{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6CRN3T5HCWOUVF6KEA4FGDTLS7","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":"3576557003e26bc940a50eba6e5d6d3e4b85351aa2a2f508f5f4a974aa947145","cross_cats_sorted":["cs.CL","cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-07T03:34:00Z","title_canon_sha256":"0a85d3ba640e33adae517a0da42237e37a0d8b61a3f63c2e9037dd15e9e59ac0"},"schema_version":"1.0","source":{"id":"2605.05629","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.05629","created_at":"2026-06-03T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"2605.05629v3","created_at":"2026-06-03T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.05629","created_at":"2026-06-03T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"6CRN3T5HCWOU","created_at":"2026-06-03T01:05:50Z"},{"alias_kind":"pith_short_16","alias_value":"6CRN3T5HCWOUVF6K","created_at":"2026-06-03T01:05:50Z"},{"alias_kind":"pith_short_8","alias_value":"6CRN3T5H","created_at":"2026-06-03T01:05:50Z"}],"graph_snapshots":[{"event_id":"sha256:21496b042d6feb9e5708e7b2d26ab44983b05e9d467beeba9749092159a8652b","target":"graph","created_at":"2026-06-03T01:05:50Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Exploiting the radial symmetry of the vMF density we reduce the continuity equation on S^{d-1} to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on (S^{d-1})^L both decompose into posterior-weighted tangent sums."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the learned posterior (trained only by cross-entropy) is sufficiently accurate to produce stable posterior-weighted sums for both velocity and score during sampling on real discrete data."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Spherical vMF flows reduce the continuity equation on the sphere to a scalar ODE in cosine similarity, enabling posterior-weighted sampling of categorical sequences via cross-entropy trained posteriors."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Spherical flows using the von Mises-Fisher distribution reduce categorical sequence sampling to solving a scalar ODE in cosine similarity."}],"snapshot_sha256":"5dba8ad76b754c2ccce72edc53616688e31ad48c202b926eead51abc737cd001"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"c78bc3072ef5ee2433ae6dc26c0c34cdaf3450b1d512b9ffb2061b55ed49c911"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-20T14:02:04.714146Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T09:38:52.990973Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.897579Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T13:24:31.981767Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.05629/integrity.json","findings":[],"snapshot_sha256":"acfaac3f4c82d2e922172bb038e481a681472287bb125c8285606cd14f158427","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of learning generative models for discrete sequences in a continuous embedding space. Whereas prior approaches typically operate in Euclidean space or on the probability simplex, we instead work on the sphere $\\mathbb S^{d-1}$. There the von Mises-Fisher (vMF) distribution induces a natural noise process and admits a closed-form conditional score. The conditional velocity is in general intractable. Exploiting the radial symmetry of the vMF density we reduce the continuity equation on $\\mathbb S^{d-1}$ to a scalar ODE in the cosine similarity, whose unique bounded solution ","authors_text":"Gabriele Steidl, Gregor Kornhardt, Jannis Chemseddine","cross_cats":["cs.CL","cs.LG"],"headline":"Spherical flows using the von Mises-Fisher distribution reduce categorical sequence sampling to solving a scalar ODE in cosine similarity.","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-07T03:34:00Z","title":"Spherical Flows for Sampling Categorical Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.05629","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-12T01:33:40.029370Z","id":"46e8b717-95a6-4529-9d2a-318bbb9dc7be","model_set":{"reader":"grok-4.3"},"one_line_summary":"Spherical vMF flows reduce the continuity equation on the sphere to a scalar ODE in cosine similarity, enabling posterior-weighted sampling of categorical sequences via cross-entropy trained posteriors.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Spherical flows using the von Mises-Fisher distribution reduce categorical sequence sampling to solving a scalar ODE in cosine similarity.","strongest_claim":"Exploiting the radial symmetry of the vMF density we reduce the continuity equation on S^{d-1} to a scalar ODE in the cosine similarity, whose unique bounded solution determines the velocity. The marginal velocity and marginal score on (S^{d-1})^L both decompose into posterior-weighted tangent sums.","weakest_assumption":"That the learned posterior (trained only by cross-entropy) is sufficiently accurate to produce stable posterior-weighted sums for both velocity and score during sampling on real discrete data."}},"verdict_id":"46e8b717-95a6-4529-9d2a-318bbb9dc7be"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d6d6fcece214ec6c36770521ee9443a6200765fb733eb5bc249cff42a50681d3","target":"record","created_at":"2026-06-03T01:05:50Z","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":"3576557003e26bc940a50eba6e5d6d3e4b85351aa2a2f508f5f4a974aa947145","cross_cats_sorted":["cs.CL","cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"stat.ML","submitted_at":"2026-05-07T03:34:00Z","title_canon_sha256":"0a85d3ba640e33adae517a0da42237e37a0d8b61a3f63c2e9037dd15e9e59ac0"},"schema_version":"1.0","source":{"id":"2605.05629","kind":"arxiv","version":3}},"canonical_sha256":"f0a2ddcfa7159d4a97ca2038530e6b97dbd71545b389f9b26bee647b6fec00fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0a2ddcfa7159d4a97ca2038530e6b97dbd71545b389f9b26bee647b6fec00fc","first_computed_at":"2026-06-03T01:05:50.993923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:50.993923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HRrh2m5xHTpYcF5EscU9ZqeSYubukmSmBN276kVAhhH0ZEYPbrAf/83xsu8oXutT1Si7TQJOJwNRbGt2XS65Ag==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:50.994325Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.05629","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6d6fcece214ec6c36770521ee9443a6200765fb733eb5bc249cff42a50681d3","sha256:21496b042d6feb9e5708e7b2d26ab44983b05e9d467beeba9749092159a8652b"],"state_sha256":"bf7ac85c018d4d940519f04652b6ecbcbc35bfac88dc26c43678cf98098f998b"}