{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YNSHVVOXIFV63FOT6M26VCEXSH","short_pith_number":"pith:YNSHVVOX","canonical_record":{"source":{"id":"2507.05219","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T17:30:29Z","cross_cats_sorted":["cs.CL","cs.LO"],"title_canon_sha256":"408b8ddbcf327e2d1360009d91284bfedc158dad5394cda1dd63493201a24435","abstract_canon_sha256":"fbdedb4898bc409d2e91296d654befaebd15048098f6f023bd9739887787ecd3"},"schema_version":"1.0"},"canonical_sha256":"c3647ad5d7416bed95d3f335ea889791cb449d817cfd5fc292cd95aa85bcda92","source":{"kind":"arxiv","id":"2507.05219","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05219","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05219v1","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05219","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"pith_short_12","alias_value":"YNSHVVOXIFV6","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"YNSHVVOXIFV63FOT","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"YNSHVVOX","created_at":"2026-07-05T11:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YNSHVVOXIFV63FOT6M26VCEXSH","target":"record","payload":{"canonical_record":{"source":{"id":"2507.05219","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T17:30:29Z","cross_cats_sorted":["cs.CL","cs.LO"],"title_canon_sha256":"408b8ddbcf327e2d1360009d91284bfedc158dad5394cda1dd63493201a24435","abstract_canon_sha256":"fbdedb4898bc409d2e91296d654befaebd15048098f6f023bd9739887787ecd3"},"schema_version":"1.0"},"canonical_sha256":"c3647ad5d7416bed95d3f335ea889791cb449d817cfd5fc292cd95aa85bcda92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:10.802757Z","signature_b64":"hlF2mw4f2LxhtXfcp1LuO7arKiMdq3AHaGF1RQWJkxUxBMhoaoMr02vIfQ+mQ0clFLQHPSQrgf6GdmWMzypEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3647ad5d7416bed95d3f335ea889791cb449d817cfd5fc292cd95aa85bcda92","last_reissued_at":"2026-07-05T11:33:10.802281Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:10.802281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.05219","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":"2026-07-05T11:33:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"su+zwzxHPqNzk4tvViAsV1Q/cbuQ5blnE5qB/gvt84t6opCGBKfvv10fmn1lAYbxk/sWriNBFqgSP3x/akHhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T15:54:01.624974Z"},"content_sha256":"de9439dcd310f035b65320cd186543ee5777c700ce30ffb89b941df1709608e1","schema_version":"1.0","event_id":"sha256:de9439dcd310f035b65320cd186543ee5777c700ce30ffb89b941df1709608e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YNSHVVOXIFV63FOT6M26VCEXSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interleaving Logic and Counting","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CL","cs.LO"],"primary_cat":"math.LO","authors_text":"Johan van Benthem, Thomas Icard","submitted_at":"2025-07-07T17:30:29Z","abstract_excerpt":"Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common linguistic usage and its extension into the broader practice of natural language plus \"grassroots mathematics\".\n  We begin with a brief review of first-order logic with counting operators and cardinality comparisons. This system is known to be of high complexity, and drowns out finer aspects of the combination of logic and counting. We move to a small fragment that c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05219","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/2507.05219/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":"2026-07-05T11:33:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBl7FWD9q3LvcYYNLllKW8FH6qm/G0NSaCmilFfKw3+z+2ltcIIPFZ7iyjmbjAUwMckoU/i54qx/dsJuUVAbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T15:54:01.625354Z"},"content_sha256":"03e11828bc5743d1066da4b4d678da67599abdfe93a8ad0ed281c6da12b6048f","schema_version":"1.0","event_id":"sha256:03e11828bc5743d1066da4b4d678da67599abdfe93a8ad0ed281c6da12b6048f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YNSHVVOXIFV63FOT6M26VCEXSH/bundle.json","state_url":"https://pith.science/pith/YNSHVVOXIFV63FOT6M26VCEXSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YNSHVVOXIFV63FOT6M26VCEXSH/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":"2026-07-07T15:54:01Z","links":{"resolver":"https://pith.science/pith/YNSHVVOXIFV63FOT6M26VCEXSH","bundle":"https://pith.science/pith/YNSHVVOXIFV63FOT6M26VCEXSH/bundle.json","state":"https://pith.science/pith/YNSHVVOXIFV63FOT6M26VCEXSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YNSHVVOXIFV63FOT6M26VCEXSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YNSHVVOXIFV63FOT6M26VCEXSH","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":"fbdedb4898bc409d2e91296d654befaebd15048098f6f023bd9739887787ecd3","cross_cats_sorted":["cs.CL","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T17:30:29Z","title_canon_sha256":"408b8ddbcf327e2d1360009d91284bfedc158dad5394cda1dd63493201a24435"},"schema_version":"1.0","source":{"id":"2507.05219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.05219","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"arxiv_version","alias_value":"2507.05219v1","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.05219","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"pith_short_12","alias_value":"YNSHVVOXIFV6","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"YNSHVVOXIFV63FOT","created_at":"2026-07-05T11:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"YNSHVVOX","created_at":"2026-07-05T11:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:03e11828bc5743d1066da4b4d678da67599abdfe93a8ad0ed281c6da12b6048f","target":"graph","created_at":"2026-07-05T11:33:10Z","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/2507.05219/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common linguistic usage and its extension into the broader practice of natural language plus \"grassroots mathematics\".\n  We begin with a brief review of first-order logic with counting operators and cardinality comparisons. This system is known to be of high complexity, and drowns out finer aspects of the combination of logic and counting. We move to a small fragment that c","authors_text":"Johan van Benthem, Thomas Icard","cross_cats":["cs.CL","cs.LO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T17:30:29Z","title":"Interleaving Logic and Counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05219","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:de9439dcd310f035b65320cd186543ee5777c700ce30ffb89b941df1709608e1","target":"record","created_at":"2026-07-05T11:33:10Z","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":"fbdedb4898bc409d2e91296d654befaebd15048098f6f023bd9739887787ecd3","cross_cats_sorted":["cs.CL","cs.LO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2025-07-07T17:30:29Z","title_canon_sha256":"408b8ddbcf327e2d1360009d91284bfedc158dad5394cda1dd63493201a24435"},"schema_version":"1.0","source":{"id":"2507.05219","kind":"arxiv","version":1}},"canonical_sha256":"c3647ad5d7416bed95d3f335ea889791cb449d817cfd5fc292cd95aa85bcda92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3647ad5d7416bed95d3f335ea889791cb449d817cfd5fc292cd95aa85bcda92","first_computed_at":"2026-07-05T11:33:10.802281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:10.802281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hlF2mw4f2LxhtXfcp1LuO7arKiMdq3AHaGF1RQWJkxUxBMhoaoMr02vIfQ+mQ0clFLQHPSQrgf6GdmWMzypEBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:10.802757Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.05219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de9439dcd310f035b65320cd186543ee5777c700ce30ffb89b941df1709608e1","sha256:03e11828bc5743d1066da4b4d678da67599abdfe93a8ad0ed281c6da12b6048f"],"state_sha256":"64e8cfd451fd9e2450143ffe29f8ee9a1dcfcc8fcef799c854d78ea551449760"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HGzk3Xd+4//69EmBZtzT9dtMKhZjp+O9YFMw+qQtEZG6LYJOwPAF/T0WmA04RB2bS9YpOtmSTVfqteRWjovoBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T15:54:01.627271Z","bundle_sha256":"4a04414d3a22d15a76ccdb9055c8f93b072f48536213a282769c0179662a9f83"}}