{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6QDD6OMROYDSD4JRBPTRAR3VPC","short_pith_number":"pith:6QDD6OMR","canonical_record":{"source":{"id":"1803.02228","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-06T14:44:10Z","cross_cats_sorted":["math.MP","math.PR","math.SP"],"title_canon_sha256":"1934387697957c3b1219e8f63777a7cdedd17ac6fc7b9efb345320c317b092bf","abstract_canon_sha256":"f2f80e952ea758ed6ab10f363134794637e4dc7936a5b52462d11c5ba00da422"},"schema_version":"1.0"},"canonical_sha256":"f4063f3991760721f1310be7104775789529309f874056192baa7b0c6b705dd8","source":{"kind":"arxiv","id":"1803.02228","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02228","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02228v2","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02228","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"6QDD6OMROYDS","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6QDD6OMROYDSD4JR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6QDD6OMR","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6QDD6OMROYDSD4JRBPTRAR3VPC","target":"record","payload":{"canonical_record":{"source":{"id":"1803.02228","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-06T14:44:10Z","cross_cats_sorted":["math.MP","math.PR","math.SP"],"title_canon_sha256":"1934387697957c3b1219e8f63777a7cdedd17ac6fc7b9efb345320c317b092bf","abstract_canon_sha256":"f2f80e952ea758ed6ab10f363134794637e4dc7936a5b52462d11c5ba00da422"},"schema_version":"1.0"},"canonical_sha256":"f4063f3991760721f1310be7104775789529309f874056192baa7b0c6b705dd8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:50.932027Z","signature_b64":"70ZRO/Wlk6bYdKekC5Cp2m6nBmogHT/VIMH80BDT8pVkN9XsOldHDajyB1K7pXr+Fhhl898PWpnykdMRPr3tBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4063f3991760721f1310be7104775789529309f874056192baa7b0c6b705dd8","last_reissued_at":"2026-05-18T00:05:50.931406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:50.931406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.02228","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":"2026-05-18T00:05:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MYqdxhP5GwizyM5A7r/bBtQs7lOOkiQTFfzqk4aG7BB1tWHE4vumTKZ+ALa74/javYz7TqF1VvGZ2yHNigH6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:25:26.720303Z"},"content_sha256":"bd3f7b9ff47661b7ab1747d1824b829aa25f85b6b44dd6f125ec39442c8ad732","schema_version":"1.0","event_id":"sha256:bd3f7b9ff47661b7ab1747d1824b829aa25f85b6b44dd6f125ec39442c8ad732"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6QDD6OMROYDSD4JRBPTRAR3VPC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A lower bound for the Bogomolny-Schmit constant for random monochromatic plane waves","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR","math.SP"],"primary_cat":"math-ph","authors_text":"Alejandro Rivera, Maxime Ingremeau","submitted_at":"2018-03-06T14:44:10Z","abstract_excerpt":"This note deals with nodal domains of random monochromatic plane waves. It was shown by Nazarov and Sodin that the expected number of such nodal domains included in a disk of radius $R$ is proportional to $\\pi R^2$ in the large $R$ limit. However, very little is known on the value of the proportionality constant from a mathematical point of view. The aim of this note is to obtain a lower bound on the value of this constant my elementary means."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02228","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":"2026-05-18T00:05:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EO8lBCvSk4RTJgD4zh4l1iZayi33YUPwvQIgXEozXxnzS+iPtotFt1Jhny6Ipu1YRR330DU8ci3fl5MRvYssCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:25:26.720665Z"},"content_sha256":"2e7997b06386b2be7881a1a0045c9275ab6458db7e1f6c3bb88fb2f894beafd8","schema_version":"1.0","event_id":"sha256:2e7997b06386b2be7881a1a0045c9275ab6458db7e1f6c3bb88fb2f894beafd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QDD6OMROYDSD4JRBPTRAR3VPC/bundle.json","state_url":"https://pith.science/pith/6QDD6OMROYDSD4JRBPTRAR3VPC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QDD6OMROYDSD4JRBPTRAR3VPC/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":"2026-06-22T14:25:26Z","links":{"resolver":"https://pith.science/pith/6QDD6OMROYDSD4JRBPTRAR3VPC","bundle":"https://pith.science/pith/6QDD6OMROYDSD4JRBPTRAR3VPC/bundle.json","state":"https://pith.science/pith/6QDD6OMROYDSD4JRBPTRAR3VPC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QDD6OMROYDSD4JRBPTRAR3VPC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6QDD6OMROYDSD4JRBPTRAR3VPC","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":"f2f80e952ea758ed6ab10f363134794637e4dc7936a5b52462d11c5ba00da422","cross_cats_sorted":["math.MP","math.PR","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-06T14:44:10Z","title_canon_sha256":"1934387697957c3b1219e8f63777a7cdedd17ac6fc7b9efb345320c317b092bf"},"schema_version":"1.0","source":{"id":"1803.02228","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02228","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02228v2","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02228","created_at":"2026-05-18T00:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"6QDD6OMROYDS","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6QDD6OMROYDSD4JR","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6QDD6OMR","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:2e7997b06386b2be7881a1a0045c9275ab6458db7e1f6c3bb88fb2f894beafd8","target":"graph","created_at":"2026-05-18T00:05:50Z","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":"This note deals with nodal domains of random monochromatic plane waves. It was shown by Nazarov and Sodin that the expected number of such nodal domains included in a disk of radius $R$ is proportional to $\\pi R^2$ in the large $R$ limit. However, very little is known on the value of the proportionality constant from a mathematical point of view. The aim of this note is to obtain a lower bound on the value of this constant my elementary means.","authors_text":"Alejandro Rivera, Maxime Ingremeau","cross_cats":["math.MP","math.PR","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-06T14:44:10Z","title":"A lower bound for the Bogomolny-Schmit constant for random monochromatic plane waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02228","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:bd3f7b9ff47661b7ab1747d1824b829aa25f85b6b44dd6f125ec39442c8ad732","target":"record","created_at":"2026-05-18T00:05:50Z","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":"f2f80e952ea758ed6ab10f363134794637e4dc7936a5b52462d11c5ba00da422","cross_cats_sorted":["math.MP","math.PR","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2018-03-06T14:44:10Z","title_canon_sha256":"1934387697957c3b1219e8f63777a7cdedd17ac6fc7b9efb345320c317b092bf"},"schema_version":"1.0","source":{"id":"1803.02228","kind":"arxiv","version":2}},"canonical_sha256":"f4063f3991760721f1310be7104775789529309f874056192baa7b0c6b705dd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4063f3991760721f1310be7104775789529309f874056192baa7b0c6b705dd8","first_computed_at":"2026-05-18T00:05:50.931406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:50.931406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"70ZRO/Wlk6bYdKekC5Cp2m6nBmogHT/VIMH80BDT8pVkN9XsOldHDajyB1K7pXr+Fhhl898PWpnykdMRPr3tBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:50.932027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02228","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd3f7b9ff47661b7ab1747d1824b829aa25f85b6b44dd6f125ec39442c8ad732","sha256:2e7997b06386b2be7881a1a0045c9275ab6458db7e1f6c3bb88fb2f894beafd8"],"state_sha256":"097c8c278d94e6552c80d94b3c42d8dc5ea0530728d26b9979c7e00206140451"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uwoXMuZvuu8VNPg8rT/PPn5+1ssF/kxAM/QREO0TPK6NbhIPbGm0yEbbUsHM4DFen8tZvbpJcVt1Cxs3Bs5TBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:25:26.722912Z","bundle_sha256":"f34c6550b7da0dd8c1e5346b921b1820cf0681b01e592ca7cb5767233624249f"}}