{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7FNGNFEZXPKVFIZJZNQLYNOW54","short_pith_number":"pith:7FNGNFEZ","canonical_record":{"source":{"id":"1703.05976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-17T11:50:16Z","cross_cats_sorted":[],"title_canon_sha256":"c3e1f386e72510325a1695ae48578a2104683a32e45f09781de3ad9935e71dd3","abstract_canon_sha256":"19819f39adc8c7f688c4d5746b4384952429c0177a28cde3fcb69b155629659e"},"schema_version":"1.0"},"canonical_sha256":"f95a669499bbd552a329cb60bc35d6ef0586c3f49ce1fa3b164fdfc8ee0e708e","source":{"kind":"arxiv","id":"1703.05976","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05976","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05976v1","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05976","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"7FNGNFEZXPKV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7FNGNFEZXPKVFIZJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7FNGNFEZ","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7FNGNFEZXPKVFIZJZNQLYNOW54","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-17T11:50:16Z","cross_cats_sorted":[],"title_canon_sha256":"c3e1f386e72510325a1695ae48578a2104683a32e45f09781de3ad9935e71dd3","abstract_canon_sha256":"19819f39adc8c7f688c4d5746b4384952429c0177a28cde3fcb69b155629659e"},"schema_version":"1.0"},"canonical_sha256":"f95a669499bbd552a329cb60bc35d6ef0586c3f49ce1fa3b164fdfc8ee0e708e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:29.809214Z","signature_b64":"wTTrsKPNicH5nWAeNmf++RzSL/CSOJKd6u2zXN0TV8mhRut/2LhbHhmJQfxwCuP5HuUBhT2T70ALPJKdlIbzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f95a669499bbd552a329cb60bc35d6ef0586c3f49ce1fa3b164fdfc8ee0e708e","last_reissued_at":"2026-05-18T00:48:29.808589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:29.808589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05976","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4VlMChp64wyXm1NcD30k3+iB5dPVMFkNpfHb8NJlza7N5BK9Gb6tZctfWnKmbdq906WHT+ZRgWyW/gCq1WCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:39:26.555407Z"},"content_sha256":"86a49b5e6b3dee9147f982cccf66576d140122d0dbea3464aaab4e9eafa98889","schema_version":"1.0","event_id":"sha256:86a49b5e6b3dee9147f982cccf66576d140122d0dbea3464aaab4e9eafa98889"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7FNGNFEZXPKVFIZJZNQLYNOW54","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vanishing Bergman kernels on the disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Antti Per\\\"al\\\"a","submitted_at":"2017-03-17T11:50:16Z","abstract_excerpt":"We discuss topics related to zeroes of the Bergman kernels, and present a method for generating Bergman kernels with arbitrarily, but finitely, many zeroes. It is also shown that a Bergman kernel induced by a radial weight on the unit disk cannot have infinitely many zeroes. Similar questions for the Segal-Bargmann spaces of the complex plane are briefly discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05976","kind":"arxiv","version":1},"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":"2026-05-18T00:48:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7S2KsroRw2CSRF5nMiTdUhb0UixvPQEzCSpH6gSu7XDOtTMFAI0nDWwao4aI/ixhfUnjKQXL5vKFP8TDZSICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:39:26.555752Z"},"content_sha256":"9d50ea8de2464999ee8e516289f9a0c370d5192be789648ea7c4f9328cc824f5","schema_version":"1.0","event_id":"sha256:9d50ea8de2464999ee8e516289f9a0c370d5192be789648ea7c4f9328cc824f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FNGNFEZXPKVFIZJZNQLYNOW54/bundle.json","state_url":"https://pith.science/pith/7FNGNFEZXPKVFIZJZNQLYNOW54/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FNGNFEZXPKVFIZJZNQLYNOW54/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":"2026-06-02T18:39:26Z","links":{"resolver":"https://pith.science/pith/7FNGNFEZXPKVFIZJZNQLYNOW54","bundle":"https://pith.science/pith/7FNGNFEZXPKVFIZJZNQLYNOW54/bundle.json","state":"https://pith.science/pith/7FNGNFEZXPKVFIZJZNQLYNOW54/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FNGNFEZXPKVFIZJZNQLYNOW54/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7FNGNFEZXPKVFIZJZNQLYNOW54","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":"19819f39adc8c7f688c4d5746b4384952429c0177a28cde3fcb69b155629659e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-17T11:50:16Z","title_canon_sha256":"c3e1f386e72510325a1695ae48578a2104683a32e45f09781de3ad9935e71dd3"},"schema_version":"1.0","source":{"id":"1703.05976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05976","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05976v1","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05976","created_at":"2026-05-18T00:48:29Z"},{"alias_kind":"pith_short_12","alias_value":"7FNGNFEZXPKV","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7FNGNFEZXPKVFIZJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7FNGNFEZ","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:9d50ea8de2464999ee8e516289f9a0c370d5192be789648ea7c4f9328cc824f5","target":"graph","created_at":"2026-05-18T00:48:29Z","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 discuss topics related to zeroes of the Bergman kernels, and present a method for generating Bergman kernels with arbitrarily, but finitely, many zeroes. It is also shown that a Bergman kernel induced by a radial weight on the unit disk cannot have infinitely many zeroes. Similar questions for the Segal-Bargmann spaces of the complex plane are briefly discussed.","authors_text":"Antti Per\\\"al\\\"a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-17T11:50:16Z","title":"Vanishing Bergman kernels on the disk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05976","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":"sha256:86a49b5e6b3dee9147f982cccf66576d140122d0dbea3464aaab4e9eafa98889","target":"record","created_at":"2026-05-18T00:48:29Z","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":"19819f39adc8c7f688c4d5746b4384952429c0177a28cde3fcb69b155629659e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-17T11:50:16Z","title_canon_sha256":"c3e1f386e72510325a1695ae48578a2104683a32e45f09781de3ad9935e71dd3"},"schema_version":"1.0","source":{"id":"1703.05976","kind":"arxiv","version":1}},"canonical_sha256":"f95a669499bbd552a329cb60bc35d6ef0586c3f49ce1fa3b164fdfc8ee0e708e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f95a669499bbd552a329cb60bc35d6ef0586c3f49ce1fa3b164fdfc8ee0e708e","first_computed_at":"2026-05-18T00:48:29.808589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:29.808589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wTTrsKPNicH5nWAeNmf++RzSL/CSOJKd6u2zXN0TV8mhRut/2LhbHhmJQfxwCuP5HuUBhT2T70ALPJKdlIbzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:29.809214Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86a49b5e6b3dee9147f982cccf66576d140122d0dbea3464aaab4e9eafa98889","sha256:9d50ea8de2464999ee8e516289f9a0c370d5192be789648ea7c4f9328cc824f5"],"state_sha256":"fd8e43a82c963130f4a32caf00a10a67940caefcbd8c8d0deb1fed0bd3f6b869"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qTabprcdgOoG/S22ocqVr3p9kFmQOgtcYyQF/2nUsbJCf6puOVOK1zgZG+FIiGKjo8LBOq+QN8Z/Bl+o3s0LBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:39:26.557573Z","bundle_sha256":"a0c5fc15852cea6d5d719c599f253bced091bef847547de126564d43f7879e6a"}}