{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:AOL5HX5KUSPCH45ESGXSMJ4RZX","short_pith_number":"pith:AOL5HX5K","canonical_record":{"source":{"id":"2011.04409","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-11-09T13:25:25Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"d42388eed00fe64f55149be509acb5c37441a6de1093c8eff17cfe78aabdcb27","abstract_canon_sha256":"767b0b21fdaf9adc144f5ea603e5422cc5633edfa4511940ff27db9f3c3aa816"},"schema_version":"1.0"},"canonical_sha256":"0397d3dfaaa49e23f3a491af262791cdd9739bae305b26a095e1cbf8bef13bd7","source":{"kind":"arxiv","id":"2011.04409","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.04409","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"2011.04409v2","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.04409","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"AOL5HX5KUSPC","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"AOL5HX5KUSPCH45E","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"AOL5HX5K","created_at":"2026-07-05T02:05:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:AOL5HX5KUSPCH45ESGXSMJ4RZX","target":"record","payload":{"canonical_record":{"source":{"id":"2011.04409","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-11-09T13:25:25Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"d42388eed00fe64f55149be509acb5c37441a6de1093c8eff17cfe78aabdcb27","abstract_canon_sha256":"767b0b21fdaf9adc144f5ea603e5422cc5633edfa4511940ff27db9f3c3aa816"},"schema_version":"1.0"},"canonical_sha256":"0397d3dfaaa49e23f3a491af262791cdd9739bae305b26a095e1cbf8bef13bd7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:05:45.102332Z","signature_b64":"wHneOFldOqcz60t9rRLot7kmsQCryxHvPRipl6+pP0ZvK2dtoaSaxZbu5QhOquHmvkY4FmgYidqeU/yKfhe/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0397d3dfaaa49e23f3a491af262791cdd9739bae305b26a095e1cbf8bef13bd7","last_reissued_at":"2026-07-05T02:05:45.101964Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:05:45.101964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.04409","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":"2026-07-05T02:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xJ0pdnN6QC52rc8lhbB9WJ33/DM5uwE+i5+raDrs9248H1Tuvqq12+KNgp7J5r5lS3MzIAsrH7IJLpRzvTfnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:30:35.490059Z"},"content_sha256":"e6de0eb3a839ada6334938e48a6873ca8be0a38906c15ead47201635adbb5216","schema_version":"1.0","event_id":"sha256:e6de0eb3a839ada6334938e48a6873ca8be0a38906c15ead47201635adbb5216"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:AOL5HX5KUSPCH45ESGXSMJ4RZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Indeterminacy estimates and the size of nodal sets in singular spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Fabio Cavalletti, Sara Farinelli","submitted_at":"2020-11-09T13:25:25Z","abstract_excerpt":"We obtain the sharp version of the uncertainty principle recently introduced in [47], and improved by [13], relating the size of the zero set of a continuous function having zero mean and the optimal transport cost between the mass of the positive part and the negative one. The result is actually valid for the wide family of metric measure spaces verifying a synthetic lower bound on the Ricci curvature, namely the MCP(K,N) or CD(K,N) condition, thus also extending the scope beyond the smooth setting of Riemannian manifolds. Applying the uncertainty principle to eigenfunctions of the Laplacian "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04409","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.04409/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WubGW5/MsnKyYbd/P9BQN5KpMl1MucpguOKqldgW1DRKE4p/GXYLDSqDxAojlRC8Y90sBWAM3riIgwMN7fP8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:30:35.490447Z"},"content_sha256":"f943d089c6a72d504ad217e6d3e0eb3b20ff7312bfd063adea5b91250514024b","schema_version":"1.0","event_id":"sha256:f943d089c6a72d504ad217e6d3e0eb3b20ff7312bfd063adea5b91250514024b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AOL5HX5KUSPCH45ESGXSMJ4RZX/bundle.json","state_url":"https://pith.science/pith/AOL5HX5KUSPCH45ESGXSMJ4RZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AOL5HX5KUSPCH45ESGXSMJ4RZX/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":"2026-07-06T23:30:35Z","links":{"resolver":"https://pith.science/pith/AOL5HX5KUSPCH45ESGXSMJ4RZX","bundle":"https://pith.science/pith/AOL5HX5KUSPCH45ESGXSMJ4RZX/bundle.json","state":"https://pith.science/pith/AOL5HX5KUSPCH45ESGXSMJ4RZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AOL5HX5KUSPCH45ESGXSMJ4RZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:AOL5HX5KUSPCH45ESGXSMJ4RZX","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":"767b0b21fdaf9adc144f5ea603e5422cc5633edfa4511940ff27db9f3c3aa816","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-11-09T13:25:25Z","title_canon_sha256":"d42388eed00fe64f55149be509acb5c37441a6de1093c8eff17cfe78aabdcb27"},"schema_version":"1.0","source":{"id":"2011.04409","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.04409","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"2011.04409v2","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.04409","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"AOL5HX5KUSPC","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"pith_short_16","alias_value":"AOL5HX5KUSPCH45E","created_at":"2026-07-05T02:05:45Z"},{"alias_kind":"pith_short_8","alias_value":"AOL5HX5K","created_at":"2026-07-05T02:05:45Z"}],"graph_snapshots":[{"event_id":"sha256:f943d089c6a72d504ad217e6d3e0eb3b20ff7312bfd063adea5b91250514024b","target":"graph","created_at":"2026-07-05T02:05:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2011.04409/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We obtain the sharp version of the uncertainty principle recently introduced in [47], and improved by [13], relating the size of the zero set of a continuous function having zero mean and the optimal transport cost between the mass of the positive part and the negative one. The result is actually valid for the wide family of metric measure spaces verifying a synthetic lower bound on the Ricci curvature, namely the MCP(K,N) or CD(K,N) condition, thus also extending the scope beyond the smooth setting of Riemannian manifolds. Applying the uncertainty principle to eigenfunctions of the Laplacian ","authors_text":"Fabio Cavalletti, Sara Farinelli","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-11-09T13:25:25Z","title":"Indeterminacy estimates and the size of nodal sets in singular spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04409","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:e6de0eb3a839ada6334938e48a6873ca8be0a38906c15ead47201635adbb5216","target":"record","created_at":"2026-07-05T02:05:45Z","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":"767b0b21fdaf9adc144f5ea603e5422cc5633edfa4511940ff27db9f3c3aa816","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-11-09T13:25:25Z","title_canon_sha256":"d42388eed00fe64f55149be509acb5c37441a6de1093c8eff17cfe78aabdcb27"},"schema_version":"1.0","source":{"id":"2011.04409","kind":"arxiv","version":2}},"canonical_sha256":"0397d3dfaaa49e23f3a491af262791cdd9739bae305b26a095e1cbf8bef13bd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0397d3dfaaa49e23f3a491af262791cdd9739bae305b26a095e1cbf8bef13bd7","first_computed_at":"2026-07-05T02:05:45.101964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:05:45.101964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wHneOFldOqcz60t9rRLot7kmsQCryxHvPRipl6+pP0ZvK2dtoaSaxZbu5QhOquHmvkY4FmgYidqeU/yKfhe/Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:05:45.102332Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.04409","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6de0eb3a839ada6334938e48a6873ca8be0a38906c15ead47201635adbb5216","sha256:f943d089c6a72d504ad217e6d3e0eb3b20ff7312bfd063adea5b91250514024b"],"state_sha256":"4f9e3d76213b9c3cbcad730a09e0addf00464022ac34c05f590b2fd7cd3bf9af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PdE4M5Q0FRG+2PtUB/0hMtT838nZUfzfLzMABwSp2xFyTypQznlSuxRvr6VRxlAVifxFhsNSWYKurHBSL6K7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T23:30:35.492478Z","bundle_sha256":"becde7cad3578cdc40189d1f1842542737f026d089b78948b80a597ded940095"}}