{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XTLQNJF3E3CEVZC3Q3PZUX4D6D","short_pith_number":"pith:XTLQNJF3","canonical_record":{"source":{"id":"1611.08723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-26T17:18:59Z","cross_cats_sorted":[],"title_canon_sha256":"0ef44aade87431e836bfcbc1d0a5df1aa0d444fcfc954f81ec764f1cd6add623","abstract_canon_sha256":"7d3d6c0c94dc67729946f663358740adeae8d10a703352a203089aef8e526cbd"},"schema_version":"1.0"},"canonical_sha256":"bcd706a4bb26c44ae45b86df9a5f83f0d4e509a2b6130fabec6e8266d9566681","source":{"kind":"arxiv","id":"1611.08723","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08723","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08723v1","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08723","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"pith_short_12","alias_value":"XTLQNJF3E3CE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XTLQNJF3E3CEVZC3","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XTLQNJF3","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XTLQNJF3E3CEVZC3Q3PZUX4D6D","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-26T17:18:59Z","cross_cats_sorted":[],"title_canon_sha256":"0ef44aade87431e836bfcbc1d0a5df1aa0d444fcfc954f81ec764f1cd6add623","abstract_canon_sha256":"7d3d6c0c94dc67729946f663358740adeae8d10a703352a203089aef8e526cbd"},"schema_version":"1.0"},"canonical_sha256":"bcd706a4bb26c44ae45b86df9a5f83f0d4e509a2b6130fabec6e8266d9566681","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:37.019716Z","signature_b64":"y5w2LC537kCl8nDXp7GmVJ3wU8fym0kBb89Wp//ctSCHYIISooAugr0rWdw56aE9B6A3E5i1abfDGUEq/3kODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcd706a4bb26c44ae45b86df9a5f83f0d4e509a2b6130fabec6e8266d9566681","last_reissued_at":"2026-05-18T00:56:37.018962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:37.018962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08723","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":"2026-05-18T00:56:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrvu9gh7sukM2122NbUxiC+TB7f5ldqRkqoEaTyBp9pbv2QNnqzB88oVEXX7DMbfg+lj+CP8AsZqP8/eQITDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T12:14:36.530711Z"},"content_sha256":"42a8c0e6ceaf9b61db9ef5b43a2046b8c4cdb577e9b482871e79e0cb7ea1683d","schema_version":"1.0","event_id":"sha256:42a8c0e6ceaf9b61db9ef5b43a2046b8c4cdb577e9b482871e79e0cb7ea1683d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XTLQNJF3E3CEVZC3Q3PZUX4D6D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Division Algorithm in Sextic Truncated Moment Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Raul E. Curto, Seonguk Yoo","submitted_at":"2016-11-26T17:18:59Z","abstract_excerpt":"For a degree 2n finite sequence of real numbers $\\beta \\equiv \\beta^{(2n)}= \\{ \\beta_{00},\\beta_{10}, \\beta_{01},\\cdots, \\beta_{2n,0}, \\beta_{2n-1,1},\\cdots, \\beta_{1,2n-1},\\beta_{0,2n} \\}$ to have a representing measure $\\mu $, it is necessary for the associated moment matrix $\\mathcal{M}(n)$ to be positive semidefinite, and for the algebraic variety associated to $\\beta $, $\\mathcal{V}_{\\beta} \\equiv \\mathcal{V}(\\mathcal{M}(n))$, to satisfy $\\operatorname{rank} \\mathcal{M}(n)\\leq \\operatorname{card} \\mathcal{V}_{\\beta}$ as well as the following consistency} condition: if a polynomial $p(x,y)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08723","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":""},"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":"2026-05-18T00:56:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nT6jC70RpZPK1cSysu3mzv7LDVQEJ+WmvcTHJJLYRmyYFm08emFaeahiYto/elZOgNxvyX7e0Zspzbhs95PHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T12:14:36.531042Z"},"content_sha256":"1f3508f50bb220af2e070634d5ecdc6ad2dd5457d25e62bfbee1263c365dd6db","schema_version":"1.0","event_id":"sha256:1f3508f50bb220af2e070634d5ecdc6ad2dd5457d25e62bfbee1263c365dd6db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XTLQNJF3E3CEVZC3Q3PZUX4D6D/bundle.json","state_url