{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:GQNDTUUJIIGEAQ62HLSS55JZ6B","short_pith_number":"pith:GQNDTUUJ","canonical_record":{"source":{"id":"2311.15550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2023-11-27T05:32:37Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0583a13e5a65681f35ed8ec0f0c32e9e4991c9cdd439cba16078f75bbe8bbb45","abstract_canon_sha256":"0941207126c1858ae48dabac92d890943f137e877262d41a2a9e4946d16359f9"},"schema_version":"1.0"},"canonical_sha256":"341a39d289420c4043da3ae52ef539f05bfe5c49da756e400149aaf7054741f0","source":{"kind":"arxiv","id":"2311.15550","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.15550","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"2311.15550v2","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.15550","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"GQNDTUUJIIGE","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"pith_short_16","alias_value":"GQNDTUUJIIGEAQ62","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"pith_short_8","alias_value":"GQNDTUUJ","created_at":"2026-07-05T07:30:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:GQNDTUUJIIGEAQ62HLSS55JZ6B","target":"record","payload":{"canonical_record":{"source":{"id":"2311.15550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2023-11-27T05:32:37Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"0583a13e5a65681f35ed8ec0f0c32e9e4991c9cdd439cba16078f75bbe8bbb45","abstract_canon_sha256":"0941207126c1858ae48dabac92d890943f137e877262d41a2a9e4946d16359f9"},"schema_version":"1.0"},"canonical_sha256":"341a39d289420c4043da3ae52ef539f05bfe5c49da756e400149aaf7054741f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:30:23.808532Z","signature_b64":"LL7aUuDnKUNqtqi1Ynyk45RcsHmzl38NJwxTHhBJ1BzvqyeMfkr49zCwLrqdbkPhID/v4LibKdYajWGx2TmsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"341a39d289420c4043da3ae52ef539f05bfe5c49da756e400149aaf7054741f0","last_reissued_at":"2026-07-05T07:30:23.808075Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:30:23.808075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.15550","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":"2026-07-05T07:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iGLOM5EvQG44RwME33k0ZR08nri2A9egg/KUmG26HzbLK35nuP072b5BH2gtLWv5+z0f9SJq1sNvNt7ascsLAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T07:53:02.624130Z"},"content_sha256":"6b6b1a7d584530f1661e6ad20f62ebffd5f2ed6fc65321cdefc95ae9e081fcbf","schema_version":"1.0","event_id":"sha256:6b6b1a7d584530f1661e6ad20f62ebffd5f2ed6fc65321cdefc95ae9e081fcbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:GQNDTUUJIIGEAQ62HLSS55JZ6B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on free divergence-free vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.OA","authors_text":"Akihiro Miyagawa, Hyuga Ito","submitted_at":"2023-11-27T05:32:37Z","abstract_excerpt":"We exhibit an orthonormal basis of cyclic gradients and a (non-orthogonal) basis of the homogeneous free divergence-free vector field on the full Fock space and determine the dimension of Voiculescu's free divergence-free vector field of degree k or less. Moreover, we also give a concrete formula for the orthogonal projection onto the space of cyclic gradients as well as the free Leray projection."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.15550","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/2311.15550/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":"2026-07-05T07:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pGYlHWPb/OJG53IH0djPrScH+BVa4KKVQMDcCyqKU8Hywv3i9ipVvph7YcvalMFxFpSFDnvBxk8K3Dm1C3hpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T07:53:02.624842Z"},"content_sha256":"ad24d4ae18728103c335453c97693a9fe18a2fe5353e91ef960c39656351a3ef","schema_version":"1.0","event_id":"sha256:ad24d4ae18728103c335453c97693a9fe18a2fe5353e91ef960c39656351a3ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GQNDTUUJIIGEAQ62HLSS55JZ6B/bundle.json","state_url":"https://pith