{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:DS4SQER5JMF524ZY7VZIJEL3OW","short_pith_number":"pith:DS4SQER5","canonical_record":{"source":{"id":"2202.06829","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2022-02-14T16:06:29Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"title_canon_sha256":"241e91e8482e66f1c03f2593a3237fd7e450d75726ea001b8b7cd36f8835bc62","abstract_canon_sha256":"0fa6c7d926b6463f62b40881a0d4b1961dbc8b5d4b4fb7b1e539043c131cc43a"},"schema_version":"1.0"},"canonical_sha256":"1cb928123d4b0bdd7338fd7284917b75b4f7113112414c29c07085c93e5bab8b","source":{"kind":"arxiv","id":"2202.06829","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.06829","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"2202.06829v2","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.06829","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"DS4SQER5JMF5","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"pith_short_16","alias_value":"DS4SQER5JMF524ZY","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"pith_short_8","alias_value":"DS4SQER5","created_at":"2026-07-05T06:54:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:DS4SQER5JMF524ZY7VZIJEL3OW","target":"record","payload":{"canonical_record":{"source":{"id":"2202.06829","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2022-02-14T16:06:29Z","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"title_canon_sha256":"241e91e8482e66f1c03f2593a3237fd7e450d75726ea001b8b7cd36f8835bc62","abstract_canon_sha256":"0fa6c7d926b6463f62b40881a0d4b1961dbc8b5d4b4fb7b1e539043c131cc43a"},"schema_version":"1.0"},"canonical_sha256":"1cb928123d4b0bdd7338fd7284917b75b4f7113112414c29c07085c93e5bab8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:54:11.884397Z","signature_b64":"kFL+eqmmILvwcl2pQKJtjvA9wuY3yg9LKi6zWjyli1Iw8Q5OJyyiKH6mvrEI9S/D93aXKuhgAqr+KxlI49OECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cb928123d4b0bdd7338fd7284917b75b4f7113112414c29c07085c93e5bab8b","last_reissued_at":"2026-07-05T06:54:11.883787Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:54:11.883787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.06829","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":"2026-07-05T06:54:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ci5OtM9kG5EwosE9hLWbca8LNAbfGkWsEE3iYEmsmvPBoVSjG15pF/07HWynmsZ8rIEDJy0fYU2BImShkKrWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:21:32.426572Z"},"content_sha256":"20f69e55d491e349da157c368214f4d81ebd64dd1157ab6c33c73b02f4073ae6","schema_version":"1.0","event_id":"sha256:20f69e55d491e349da157c368214f4d81ebd64dd1157ab6c33c73b02f4073ae6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:DS4SQER5JMF524ZY7VZIJEL3OW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Permutation invariant matrix statistics and computational language tasks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","hep-th"],"primary_cat":"cs.CL","authors_text":"Adriana Correia, Manuel Accettulli Huber, Mehrnoosh Sadrzadeh, Sanjaye Ramgoolam","submitted_at":"2022-02-14T16:06:29Z","abstract_excerpt":"The Linguistic Matrix Theory programme introduced by Kartsaklis, Ramgoolam and Sadrzadeh is an approach to the statistics of matrices that are generated in type-driven distributional semantics, based on permutation invariant polynomial functions which are regarded as the key observables encoding the significant statistics. In this paper we generalize the previous results on the approximate Gaussianity of matrix distributions arising from compositional distributional semantics. We also introduce a geometry of observable vectors for words, defined by exploiting the graph-theoretic basis for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06829","kind":"arxiv","version":2},"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/2202.06829/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":"2026-07-05T06:54:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LmD15P16nhmqf9nKW4Hlwqy7BWXAc5LWtsKYvlnA5MKYXvTUUoGU7rjUthfwBZjge5Z0vT9v4OuhryRg+6DQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T18:21:32.427570Z"},"content_sha256":"2c7ca6222703c057d1a3b48bb00d33452e7426494710c35366cabfc02584c96a","schema_version":"1.0","event_id":"sha256:2c7ca6222703c057d1a3b48bb00d33452e7426494710c35366cabfc02584c96a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DS4SQER5JMF524ZY7VZIJEL3OW/bundle.json","state_url":"https://pith.science/pith/DS4SQER5JMF524ZY7VZIJEL3OW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DS4SQER5JMF524ZY7VZIJEL3OW/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":"2026-08-13T18:21:32Z","links":{"resolver":"https://pith.science/pith/DS4SQER5JMF524ZY7VZIJEL3OW","bundle":"https://pith.science/pith/DS4SQER5JMF524ZY7VZIJEL3OW/bundle.json","state":"https://pith.science/pith/DS4SQER5JMF524ZY7VZIJEL3OW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DS4SQER5JMF524ZY7VZIJEL3OW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:DS4SQER5JMF524ZY7VZIJEL3OW","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":"0fa6c7d926b6463f62b40881a0d4b1961dbc8b5d4b4fb7b1e539043c131cc43a","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2022-02-14T16:06:29Z","title_canon_sha256":"241e91e8482e66f1c03f2593a3237fd7e450d75726ea001b8b7cd36f8835bc62"},"schema_version":"1.0","source":{"id":"2202.06829","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.06829","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"arxiv_version","alias_value":"2202.06829v2","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.06829","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"pith_short_12","alias_value":"DS4SQER5JMF5","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"pith_short_16","alias_value":"DS4SQER5JMF524ZY","created_at":"2026-07-05T06:54:11Z"},{"alias_kind":"pith_short_8","alias_value":"DS4SQER5","created_at":"2026-07-05T06:54:11Z"}],"graph_snapshots":[{"event_id":"sha256:2c7ca6222703c057d1a3b48bb00d33452e7426494710c35366cabfc02584c96a","target":"graph","created_at":"2026-07-05T06:54:11Z","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/2202.06829/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Linguistic Matrix Theory programme introduced by Kartsaklis, Ramgoolam and Sadrzadeh is an approach to the statistics of matrices that are generated in type-driven distributional semantics, based on permutation invariant polynomial functions which are regarded as the key observables encoding the significant statistics. In this paper we generalize the previous results on the approximate Gaussianity of matrix distributions arising from compositional distributional semantics. We also introduce a geometry of observable vectors for words, defined by exploiting the graph-theoretic basis for the ","authors_text":"Adriana Correia, Manuel Accettulli Huber, Mehrnoosh Sadrzadeh, Sanjaye Ramgoolam","cross_cats":["cond-mat.stat-mech","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2022-02-14T16:06:29Z","title":"Permutation invariant matrix statistics and computational language tasks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.06829","kind":"arxiv","version":2},"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":"sha256:20f69e55d491e349da157c368214f4d81ebd64dd1157ab6c33c73b02f4073ae6","target":"record","created_at":"2026-07-05T06:54:11Z","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":"0fa6c7d926b6463f62b40881a0d4b1961dbc8b5d4b4fb7b1e539043c131cc43a","cross_cats_sorted":["cond-mat.stat-mech","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2022-02-14T16:06:29Z","title_canon_sha256":"241e91e8482e66f1c03f2593a3237fd7e450d75726ea001b8b7cd36f8835bc62"},"schema_version":"1.0","source":{"id":"2202.06829","kind":"arxiv","version":2}},"canonical_sha256":"1cb928123d4b0bdd7338fd7284917b75b4f7113112414c29c07085c93e5bab8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cb928123d4b0bdd7338fd7284917b75b4f7113112414c29c07085c93e5bab8b","first_computed_at":"2026-07-05T06:54:11.883787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:54:11.883787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kFL+eqmmILvwcl2pQKJtjvA9wuY3yg9LKi6zWjyli1Iw8Q5OJyyiKH6mvrEI9S/D93aXKuhgAqr+KxlI49OECQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:54:11.884397Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.06829","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20f69e55d491e349da157c368214f4d81ebd64dd1157ab6c33c73b02f4073ae6","sha256:2c7ca6222703c057d1a3b48bb00d33452e7426494710c35366cabfc02584c96a"],"state_sha256":"dd15c0bed706e566c6ab162f9442d9a77a7c1ee18000fb3c25a292b7332a3e9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UO8WSmGIDnHCJXoIEg8SGgRVZTF6FJ+ogRfsL2gMTO+nJPoqxQcm+EGtL8nyT0rjtOfyheRiQdHyzMPsUzw1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T18:21:32.490002Z","bundle_sha256":"4a3d0a5783de3466d05e143f27839853ded922050a55865757f69190286bfc9d"}}