":"https://pith.science/pith/XTLQNJF3E3CEVZC3Q3PZUX4D6D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XTLQNJF3E3CEVZC3Q3PZUX4D6D/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":"2026-06-20T12:14:36Z","links":{"resolver":"https://pith.science/pith/XTLQNJF3E3CEVZC3Q3PZUX4D6D","bundle":"https://pith.science/pith/XTLQNJF3E3CEVZC3Q3PZUX4D6D/bundle.json","state":"https://pith.science/pith/XTLQNJF3E3CEVZC3Q3PZUX4D6D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XTLQNJF3E3CEVZC3Q3PZUX4D6D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XTLQNJF3E3CEVZC3Q3PZUX4D6D","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":"7d3d6c0c94dc67729946f663358740adeae8d10a703352a203089aef8e526cbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-26T17:18:59Z","title_canon_sha256":"0ef44aade87431e836bfcbc1d0a5df1aa0d444fcfc954f81ec764f1cd6add623"},"schema_version":"1.0","source":{"id":"1611.08723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08723","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08723v1","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08723","created_at":"2026-05-18T00:56:37Z"},{"alias_kind":"pith_short_12","alias_value":"XTLQNJF3E3CE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XTLQNJF3E3CEVZC3","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XTLQNJF3","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:1f3508f50bb220af2e070634d5ecdc6ad2dd5457d25e62bfbee1263c365dd6db","target":"graph","created_at":"2026-05-18T00:56:37Z","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":"For a degree 2n finite sequence of real numbers $\\beta \\equiv \\beta^{(2n)}= \\{ \\beta_{00},\\beta_{10}, \\beta_{01},\\cdots, \\beta_{2n,0}, \\beta_{2n-1,1},\\cdots, \\beta_{1,2n-1},\\beta_{0,2n} \\}$ to have a representing measure $\\mu $, it is necessary for the associated moment matrix $\\mathcal{M}(n)$ to be positive semidefinite, and for the algebraic variety associated to $\\beta $, $\\mathcal{V}_{\\beta} \\equiv \\mathcal{V}(\\mathcal{M}(n))$, to satisfy $\\operatorname{rank} \\mathcal{M}(n)\\leq \\operatorname{card} \\mathcal{V}_{\\beta}$ as well as the following consistency} condition: if a polynomial $p(x,y)","authors_text":"Raul E. Curto, Seonguk Yoo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-26T17:18:59Z","title":"The Division Algorithm in Sextic Truncated Moment Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08723","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":"sha256:42a8c0e6ceaf9b61db9ef5b43a2046b8c4cdb577e9b482871e79e0cb7ea1683d","target":"record","created_at":"2026-05-18T00:56:37Z","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":"7d3d6c0c94dc67729946f663358740adeae8d10a703352a203089aef8e526cbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-26T17:18:59Z","title_canon_sha256":"0ef44aade87431e836bfcbc1d0a5df1aa0d444fcfc954f81ec764f1cd6add623"},"schema_version":"1.0","source":{"id":"1611.08723","kind":"arxiv","version":1}},"canonical_sha256":"bcd706a4bb26c44ae45b86df9a5f83f0d4e509a2b6130fabec6e8266d9566681","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcd706a4bb26c44ae45b86df9a5f83f0d4e509a2b6130fabec6e8266d9566681","first_computed_at":"2026-05-18T00:56:37.018962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:37.018962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y5w2LC537kCl8nDXp7GmVJ3wU8fym0kBb89Wp//ctSCHYIISooAugr0rWdw56aE9B6A3E5i1abfDGUEq/3kODw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:37.019716Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42a8c0e6ceaf9b61db9ef5b43a2046b8c4cdb577e9b482871e79e0cb7ea1683d","sha256:1f3508f50bb220af2e070634d5ecdc6ad2dd5457d25e62bfbee1263c365dd6db"],"state_sha256":"9d346c1ff06d27e3ea64c4b70a911ca4ff45210847b58b119eb952cac3ecb8b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RXoJm5sjcLkXxvDNIYPzg7UJRf3yHKpXabS+iHbsqDgp+Ywbd2z3bj0iRi5vZMp7FRCayJHRLK7j+ZdUgVKWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T12:14:36.532857Z","bundle_sha256":"17259fbc211241e3656eca5096b30ddc370b3f16ed18241d27bb9c3dfdd43896"}}