{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P7SKP72KPWWDTCIJDA5SESVKBJ","short_pith_number":"pith:P7SKP72K","canonical_record":{"source":{"id":"1310.7977","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-29T22:21:35Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"a4b84c3564e31e2be83034d3304e412ab8f99eb05935476793fccdc44e26d2e0","abstract_canon_sha256":"c8f2d591d3fc4844cdecf271dfe4fa116bbebd22a2bd8ba7a060e79580997eca"},"schema_version":"1.0"},"canonical_sha256":"7fe4a7ff4a7dac398909183b224aaa0a795a3abe1f90c2a5056381aed5d56576","source":{"kind":"arxiv","id":"1310.7977","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7977","created_at":"2026-05-18T02:02:08Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7977v2","created_at":"2026-05-18T02:02:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7977","created_at":"2026-05-18T02:02:08Z"},{"alias_kind":"pith_short_12","alias_value":"P7SKP72KPWWD","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P7SKP72KPWWDTCIJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P7SKP72K","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P7SKP72KPWWDTCIJDA5SESVKBJ","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7977","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-29T22:21:35Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"a4b84c3564e31e2be83034d3304e412ab8f99eb05935476793fccdc44e26d2e0","abstract_canon_sha256":"c8f2d591d3fc4844cdecf271dfe4fa116bbebd22a2bd8ba7a060e79580997eca"},"schema_version":"1.0"},"canonical_sha256":"7fe4a7ff4a7dac398909183b224aaa0a795a3abe1f90c2a5056381aed5d56576","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:08.541677Z","signature_b64":"WK/eyF/uXzREXIFwIDl6TCO/j25aKnKnQHvU9lCHaXlIH1ybpZX9LraI+3XfeiORuNJeuTrK1mGsClH5FkdUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fe4a7ff4a7dac398909183b224aaa0a795a3abe1f90c2a5056381aed5d56576","last_reissued_at":"2026-05-18T02:02:08.541084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:08.541084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7977","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":"2026-05-18T02:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"46+6ailTYl46gb1Izdn+Cqd4hfhmWJhikbCh81i1+MzCbJW4Yaxqwf40gbWEsJrkQ8H9zun+v39UiAUiQPFnDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:17:30.579553Z"},"content_sha256":"52c72124315324e8090ea6a273e4a442421200d9447409f304bd6a06f598ed72","schema_version":"1.0","event_id":"sha256:52c72124315324e8090ea6a273e4a442421200d9447409f304bd6a06f598ed72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P7SKP72KPWWDTCIJDA5SESVKBJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic, zeros, and nodal domains on the sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.NT","authors_text":"Michael Magee","submitted_at":"2013-10-29T22:21:35Z","abstract_excerpt":"We obtain lower bounds for the number of nodal domains of Hecke eigenfunctions on the sphere. Assuming the generalized Lindelof hypothesis we prove that the number of nodal domains of any Hecke eigenfunction grows with the eigenvalue of the Laplacian. By a very different method, we show unconditionally that the average number of nodal domains of degree l Hecke eigenfunctions grows significantly faster than the uniform growth obtained under Lindelof."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7977","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":"2026-05-18T02:02:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"76Bd1ysx2B8NN8yjJrJtQG4DGSJemFVOMuHA4zokAwYmD5By0wzAEzczmhPCeEF2U5EncPRybnWUr7nv3sMFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:17:30.579901Z"},"content_sha256":"24b8753837bc5ac41a67d28b3c0165e3ca5aab13512f52a52653bb56ee68d4f7","schema_version":"1.0","event_id":"sha256:24b8753837bc5ac41a67d28b3c0165e3ca5aab13512f52a52653bb56ee68d4f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7SKP72KPWWDTCIJDA5SESVKBJ/bundle.json","state_url":"https://pith.science/pith/P7SKP72KPWWDTCIJDA5SESVKBJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7SKP72KPWWDTCIJDA5SESVKBJ/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":"2026-06-04T19:17:30Z","links":{"resolver":"https://pith.science/pith/P7SKP72KPWWDTCIJDA5SESVKBJ","bundle":"https://pith.science/pith/P7SKP72KPWWDTCIJDA5SESVKBJ/bundle.json","state":"https://pith.science/pith/P7SKP72KPWWDTCIJDA5SESVKBJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7SKP72KPWWDTCIJDA5SESVKBJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P7SKP72KPWWDTCIJDA5SESVKBJ","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":"c8f2d591d3fc4844cdecf271dfe4fa116bbebd22a2bd8ba7a060e79580997eca","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-29T22:21:35Z","title_canon_sha256":"a4b84c3564e31e2be83034d3304e412ab8f99eb05935476793fccdc44e26d2e0"},"schema_version":"1.0","source":{"id":"1310.7977","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7977","created_at":"2026-05-18T02:02:08Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7977v2","created_at":"2026-05-18T02:02:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7977","created_at":"2026-05-18T02:02:08Z"},{"alias_kind":"pith_short_12","alias_value":"P7SKP72KPWWD","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P7SKP72KPWWDTCIJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P7SKP72K","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:24b8753837bc5ac41a67d28b3c0165e3ca5aab13512f52a52653bb56ee68d4f7","target":"graph","created_at":"2026-05-18T02:02:08Z","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 lower bounds for the number of nodal domains of Hecke eigenfunctions on the sphere. Assuming the generalized Lindelof hypothesis we prove that the number of nodal domains of any Hecke eigenfunction grows with the eigenvalue of the Laplacian. By a very different method, we show unconditionally that the average number of nodal domains of degree l Hecke eigenfunctions grows significantly faster than the uniform growth obtained under Lindelof.","authors_text":"Michael Magee","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-29T22:21:35Z","title":"Arithmetic, zeros, and nodal domains on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7977","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":"sha256:52c72124315324e8090ea6a273e4a442421200d9447409f304bd6a06f598ed72","target":"record","created_at":"2026-05-18T02:02:08Z","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":"c8f2d591d3fc4844cdecf271dfe4fa116bbebd22a2bd8ba7a060e79580997eca","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-29T22:21:35Z","title_canon_sha256":"a4b84c3564e31e2be83034d3304e412ab8f99eb05935476793fccdc44e26d2e0"},"schema_version":"1.0","source":{"id":"1310.7977","kind":"arxiv","version":2}},"canonical_sha256":"7fe4a7ff4a7dac398909183b224aaa0a795a3abe1f90c2a5056381aed5d56576","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fe4a7ff4a7dac398909183b224aaa0a795a3abe1f90c2a5056381aed5d56576","first_computed_at":"2026-05-18T02:02:08.541084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:08.541084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WK/eyF/uXzREXIFwIDl6TCO/j25aKnKnQHvU9lCHaXlIH1ybpZX9LraI+3XfeiORuNJeuTrK1mGsClH5FkdUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:08.541677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7977","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52c72124315324e8090ea6a273e4a442421200d9447409f304bd6a06f598ed72","sha256:24b8753837bc5ac41a67d28b3c0165e3ca5aab13512f52a52653bb56ee68d4f7"],"state_sha256":"b829bbdb08d2c3a6401bbc03c92bb34ae95d6a22e4115bcc18bf244431116ef2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttGUCUqiMHpTFE7Skji+pR4drScZpEqUkRoFyq5FPMjOwt8/G5yGCp0rXpixgxHSfysJ8fHkWZ6KA6xFDmQDCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:17:30.581809Z","bundle_sha256":"6adbe2ebd9dcd7c7eb98842454d905d3abff8f1c7c8639908447725119d827e3"}}