{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DPQSFD7HMB6ZBA2FKWUCPY3GZH","short_pith_number":"pith:DPQSFD7H","canonical_record":{"source":{"id":"1611.00494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T07:48:25Z","cross_cats_sorted":[],"title_canon_sha256":"4038b854b6f90095945dca558521685c3f5fcb2eba881c17cc9d4c10b5d9643a","abstract_canon_sha256":"a8b77501c943df367fd6227e5ec7f0fa095089074760826c2830528ec25d5749"},"schema_version":"1.0"},"canonical_sha256":"1be1228fe7607d90834555a827e366c9c4e9f5827cfbd9ae9b23a89934a90d29","source":{"kind":"arxiv","id":"1611.00494","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00494","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00494v2","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00494","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"DPQSFD7HMB6Z","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DPQSFD7HMB6ZBA2F","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DPQSFD7H","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DPQSFD7HMB6ZBA2FKWUCPY3GZH","target":"record","payload":{"canonical_record":{"source":{"id":"1611.00494","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T07:48:25Z","cross_cats_sorted":[],"title_canon_sha256":"4038b854b6f90095945dca558521685c3f5fcb2eba881c17cc9d4c10b5d9643a","abstract_canon_sha256":"a8b77501c943df367fd6227e5ec7f0fa095089074760826c2830528ec25d5749"},"schema_version":"1.0"},"canonical_sha256":"1be1228fe7607d90834555a827e366c9c4e9f5827cfbd9ae9b23a89934a90d29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:16.646798Z","signature_b64":"qJ7dIFZT5GJdk1w00tJRxoVCTI0enxwmHXVDm+R89TZPdASErJUhlxpdWQqLtTqAPfWMG8ik4EahD4YZLMMjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1be1228fe7607d90834555a827e366c9c4e9f5827cfbd9ae9b23a89934a90d29","last_reissued_at":"2026-05-18T00:14:16.646130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:16.646130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.00494","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":"2026-05-18T00:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fNdojA7dQm8HjkjHK36Q7L1ENMtb7+ItveHupT8f9aYRcQwmAglr059+T7hVBvKmUsF/ZZI6D4xRE2DoPjxuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:33:09.899202Z"},"content_sha256":"5a3e3b9c51dde2ff2fe92476ea237377d1bd36f80607954cb449e3296c4c0b1f","schema_version":"1.0","event_id":"sha256:5a3e3b9c51dde2ff2fe92476ea237377d1bd36f80607954cb449e3296c4c0b1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DPQSFD7HMB6ZBA2FKWUCPY3GZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The singular bivariate quartic tracial moment problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abhishek Bhardwaj, Alja\\v{z} Zalar","submitted_at":"2016-11-02T07:48:25Z","abstract_excerpt":"The (classical) truncated moment problem, extensively studied by Curto and Fialkow, asks to characterize when a finite sequence of real numbers indexes by words in commuting variables can be represented with moments of a positive Borel measure $\\mu$ on $\\mathbb R^n$. In \\cite{BK12} Burgdorf and Klep introduced its tracial analog, the truncated tracial moment problem, which replaces commuting variables with non-commuting ones and moments of $\\mu$ with tracial moments of matrices. In the bivariate quartic case, where indices run over words in two variables of degree at most four, every sequence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00494","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":""},"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":"2026-05-18T00:14:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLw5nClTFHU0wCkDeZxxjvB5OK7TZHUQa3yGWPsi4tLtL+5zVrv6hI5rOyNLrwbs5q30ZdG9vmCVle0xtLBZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:33:09.899564Z"},"content_sha256":"dc1da068020b500894515d7b1b942eec61d4fdbdede76dbd558c37ed74ef6342","schema_version":"1.0","event_id":"sha256:dc1da068020b500894515d7b1b942eec61d4fdbdede76dbd558c37ed74ef6342"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPQSFD7HMB6ZBA2FKWUCPY3GZH/bundle.json","state_url":"https://pith.science/pith/DPQSFD7HMB6ZBA2FKWUCPY3GZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPQSFD7HMB6ZBA2FKWUCPY3GZH/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":"2026-05-30T23:33:09Z","links":{"resolver":"https://pith.science/pith/DPQSFD7HMB6ZBA2FKWUCPY3GZH","bundle":"https://pith.science/pith/DPQSFD7HMB6ZBA2FKWUCPY3GZH/bundle.json","state":"https://pith.science/pith/DPQSFD7HMB6ZBA2FKWUCPY3GZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPQSFD7HMB6ZBA2FKWUCPY3GZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DPQSFD7HMB6ZBA2FKWUCPY3GZH","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":"a8b77501c943df367fd6227e5ec7f0fa095089074760826c2830528ec25d5749","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T07:48:25Z","title_canon_sha256":"4038b854b6f90095945dca558521685c3f5fcb2eba881c17cc9d4c10b5d9643a"},"schema_version":"1.0","source":{"id":"1611.00494","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.00494","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"arxiv_version","alias_value":"1611.00494v2","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.00494","created_at":"2026-05-18T00:14:16Z"},{"alias_kind":"pith_short_12","alias_value":"DPQSFD7HMB6Z","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DPQSFD7HMB6ZBA2F","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DPQSFD7H","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:dc1da068020b500894515d7b1b942eec61d4fdbdede76dbd558c37ed74ef6342","target":"graph","created_at":"2026-05-18T00:14:16Z","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"},"paper":{"abstract_excerpt":"The (classical) truncated moment problem, extensively studied by Curto and Fialkow, asks to characterize when a finite sequence of real numbers indexes by words in commuting variables can be represented with moments of a positive Borel measure $\\mu$ on $\\mathbb R^n$. In \\cite{BK12} Burgdorf and Klep introduced its tracial analog, the truncated tracial moment problem, which replaces commuting variables with non-commuting ones and moments of $\\mu$ with tracial moments of matrices. In the bivariate quartic case, where indices run over words in two variables of degree at most four, every sequence ","authors_text":"Abhishek Bhardwaj, Alja\\v{z} Zalar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T07:48:25Z","title":"The singular bivariate quartic tracial moment problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.00494","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":"sha256:5a3e3b9c51dde2ff2fe92476ea237377d1bd36f80607954cb449e3296c4c0b1f","target":"record","created_at":"2026-05-18T00:14:16Z","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":"a8b77501c943df367fd6227e5ec7f0fa095089074760826c2830528ec25d5749","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-02T07:48:25Z","title_canon_sha256":"4038b854b6f90095945dca558521685c3f5fcb2eba881c17cc9d4c10b5d9643a"},"schema_version":"1.0","source":{"id":"1611.00494","kind":"arxiv","version":2}},"canonical_sha256":"1be1228fe7607d90834555a827e366c9c4e9f5827cfbd9ae9b23a89934a90d29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1be1228fe7607d90834555a827e366c9c4e9f5827cfbd9ae9b23a89934a90d29","first_computed_at":"2026-05-18T00:14:16.646130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:16.646130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qJ7dIFZT5GJdk1w00tJRxoVCTI0enxwmHXVDm+R89TZPdASErJUhlxpdWQqLtTqAPfWMG8ik4EahD4YZLMMjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:16.646798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.00494","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a3e3b9c51dde2ff2fe92476ea237377d1bd36f80607954cb449e3296c4c0b1f","sha256:dc1da068020b500894515d7b1b942eec61d4fdbdede76dbd558c37ed74ef6342"],"state_sha256":"5cdad8532b46c632fe13ee1f6d00b28c3221e08677bc3624cbc6494a5498271b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ivsD9jLBqFDmCB8LOxemG48tA5JUz2k/6No+5/KHmpGY42PiChGPI1D4HuBvE55igVWi1Lea3edp+mCKh3cSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:33:09.902240Z","bundle_sha256":"409b7ffa668e2fca43de4c55d024d4d7df63301c59d570e7f17aa830971dd6ca"}}