{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BXJNENLIMOFL7EDBREB44HJWX4","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":"0d1f175ad3c86c9a5fedef46540efe5a4478f9490037d82117628be16d1e9750","cross_cats_sorted":["cs.AI","cs.SC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-30T12:40:01Z","title_canon_sha256":"b87f31b22b452ccac93777d13a04f513a316dfce77142d16ba040a6cf7d10d1f"},"schema_version":"1.0","source":{"id":"2505.24533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24533","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24533v1","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24533","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"pith_short_12","alias_value":"BXJNENLIMOFL","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"pith_short_16","alias_value":"BXJNENLIMOFL7EDB","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"pith_short_8","alias_value":"BXJNENLI","created_at":"2026-07-05T11:12:51Z"}],"graph_snapshots":[{"event_id":"sha256:cebe3929ca00d678d30d136cd8017f3395c7581b423f1ab2d263f23ed0974bef","target":"graph","created_at":"2026-07-05T11:12:51Z","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/2505.24533/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a novel framework consisting of a class of algebraic structures that generalize one-dimensional monoidal systems into higher dimensions by defining per-axis composition operators subject to non-commutativity and a global interchange law. These structures, defined recursively from a base case of vector-matrix pairs, model directional composition in multiple dimensions while preserving structural coherence through commutative linear operators.\n  We show that the framework that unifies several well-known linear transforms in signal processing and data analysis. In this framework, dat","authors_text":"Mahesh Godavarti","cross_cats":["cs.AI","cs.SC"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-30T12:40:01Z","title":"Directional Non-Commutative Monoidal Structures with Interchange Law via Commutative Generators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24533","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:b3a13f6d490c0eacf0489af814e2cd6b113317e0aa97b302a3c0be92c059bdbb","target":"record","created_at":"2026-07-05T11:12:51Z","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":"0d1f175ad3c86c9a5fedef46540efe5a4478f9490037d82117628be16d1e9750","cross_cats_sorted":["cs.AI","cs.SC"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-30T12:40:01Z","title_canon_sha256":"b87f31b22b452ccac93777d13a04f513a316dfce77142d16ba040a6cf7d10d1f"},"schema_version":"1.0","source":{"id":"2505.24533","kind":"arxiv","version":1}},"canonical_sha256":"0dd2d23568638abf90618903ce1d36bf3f6ec816ca976581f320ca182d31c678","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dd2d23568638abf90618903ce1d36bf3f6ec816ca976581f320ca182d31c678","first_computed_at":"2026-07-05T11:12:51.874163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:51.874163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AkBYVeVb8Fe59BhJ/1ZL2cegTlf4F7fGtdhK/JbwFBZBaYCAsR8eHPLQ3dk+8nWzjKcZmLEQ5dZs6SIqSIsWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:51.874666Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3a13f6d490c0eacf0489af814e2cd6b113317e0aa97b302a3c0be92c059bdbb","sha256:cebe3929ca00d678d30d136cd8017f3395c7581b423f1ab2d263f23ed0974bef"],"state_sha256":"6de07c5eb80b86efcbecd19e36bdb2f161c48795635c1a07c1b41fa2b83c96fd"}