{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:CWNNH6X2VHMPW3DGXSQQFYV5B5","short_pith_number":"pith:CWNNH6X2","canonical_record":{"source":{"id":"1203.3235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-14T23:33:42Z","cross_cats_sorted":["math.CV","math.OC"],"title_canon_sha256":"3070a2f7d251e1b207fada5c22e1b35e3bbc7f39d87fc87f123a7e777c6907fa","abstract_canon_sha256":"b181fb94ca4715d953f082d7ea556100710c80713c873e0f3b4dab7d369b78c2"},"schema_version":"1.0"},"canonical_sha256":"159ad3fafaa9d8fb6c66bca102e2bd0f4e29f69b32ea4cb84ece2c078d79dcd3","source":{"kind":"arxiv","id":"1203.3235","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3235","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3235v2","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3235","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"CWNNH6X2VHMP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CWNNH6X2VHMPW3DG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CWNNH6X2","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:CWNNH6X2VHMPW3DGXSQQFYV5B5","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-14T23:33:42Z","cross_cats_sorted":["math.CV","math.OC"],"title_canon_sha256":"3070a2f7d251e1b207fada5c22e1b35e3bbc7f39d87fc87f123a7e777c6907fa","abstract_canon_sha256":"b181fb94ca4715d953f082d7ea556100710c80713c873e0f3b4dab7d369b78c2"},"schema_version":"1.0"},"canonical_sha256":"159ad3fafaa9d8fb6c66bca102e2bd0f4e29f69b32ea4cb84ece2c078d79dcd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:41.423550Z","signature_b64":"TAPJMJgUgYtlLto6QptW7Sr3hJir0gdODyw6eINplzoTC4eGF7mMshiMYCBRbhRFW1o9/6CQWdv2byAz2eQSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"159ad3fafaa9d8fb6c66bca102e2bd0f4e29f69b32ea4cb84ece2c078d79dcd3","last_reissued_at":"2026-05-18T03:37:41.423077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:41.423077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3235","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":"2026-05-18T03:37:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nWhxuxGylSSJGrcTkAiBLKfU50RDbQbZ+IWXP/2ls5xjIokGF51fNHD41PxieTKYWEHPPL2eLc+jQca1OITiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:34:07.959515Z"},"content_sha256":"5bf668791fb7f07e04eb1de86efc1914c378765a70abc0cda293a57368f46965","schema_version":"1.0","event_id":"sha256:5bf668791fb7f07e04eb1de86efc1914c378765a70abc0cda293a57368f46965"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:CWNNH6X2VHMPW3DGXSQQFYV5B5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditioning moments of singular measures for entropy optimization. I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.OC"],"primary_cat":"math.FA","authors_text":"Marko Budi\\v{s}i\\'c, Mihai Putinar","submitted_at":"2012-03-14T23:33:42Z","abstract_excerpt":"In order to process a potential moment sequence by the entropy optimization method one has to be assured that the original measure is absolutely continuous with respect to Lebesgue measure. We propose a non-linear exponential transform of the moment sequence of any measure, including singular ones, so that the entropy optimization method can still be used in the reconstruction or approximation of the original. The Cauchy transform in one variable, used for this very purpose in a classical context by A.\\ A.\\ Markov and followers, is replaced in higher dimensions by the Fantappi\\`{e} transform. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3235","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":"2026-05-18T03:37:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CV53nvNzBayBHunGM35zHm9KzjNJI2J/OjGyBmcmF9rPvPnYzHs53WTWtaNPk5lpuMloLKHn7MtiwKo2VVgOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:34:07.960187Z"},"content_sha256":"d6c40f96d79110839cc1d0bb264a47637bb582960e3c78a028a05f7e34a0979a","schema_version":"1.0","event_id":"sha256:d6c40f96d79110839cc1d0bb264a47637bb582960e3c78a028a05f7e34a0979a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWNNH6X2VHMPW3DGXSQQFYV5B5/bundle.json","state_url":"https://pith.science/pith/CWNNH6X2VHMPW3DGXSQQFYV5B5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWNNH6X2VHMPW3DGXSQQFYV5B5/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":"2026-06-11T08:34:07Z","links":{"resolver":"https://pith.science/pith/CWNNH6X2VHMPW3DGXSQQFYV5B5","bundle":"https://pith.science/pith/CWNNH6X2VHMPW3DGXSQQFYV5B5/bundle.json","state":"https://pith.science/pith/CWNNH6X2VHMPW3DGXSQQFYV5B5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWNNH6X2VHMPW3DGXSQQFYV5B5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:CWNNH6X2VHMPW3DGXSQQFYV5B5","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":"b181fb94ca4715d953f082d7ea556100710c80713c873e0f3b4dab7d369b78c2","cross_cats_sorted":["math.CV","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-14T23:33:42Z","title_canon_sha256":"3070a2f7d251e1b207fada5c22e1b35e3bbc7f39d87fc87f123a7e777c6907fa"},"schema_version":"1.0","source":{"id":"1203.3235","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3235","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3235v2","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3235","created_at":"2026-05-18T03:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"CWNNH6X2VHMP","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"CWNNH6X2VHMPW3DG","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"CWNNH6X2","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:d6c40f96d79110839cc1d0bb264a47637bb582960e3c78a028a05f7e34a0979a","target":"graph","created_at":"2026-05-18T03:37:41Z","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":"In order to process a potential moment sequence by the entropy optimization method one has to be assured that the original measure is absolutely continuous with respect to Lebesgue measure. We propose a non-linear exponential transform of the moment sequence of any measure, including singular ones, so that the entropy optimization method can still be used in the reconstruction or approximation of the original. The Cauchy transform in one variable, used for this very purpose in a classical context by A.\\ A.\\ Markov and followers, is replaced in higher dimensions by the Fantappi\\`{e} transform. ","authors_text":"Marko Budi\\v{s}i\\'c, Mihai Putinar","cross_cats":["math.CV","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-14T23:33:42Z","title":"Conditioning moments of singular measures for entropy optimization. I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3235","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":"sha256:5bf668791fb7f07e04eb1de86efc1914c378765a70abc0cda293a57368f46965","target":"record","created_at":"2026-05-18T03:37:41Z","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":"b181fb94ca4715d953f082d7ea556100710c80713c873e0f3b4dab7d369b78c2","cross_cats_sorted":["math.CV","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-03-14T23:33:42Z","title_canon_sha256":"3070a2f7d251e1b207fada5c22e1b35e3bbc7f39d87fc87f123a7e777c6907fa"},"schema_version":"1.0","source":{"id":"1203.3235","kind":"arxiv","version":2}},"canonical_sha256":"159ad3fafaa9d8fb6c66bca102e2bd0f4e29f69b32ea4cb84ece2c078d79dcd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"159ad3fafaa9d8fb6c66bca102e2bd0f4e29f69b32ea4cb84ece2c078d79dcd3","first_computed_at":"2026-05-18T03:37:41.423077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:41.423077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TAPJMJgUgYtlLto6QptW7Sr3hJir0gdODyw6eINplzoTC4eGF7mMshiMYCBRbhRFW1o9/6CQWdv2byAz2eQSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:41.423550Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3235","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bf668791fb7f07e04eb1de86efc1914c378765a70abc0cda293a57368f46965","sha256:d6c40f96d79110839cc1d0bb264a47637bb582960e3c78a028a05f7e34a0979a"],"state_sha256":"fda3f23cdb0d2a7a930a9c02194a02cbe0cda6519e42830b1b8eedaf27fbc67d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hZbNuSgR4c2bD9u1lwoCiCZBFnq3B4OGKYUFnKJkT9C30aDz1NydCz+NcWhaRNFItd3R1F2eFJd5BK9/faR3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:34:07.964189Z","bundle_sha256":"241bf1dbb49238a4bc79b38fcdd54b4aa7eb12e9d7cfc4dcf5da71222f6b7ef6"}}