{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PBBTJOQYFLR54GCA5CSG3KQYWK","short_pith_number":"pith:PBBTJOQY","canonical_record":{"source":{"id":"1711.07577","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-11-20T23:15:51Z","cross_cats_sorted":["math.AP","math.AT"],"title_canon_sha256":"c87423bc72bdf9b35563c4b3fd2b63ff4498e2455d27ccd21ae635a058044b2d","abstract_canon_sha256":"2a12dda095fd0b99b866e47fc067be0ea213d709728e2778409f854f69e05732"},"schema_version":"1.0"},"canonical_sha256":"784334ba182ae3de1840e8a46daa18b2b6f40819845e603341b3960abbe2d111","source":{"kind":"arxiv","id":"1711.07577","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07577","created_at":"2026-05-17T23:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07577v3","created_at":"2026-05-17T23:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07577","created_at":"2026-05-17T23:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"PBBTJOQYFLR5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PBBTJOQYFLR54GCA","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PBBTJOQY","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PBBTJOQYFLR54GCA5CSG3KQYWK","target":"record","payload":{"canonical_record":{"source":{"id":"1711.07577","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-11-20T23:15:51Z","cross_cats_sorted":["math.AP","math.AT"],"title_canon_sha256":"c87423bc72bdf9b35563c4b3fd2b63ff4498e2455d27ccd21ae635a058044b2d","abstract_canon_sha256":"2a12dda095fd0b99b866e47fc067be0ea213d709728e2778409f854f69e05732"},"schema_version":"1.0"},"canonical_sha256":"784334ba182ae3de1840e8a46daa18b2b6f40819845e603341b3960abbe2d111","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:41.711647Z","signature_b64":"ygQqDAbeEzoPzPPtyz5ei2d/eDksjLQOSk1Am8ieBiFT1hgb/6wRXIem4i3hK3RJcsbzI9wS/8n6neO7XBZACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"784334ba182ae3de1840e8a46daa18b2b6f40819845e603341b3960abbe2d111","last_reissued_at":"2026-05-17T23:54:41.711149Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:41.711149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.07577","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9oWgYsIfnrXA5KGNKJuFqLIvoxlg2Aw5M3d5Qsjt8utmBjgelJmwqf9VxPhtYc5vsD+hIbSzpkqHPwWZPcUPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:01:02.153279Z"},"content_sha256":"970fe88925a95478b3316e31b1560e87051261781953efacecc96d1ce31b3a6f","schema_version":"1.0","event_id":"sha256:970fe88925a95478b3316e31b1560e87051261781953efacecc96d1ce31b3a6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PBBTJOQYFLR54GCA5CSG3KQYWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Persistence barcodes and Laplace eigenfunctions on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.AT"],"primary_cat":"math.SP","authors_text":"Iosif Polterovich, Leonid Polterovich, Vuka\\v{s}in Stojisavljevi\\'c","submitted_at":"2017-11-20T23:15:51Z","abstract_excerpt":"We obtain restrictions on the persistence barcodes of Laplace-Beltrami eigenfunctions and their linear combinations on compact surfaces with Riemannian metrics. Some applications to uniform approximation by linear combinations of Laplace eigenfunctions are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07577","kind":"arxiv","version":3},"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":"2026-05-17T23:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HEjzlHybEeGfCKWPE3DCd4STfFqNxgNqWQ6n02mrGWHz39ycyfI6IgzqBaNE5EV1PRUjm9CvaFlBR9U83UIWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:01:02.153642Z"},"content_sha256":"a27faf9536cfbe397633fa1f947007e4292d87b47c026591db97f2652ef2cadb","schema_version":"1.0","event_id":"sha256:a27faf9536cfbe397633fa1f947007e4292d87b47c026591db97f2652ef2cadb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBBTJOQYFLR54GCA5CSG3KQYWK/bundle.json","state_url":"https://pith.science/pith/PBBTJOQYFLR54GCA5CSG3KQYWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBBTJOQYFLR54GCA5CSG3KQYWK/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":"2026-06-01T13:01:02Z","links":{"resolver":"https://pith.science/pith/PBBTJOQYFLR54GCA5CSG3KQYWK","bundle":"https://pith.science/pith/PBBTJOQYFLR54GCA5CSG3KQYWK/bundle.json","state":"https://pith.science/pith/PBBTJOQYFLR54GCA5CSG3KQYWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBBTJOQYFLR54GCA5CSG3KQYWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PBBTJOQYFLR54GCA5CSG3KQYWK","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":"2a12dda095fd0b99b866e47fc067be0ea213d709728e2778409f854f69e05732","cross_cats_sorted":["math.AP","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-11-20T23:15:51Z","title_canon_sha256":"c87423bc72bdf9b35563c4b3fd2b63ff4498e2455d27ccd21ae635a058044b2d"},"schema_version":"1.0","source":{"id":"1711.07577","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07577","created_at":"2026-05-17T23:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07577v3","created_at":"2026-05-17T23:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07577","created_at":"2026-05-17T23:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"PBBTJOQYFLR5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PBBTJOQYFLR54GCA","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PBBTJOQY","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:a27faf9536cfbe397633fa1f947007e4292d87b47c026591db97f2652ef2cadb","target":"graph","created_at":"2026-05-17T23:54:41Z","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":"We obtain restrictions on the persistence barcodes of Laplace-Beltrami eigenfunctions and their linear combinations on compact surfaces with Riemannian metrics. Some applications to uniform approximation by linear combinations of Laplace eigenfunctions are also discussed.","authors_text":"Iosif Polterovich, Leonid Polterovich, Vuka\\v{s}in Stojisavljevi\\'c","cross_cats":["math.AP","math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-11-20T23:15:51Z","title":"Persistence barcodes and Laplace eigenfunctions on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07577","kind":"arxiv","version":3},"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":"sha256:970fe88925a95478b3316e31b1560e87051261781953efacecc96d1ce31b3a6f","target":"record","created_at":"2026-05-17T23:54:41Z","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":"2a12dda095fd0b99b866e47fc067be0ea213d709728e2778409f854f69e05732","cross_cats_sorted":["math.AP","math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-11-20T23:15:51Z","title_canon_sha256":"c87423bc72bdf9b35563c4b3fd2b63ff4498e2455d27ccd21ae635a058044b2d"},"schema_version":"1.0","source":{"id":"1711.07577","kind":"arxiv","version":3}},"canonical_sha256":"784334ba182ae3de1840e8a46daa18b2b6f40819845e603341b3960abbe2d111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"784334ba182ae3de1840e8a46daa18b2b6f40819845e603341b3960abbe2d111","first_computed_at":"2026-05-17T23:54:41.711149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:41.711149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ygQqDAbeEzoPzPPtyz5ei2d/eDksjLQOSk1Am8ieBiFT1hgb/6wRXIem4i3hK3RJcsbzI9wS/8n6neO7XBZACw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:41.711647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07577","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:970fe88925a95478b3316e31b1560e87051261781953efacecc96d1ce31b3a6f","sha256:a27faf9536cfbe397633fa1f947007e4292d87b47c026591db97f2652ef2cadb"],"state_sha256":"b9a13fc85fc5a707ea2d55a5d99d0da04ed6ab6d3191fd792860c9e7e611f9d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OzQ1gzEZMEdlP20A+l0VdWdGDmB66iU5M+NIowB/KVJwEr7PV1sB/CPfIdfM/IGXLn0mFZSdBRfqgdmKjRtbAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:01:02.155754Z","bundle_sha256":"c67b143a7b471a78521b715a418ba294cf115052d0ad223ab153c90a7cd52675"}}