.science/pith/GQNDTUUJIIGEAQ62HLSS55JZ6B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GQNDTUUJIIGEAQ62HLSS55JZ6B/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":"2026-07-08T07:53:02Z","links":{"resolver":"https://pith.science/pith/GQNDTUUJIIGEAQ62HLSS55JZ6B","bundle":"https://pith.science/pith/GQNDTUUJIIGEAQ62HLSS55JZ6B/bundle.json","state":"https://pith.science/pith/GQNDTUUJIIGEAQ62HLSS55JZ6B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GQNDTUUJIIGEAQ62HLSS55JZ6B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:GQNDTUUJIIGEAQ62HLSS55JZ6B","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":"0941207126c1858ae48dabac92d890943f137e877262d41a2a9e4946d16359f9","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2023-11-27T05:32:37Z","title_canon_sha256":"0583a13e5a65681f35ed8ec0f0c32e9e4991c9cdd439cba16078f75bbe8bbb45"},"schema_version":"1.0","source":{"id":"2311.15550","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.15550","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"2311.15550v2","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.15550","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"GQNDTUUJIIGE","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"pith_short_16","alias_value":"GQNDTUUJIIGEAQ62","created_at":"2026-07-05T07:30:23Z"},{"alias_kind":"pith_short_8","alias_value":"GQNDTUUJ","created_at":"2026-07-05T07:30:23Z"}],"graph_snapshots":[{"event_id":"sha256:ad24d4ae18728103c335453c97693a9fe18a2fe5353e91ef960c39656351a3ef","target":"graph","created_at":"2026-07-05T07:30:23Z","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/2311.15550/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We exhibit an orthonormal basis of cyclic gradients and a (non-orthogonal) basis of the homogeneous free divergence-free vector field on the full Fock space and determine the dimension of Voiculescu's free divergence-free vector field of degree k or less. Moreover, we also give a concrete formula for the orthogonal projection onto the space of cyclic gradients as well as the free Leray projection.","authors_text":"Akihiro Miyagawa, Hyuga Ito","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2023-11-27T05:32:37Z","title":"A note on free divergence-free vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.15550","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":"sha256:6b6b1a7d584530f1661e6ad20f62ebffd5f2ed6fc65321cdefc95ae9e081fcbf","target":"record","created_at":"2026-07-05T07:30:23Z","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":"0941207126c1858ae48dabac92d890943f137e877262d41a2a9e4946d16359f9","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2023-11-27T05:32:37Z","title_canon_sha256":"0583a13e5a65681f35ed8ec0f0c32e9e4991c9cdd439cba16078f75bbe8bbb45"},"schema_version":"1.0","source":{"id":"2311.15550","kind":"arxiv","version":2}},"canonical_sha256":"341a39d289420c4043da3ae52ef539f05bfe5c49da756e400149aaf7054741f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"341a39d289420c4043da3ae52ef539f05bfe5c49da756e400149aaf7054741f0","first_computed_at":"2026-07-05T07:30:23.808075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:30:23.808075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LL7aUuDnKUNqtqi1Ynyk45RcsHmzl38NJwxTHhBJ1BzvqyeMfkr49zCwLrqdbkPhID/v4LibKdYajWGx2TmsCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:30:23.808532Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.15550","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b6b1a7d584530f1661e6ad20f62ebffd5f2ed6fc65321cdefc95ae9e081fcbf","sha256:ad24d4ae18728103c335453c97693a9fe18a2fe5353e91ef960c39656351a3ef"],"state_sha256":"8f74f1d44d07c207e9b293a07b47b05685f0693a0857a185ce17e28315a45f61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9uFUdsz2MBIwRdws3NYvFkTovZepSKVuuHJIFOAH47MlhrreqgS5bEXgIjPaG/hWdIRSQ8hdrjqEf3nWFA+KBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T07:53:02.628672Z","bundle_sha256":"d7cb878049a429e34d57dddd758a40a4824d86abd37863bdfdf14c4302f1f1e5"}}