/FZ3WKIHFQ7ATTHTCF47VAQ3UUF","bundle":"https://pith.science/pith/FZ3WKIHFQ7ATTHTCF47VAQ3UUF/bundle.json","state":"https://pith.science/pith/FZ3WKIHFQ7ATTHTCF47VAQ3UUF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZ3WKIHFQ7ATTHTCF47VAQ3UUF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FZ3WKIHFQ7ATTHTCF47VAQ3UUF","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":"a655e2f47481437073b0199e059bc55da2221c058471f62d3bcf6e3704685344","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-04-12T14:52:24Z","title_canon_sha256":"de24c33b866885162a84c836c7270138a5a2d8fe7514ab5cfefa0711ed61b284"},"schema_version":"1.0","source":{"id":"2604.10669","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.10669","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"2604.10669v2","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.10669","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"FZ3WKIHFQ7AT","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"pith_short_16","alias_value":"FZ3WKIHFQ7ATTHTC","created_at":"2026-05-29T02:05:44Z"},{"alias_kind":"pith_short_8","alias_value":"FZ3WKIHF","created_at":"2026-05-29T02:05:44Z"}],"graph_snapshots":[{"event_id":"sha256:97a7f6b7892bec53cbbde588ead3db3c71016cf493c6f775113fb2524206f1c4","target":"graph","created_at":"2026-05-29T02:05:44Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the proposed Kripke-style semantics with added modal quantifiers can be defined consistently to capture both actual observed frequencies and ideal distributions without internal contradictions or loss of useful logical properties."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"LTLF adds measure-sensitive modal quantifiers to temporal logic for formalizing frequencies in event series and relating observed to ideal distributions."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system."}],"snapshot_sha256":"5154656f5cd9b59879abacfd14b86dcf3adedcdfed8b41cf3cba7be750093d9b"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.10669/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces LTLF, a temporal logic designed to express the frequency properties of event series in a natural but rigorous manner. By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers. The core novelty lies in the introduction of original modal quantifiers associated with a standard Kripke-style semantics. These quantifiers enable the explicit formalization of event series properties an","authors_text":"Alessandro Giuseppe Buda, Giuseppe Primiero, Leonardo Ceragioli, Melissa Antonelli","cross_cats":["math.LO"],"headline":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-04-12T14:52:24Z","title":"A Linear Temporal Logic of Frequencies on Series of Events"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.10669","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T15:50:06.604723Z","id":"d3bcff64-88a2-4654-b37b-0d0273a8eb3c","model_set":{"reader":"grok-4.3"},"one_line_summary":"LTLF adds measure-sensitive modal quantifiers to temporal logic for formalizing frequencies in event series and relating observed to ideal distributions.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system.","strongest_claim":"By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers.","weakest_assumption":"That the proposed Kripke-style semantics with added modal quantifiers can be defined consistently to capture both actual observed frequencies and ideal distributions without internal contradictions or loss of useful logical properties."}},"verdict_id":"d3bcff64-88a2-4654-b37b-0d0273a8eb3c"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4f82779ad38b8fe4076fcdadd47320f0f91240482f43cae80a586fa0eab34679","target":"record","created_at":"2026-05-29T02:05:44Z","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":"a655e2f47481437073b0199e059bc55da2221c058471f62d3bcf6e3704685344","cross_cats_sorted":["math.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2026-04-12T14:52:24Z","title_canon_sha256":"de24c33b866885162a84c836c7270138a5a2d8fe7514ab5cfefa0711ed61b284"},"schema_version":"1.0","source":{"id":"2604.10669","kind":"arxiv","version":2}},"canonical_sha256":"2e776520e587c1399e622f3f504374a162aa91c5e039850a4bdce22e6b5cbde8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e776520e587c1399e622f3f504374a162aa91c5e039850a4bdce22e6b5cbde8","first_computed_at":"2026-05-29T02:05:44.774144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:44.774144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0fEo2WxUgxW49DXZoPsW9ySDEIeePe1gcBlbfDV6TgR+/wur16PvDV+/qljZTgatDTz3f7Qs6xhreif8u9HJBQ==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:44.774857Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.10669","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f82779ad38b8fe4076fcdadd47320f0f91240482f43cae80a586fa0eab34679","sha256:97a7f6b7892bec53cbbde588ead3db3c71016cf493c6f775113fb2524206f1c4"],"state_sha256":"65f10085a295c6eb1bb73857f334520a15f3a779f43e11e908be10f58860e8b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhzeTboqrLsYJYPrVFB6vFoW0RHzOFuPViWDoN3lxWqp9P6c+eKUsLJWfcoYZ9JuwOicsaBfT3cgDvbiwH+aCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:35:46.303467Z","bundle_sha256":"8a30182ca5eec798a5a971f096dc6d8e14a51f34e2780d72885d7fa47eec31d0"}}