{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JXFX2ORWKVJZWJNXVDY54JLIU7","short_pith_number":"pith:JXFX2ORW","canonical_record":{"source":{"id":"1502.00825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-03T12:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"e35342af2f2ac73bf4f6afe50b79665705709b9c686eb23dc645e1bd0e86b36f","abstract_canon_sha256":"f6c374dd9f70cd84c087b1686cc0fe474c73a09372fb3e0f7280914535a0caa1"},"schema_version":"1.0"},"canonical_sha256":"4dcb7d3a3655539b25b7a8f1de2568a7c8fd5d615fd1b19645fb153c2a73067e","source":{"kind":"arxiv","id":"1502.00825","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00825","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00825v2","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00825","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"JXFX2ORWKVJZ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JXFX2ORWKVJZWJNX","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JXFX2ORW","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JXFX2ORWKVJZWJNXVDY54JLIU7","target":"record","payload":{"canonical_record":{"source":{"id":"1502.00825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-03T12:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"e35342af2f2ac73bf4f6afe50b79665705709b9c686eb23dc645e1bd0e86b36f","abstract_canon_sha256":"f6c374dd9f70cd84c087b1686cc0fe474c73a09372fb3e0f7280914535a0caa1"},"schema_version":"1.0"},"canonical_sha256":"4dcb7d3a3655539b25b7a8f1de2568a7c8fd5d615fd1b19645fb153c2a73067e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:11.072681Z","signature_b64":"osnpxPnFdkEQXSJNzkJJpts+VEIOvA5bYPkH3lbGjLEJTcjmIwkZf+85OuMz77oHdQl6D+TigOsPoDgE4AKgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dcb7d3a3655539b25b7a8f1de2568a7c8fd5d615fd1b19645fb153c2a73067e","last_reissued_at":"2026-05-18T01:37:11.072163Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:11.072163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.00825","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":"2026-05-18T01:37:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JwgWtuoYHJtWvZpJQQyVeD2XB0jY1JPUXVpTiajqj08D4dtXRF02Sq/Gg17CU3wbaZzWxBiRDv8kLNyMBJHrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:15:06.330057Z"},"content_sha256":"f6111b3dec4358c0b6f881adc363a40235ec39e9df0cb838f0d204147da61ac7","schema_version":"1.0","event_id":"sha256:f6111b3dec4358c0b6f881adc363a40235ec39e9df0cb838f0d204147da61ac7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JXFX2ORWKVJZWJNXVDY54JLIU7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A general fibre theorem for moment problems and some applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Konrad Schm\\\"udgen","submitted_at":"2015-02-03T12:04:45Z","abstract_excerpt":"The fibre theorem \\cite{schm2003} for the moment problem on closed semi-algebraic subsets of $\\R^d$ is generalized to finitely generated real unital algebras. As an application two new theorems on the rational multidimensional moment problem are proved. Another application is a characterization of moment functionals on the polynomial algebra $\\R[x_1,\\dots,x_d]$ in terms of extensions. Finally, the fibre theorem and the extension theorem are used to reprove basic results on the complex moment problem due to Stochel and Szafraniec \\cite{stochelsz} and Bisgaard \\cite{bisgaard}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00825","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":"2026-05-18T01:37:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7vIPikSnNeeFhczaR5BmywvLhKkYko4zWFMYyfKFVz9XhFQiVml7xws6AmuhYOyaLGmylmQ8s9HG4gK7LNECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:15:06.330511Z"},"content_sha256":"f8861371a43ca883d7e6a2a764eb336075f1654c1ad8b8ae6bcd191fa1cecad5","schema_version":"1.0","event_id":"sha256:f8861371a43ca883d7e6a2a764eb336075f1654c1ad8b8ae6bcd191fa1cecad5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JXFX2ORWKVJZWJNXVDY54JLIU7/bundle.json","state_url":"https://pith.science/pith/JXFX2ORWKVJZWJNXVDY54JLIU7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JXFX2ORWKVJZWJNXVDY54JLIU7/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":"2026-05-29T15:15:06Z","links":{"resolver":"https://pith.science/pith/JXFX2ORWKVJZWJNXVDY54JLIU7","bundle":"https://pith.science/pith/JXFX2ORWKVJZWJNXVDY54JLIU7/bundle.json","state":"https://pith.science/pith/JXFX2ORWKVJZWJNXVDY54JLIU7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JXFX2ORWKVJZWJNXVDY54JLIU7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JXFX2ORWKVJZWJNXVDY54JLIU7","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":"f6c374dd9f70cd84c087b1686cc0fe474c73a09372fb3e0f7280914535a0caa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-03T12:04:45Z","title_canon_sha256":"e35342af2f2ac73bf4f6afe50b79665705709b9c686eb23dc645e1bd0e86b36f"},"schema_version":"1.0","source":{"id":"1502.00825","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00825","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00825v2","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00825","created_at":"2026-05-18T01:37:11Z"},{"alias_kind":"pith_short_12","alias_value":"JXFX2ORWKVJZ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JXFX2ORWKVJZWJNX","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JXFX2ORW","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:f8861371a43ca883d7e6a2a764eb336075f1654c1ad8b8ae6bcd191fa1cecad5","target":"graph","created_at":"2026-05-18T01:37:11Z","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 fibre theorem \\cite{schm2003} for the moment problem on closed semi-algebraic subsets of $\\R^d$ is generalized to finitely generated real unital algebras. As an application two new theorems on the rational multidimensional moment problem are proved. Another application is a characterization of moment functionals on the polynomial algebra $\\R[x_1,\\dots,x_d]$ in terms of extensions. Finally, the fibre theorem and the extension theorem are used to reprove basic results on the complex moment problem due to Stochel and Szafraniec \\cite{stochelsz} and Bisgaard \\cite{bisgaard}.","authors_text":"Konrad Schm\\\"udgen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-03T12:04:45Z","title":"A general fibre theorem for moment problems and some applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00825","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:f6111b3dec4358c0b6f881adc363a40235ec39e9df0cb838f0d204147da61ac7","target":"record","created_at":"2026-05-18T01:37:11Z","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":"f6c374dd9f70cd84c087b1686cc0fe474c73a09372fb3e0f7280914535a0caa1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-03T12:04:45Z","title_canon_sha256":"e35342af2f2ac73bf4f6afe50b79665705709b9c686eb23dc645e1bd0e86b36f"},"schema_version":"1.0","source":{"id":"1502.00825","kind":"arxiv","version":2}},"canonical_sha256":"4dcb7d3a3655539b25b7a8f1de2568a7c8fd5d615fd1b19645fb153c2a73067e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dcb7d3a3655539b25b7a8f1de2568a7c8fd5d615fd1b19645fb153c2a73067e","first_computed_at":"2026-05-18T01:37:11.072163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:11.072163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"osnpxPnFdkEQXSJNzkJJpts+VEIOvA5bYPkH3lbGjLEJTcjmIwkZf+85OuMz77oHdQl6D+TigOsPoDgE4AKgAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:11.072681Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00825","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6111b3dec4358c0b6f881adc363a40235ec39e9df0cb838f0d204147da61ac7","sha256:f8861371a43ca883d7e6a2a764eb336075f1654c1ad8b8ae6bcd191fa1cecad5"],"state_sha256":"56ce7554e1ba6dd54bc9ba3a4860d7fc7165e007d2157f3b57439d8ad42416fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nc27VpbI6qlbiWnE6WozRs25ebw6f7WTBikqzOE13oi33q6kfrMPNW4oRq+W1AToHBZw4yhFtSLZ1hG7O14NBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:15:06.333796Z","bundle_sha256":"55dc9223f0b1868de138884cf1af877389d8d4078755dd6ac3332f87354a8858"}}