{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:D5CLGPVHLYBQMHUDWAWYFLAL3I","short_pith_number":"pith:D5CLGPVH","canonical_record":{"source":{"id":"2507.21519","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-29T05:59:44Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b684e9e686fe985f9a9880413a21bd02900e3699b6678151b52983aaa90e2bc2","abstract_canon_sha256":"6fc3816fb61ff264163b325e978f89f60bf8e72334ec28185af40c946a991870"},"schema_version":"1.0"},"canonical_sha256":"1f44b33ea75e03061e83b02d82ac0bda366ad07643ddffa7309a35efaf230d68","source":{"kind":"arxiv","id":"2507.21519","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.21519","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"2507.21519v1","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.21519","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"D5CLGPVHLYBQ","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"pith_short_16","alias_value":"D5CLGPVHLYBQMHUD","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"pith_short_8","alias_value":"D5CLGPVH","created_at":"2026-07-05T11:45:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:D5CLGPVHLYBQMHUDWAWYFLAL3I","target":"record","payload":{"canonical_record":{"source":{"id":"2507.21519","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-29T05:59:44Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b684e9e686fe985f9a9880413a21bd02900e3699b6678151b52983aaa90e2bc2","abstract_canon_sha256":"6fc3816fb61ff264163b325e978f89f60bf8e72334ec28185af40c946a991870"},"schema_version":"1.0"},"canonical_sha256":"1f44b33ea75e03061e83b02d82ac0bda366ad07643ddffa7309a35efaf230d68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:45:01.619138Z","signature_b64":"xyghjbIoJ6MBwP9pksZ6Vq7FQNGhM1Y0QZcRVX4G9bZWQSd7K+gXf9uSWdtTIvegsGvXSzRpAEtbTaZ5HBhgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f44b33ea75e03061e83b02d82ac0bda366ad07643ddffa7309a35efaf230d68","last_reissued_at":"2026-07-05T11:45:01.618723Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:45:01.618723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.21519","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:45:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zlLkyFLvecLB1X6xLHDCuIsDBWAkzFu1DgWPjgbJS7ggoN4UP/s7GhLRvm8TZDG+bWPFelmuqSEFPmz62ZhdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:35:39.303920Z"},"content_sha256":"2022d01c00ebbd5260c136cef9f09118cd51236ca69839660b89d2a8bb6bab8c","schema_version":"1.0","event_id":"sha256:2022d01c00ebbd5260c136cef9f09118cd51236ca69839660b89d2a8bb6bab8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:D5CLGPVHLYBQMHUDWAWYFLAL3I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational inference and density estimation with non-negative tensor train","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Lexing Ying, Rajat Dwaraknath, Xun Tang","submitted_at":"2025-07-29T05:59:44Z","abstract_excerpt":"This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density estimation, whereby one has access to either the unnormalized analytic formula of the distribution or the samples generated from the distribution. In particular, the compression is done through a two-stage approach. In the first stage, we use existing subroutines to encode the distribution function in a tensor train format. In the second stage, we use an NTT ansatz t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.21519","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/2507.21519/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":"2026-07-05T11:45:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aU2FSaMM2xI9Fkf0lDQ33tBmUCyaytJ1hmGRjjw8zSR0Wa79bI5SQCMYxbUFJwP0jtLTclCKEeBlF5ne7wwDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T02:35:39.304472Z"},"content_sha256":"27c5dcc7345652f4344e13a5e18fff3fbca77798c01d372db80c732c92284845","schema_version":"1.0","event_id":"sha256:27c5dcc7345652f4344e13a5e18fff3fbca77798c01d372db80c732c92284845"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5CLGPVHLYBQMHUDWAWYFLAL3I/bundle.json","state_url":"https://pith.science/pith/D5CLGPVHLYBQMHUDWAWYFLAL3I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5CLGPVHLYBQMHUDWAWYFLAL3I/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":"2026-08-17T02:35:39Z","links":{"resolver":"https://pith.science/pith/D5CLGPVHLYBQMHUDWAWYFLAL3I","bundle":"https://pith.science/pith/D5CLGPVHLYBQMHUDWAWYFLAL3I/bundle.json","state":"https://pith.science/pith/D5CLGPVHLYBQMHUDWAWYFLAL3I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5CLGPVHLYBQMHUDWAWYFLAL3I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:D5CLGPVHLYBQMHUDWAWYFLAL3I","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":"6fc3816fb61ff264163b325e978f89f60bf8e72334ec28185af40c946a991870","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-29T05:59:44Z","title_canon_sha256":"b684e9e686fe985f9a9880413a21bd02900e3699b6678151b52983aaa90e2bc2"},"schema_version":"1.0","source":{"id":"2507.21519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.21519","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"arxiv_version","alias_value":"2507.21519v1","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.21519","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"pith_short_12","alias_value":"D5CLGPVHLYBQ","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"pith_short_16","alias_value":"D5CLGPVHLYBQMHUD","created_at":"2026-07-05T11:45:01Z"},{"alias_kind":"pith_short_8","alias_value":"D5CLGPVH","created_at":"2026-07-05T11:45:01Z"}],"graph_snapshots":[{"event_id":"sha256:27c5dcc7345652f4344e13a5e18fff3fbca77798c01d372db80c732c92284845","target":"graph","created_at":"2026-07-05T11:45:01Z","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/2507.21519/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density estimation, whereby one has access to either the unnormalized analytic formula of the distribution or the samples generated from the distribution. In particular, the compression is done through a two-stage approach. In the first stage, we use existing subroutines to encode the distribution function in a tensor train format. In the second stage, we use an NTT ansatz t","authors_text":"Lexing Ying, Rajat Dwaraknath, Xun Tang","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-29T05:59:44Z","title":"Variational inference and density estimation with non-negative tensor train"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.21519","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":"sha256:2022d01c00ebbd5260c136cef9f09118cd51236ca69839660b89d2a8bb6bab8c","target":"record","created_at":"2026-07-05T11:45:01Z","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":"6fc3816fb61ff264163b325e978f89f60bf8e72334ec28185af40c946a991870","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-29T05:59:44Z","title_canon_sha256":"b684e9e686fe985f9a9880413a21bd02900e3699b6678151b52983aaa90e2bc2"},"schema_version":"1.0","source":{"id":"2507.21519","kind":"arxiv","version":1}},"canonical_sha256":"1f44b33ea75e03061e83b02d82ac0bda366ad07643ddffa7309a35efaf230d68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f44b33ea75e03061e83b02d82ac0bda366ad07643ddffa7309a35efaf230d68","first_computed_at":"2026-07-05T11:45:01.618723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:45:01.618723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xyghjbIoJ6MBwP9pksZ6Vq7FQNGhM1Y0QZcRVX4G9bZWQSd7K+gXf9uSWdtTIvegsGvXSzRpAEtbTaZ5HBhgCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:45:01.619138Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.21519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2022d01c00ebbd5260c136cef9f09118cd51236ca69839660b89d2a8bb6bab8c","sha256:27c5dcc7345652f4344e13a5e18fff3fbca77798c01d372db80c732c92284845"],"state_sha256":"f3331cf0f8cc8e4a26af450e646b9235c5983904ac793ca0466b57526299414d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PceqnY9Uoc8h79bcaOjehyR7vHV4omhlU14Rvkvdrs/CXsTPh5N9G3wyjZQqpN3rfKAhlomhimdZ+9NcYEpGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T02:35:39.309171Z","bundle_sha256":"352eb53487271d4624fe7e1ee64be42b369806f38d93c661851584a41f8f5a86"}}