{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XAZ2BVFEVMVYV2GM5FCNUPZPCW","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":"7dbbadf200569b038e80c3d01734f59e7d1d3dcbdbd0067b0ab40cb598455638","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-03T07:02:41Z","title_canon_sha256":"bfdf0ea9e8d16de9ba217fd27bdcb5cb56ef695f34278c498893213ab369ae77"},"schema_version":"1.0","source":{"id":"1509.00956","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00956","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00956v1","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00956","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"XAZ2BVFEVMVY","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XAZ2BVFEVMVYV2GM","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XAZ2BVFE","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:9067d825cdced5a53cbba83f14650fbc8e0c247ef234929e9ef25d191fe4570d","target":"graph","created_at":"2026-05-18T00:14:29Z","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":"We consider the problem of stable sampling of multivariate real polynomials of large degree in a general framework where the polynomials are defined on an affine real algebraic variety $M$, equipped with a weighted measure. In particular, this framework contains the well-known setting of trigonometric polynomials (when $M$ is a torus equipped with its invariant measure), where the limit of large degree corresponds to a high frequency limit, as well as the classical setting of one-variable orthogonal algebraic polynomials (when $M$ is the real line equipped with a suitable measure), where the s","authors_text":"Joaquim Ortega-Cerd\\`a, Robert J. Berman","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-03T07:02:41Z","title":"Sampling of real multivariate polynomials and pluripotential theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00956","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:e650f87f5d48d06c041f7cd99c38137ce51bfa78cac3c2446e0ad7058dc243ee","target":"record","created_at":"2026-05-18T00:14:29Z","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":"7dbbadf200569b038e80c3d01734f59e7d1d3dcbdbd0067b0ab40cb598455638","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-09-03T07:02:41Z","title_canon_sha256":"bfdf0ea9e8d16de9ba217fd27bdcb5cb56ef695f34278c498893213ab369ae77"},"schema_version":"1.0","source":{"id":"1509.00956","kind":"arxiv","version":1}},"canonical_sha256":"b833a0d4a4ab2b8ae8cce944da3f2f15a6f8b1c4f7c8e3501bfb1aae6d213af1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b833a0d4a4ab2b8ae8cce944da3f2f15a6f8b1c4f7c8e3501bfb1aae6d213af1","first_computed_at":"2026-05-18T00:14:29.289901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.289901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xQnR5oyuV5lVYH6IJMbUsYkVVFQsgqIqwKsh92vtP1pC8GF6jwjim2atDBdEa/sFFVfiip5Qj83m28GuGQrzDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.290623Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00956","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e650f87f5d48d06c041f7cd99c38137ce51bfa78cac3c2446e0ad7058dc243ee","sha256:9067d825cdced5a53cbba83f14650fbc8e0c247ef234929e9ef25d191fe4570d"],"state_sha256":"abfa396a6966db57adc147d4122f2691e86f32572e32b1ece419dd2a459b09ed"}