{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:Y6XJDODRIZG2CXH32YBV2D3P6L","short_pith_number":"pith:Y6XJDODR","schema_version":"1.0","canonical_sha256":"c7ae91b871464da15cfbd6035d0f6ff2f8255703fe4fbd507974b2a81ba9fc46","source":{"kind":"arxiv","id":"2606.00496","version":1},"attestation_state":"computed","paper":{"title":"Torus Graphs for Large Scale Neural Phase Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Casey Hanks, David E. Carlson, Jack Goffinet","submitted_at":"2026-05-30T02:56:56Z","abstract_excerpt":"Oscillatory neural signals such as electroencephalography (EEG) and local field potentials (LFPs) show phase relationships that coordinate communication across brain regions. Modern recordings capture hundreds of channels across many frequency bins, yet standard phase analyses are restricted to only a few variables. The Torus Graph (TG) model, an exponential-family distribution over phases whose univariate and pairwise potentials generalize von Mises distributions, infers principled structure among oscillations but models only static, undirected dependencies and is limited to $\\sim \\! 100$ var"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.00496","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-30T02:56:56Z","cross_cats_sorted":[],"title_canon_sha256":"b5c782fd99989cb0c5390081c03b5390b41062b64514950d919c373bcab948ac","abstract_canon_sha256":"1bc74a6a292462d1ced4abe9d3ede2d82ce2b5153498348b4f1d399d85dace60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:56.376226Z","signature_b64":"rDdgNN74jdSS+x/LRVnHF5Tv5tQ7gXI2JJX6J1QMVP5fUM0iCtnEXatW7qzTWTRMjf/rceOIWblMSJroy4q7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c7ae91b871464da15cfbd6035d0f6ff2f8255703fe4fbd507974b2a81ba9fc46","last_reissued_at":"2026-06-02T01:03:56.375830Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:56.375830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torus Graphs for Large Scale Neural Phase Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Casey Hanks, David E. Carlson, Jack Goffinet","submitted_at":"2026-05-30T02:56:56Z","abstract_excerpt":"Oscillatory neural signals such as electroencephalography (EEG) and local field potentials (LFPs) show phase relationships that coordinate communication across brain regions. Modern recordings capture hundreds of channels across many frequency bins, yet standard phase analyses are restricted to only a few variables. The Torus Graph (TG) model, an exponential-family distribution over phases whose univariate and pairwise potentials generalize von Mises distributions, infers principled structure among oscillations but models only static, undirected dependencies and is limited to $\\sim \\! 100$ var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00496","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/2606.00496/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.00496","created_at":"2026-06-02T01:03:56.375880+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.00496v1","created_at":"2026-06-02T01:03:56.375880+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00496","created_at":"2026-06-02T01:03:56.375880+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y6XJDODRIZG2","created_at":"2026-06-02T01:03:56.375880+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y6XJDODRIZG2CXH3","created_at":"2026-06-02T01:03:56.375880+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y6XJDODR","created_at":"2026-06-02T01:03:56.375880+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L","json":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L.json","graph_json":"https://pith.science/api/pith-number/Y6XJDODRIZG2CXH32YBV2D3P6L/graph.json","events_json":"https://pith.science/api/pith-number/Y6XJDODRIZG2CXH32YBV2D3P6L/events.json","paper":"https://pith.science/paper/Y6XJDODR"},"agent_actions":{"view_html":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L","download_json":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L.json","view_paper":"https://pith.science/paper/Y6XJDODR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.00496&json=true","fetch_graph":"https://pith.science/api/pith-number/Y6XJDODRIZG2CXH32YBV2D3P6L/graph.json","fetch_events":"https://pith.science/api/pith-number/Y6XJDODRIZG2CXH32YBV2D3P6L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L/action/storage_attestation","attest_author":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L/action/author_attestation","sign_citation":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L/action/citation_signature","submit_replication":"https://pith.science/pith/Y6XJDODRIZG2CXH32YBV2D3P6L/action/replication_record"}},"created_at":"2026-06-02T01:03:56.375880+00:00","updated_at":"2026-06-02T01:03:56.375880+00:00"}