{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LTWIV64JCAVAEV2NRYNHJKGTQ5","short_pith_number":"pith:LTWIV64J","canonical_record":{"source":{"id":"1308.4247","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-20T07:51:34Z","cross_cats_sorted":["math-ph","math.MP","math.NT"],"title_canon_sha256":"5dc5ed02c54bd1794e0df2311ce11f1380de0d478ba1a425b739107b74742945","abstract_canon_sha256":"fb71a95d1a3588f88d8f338a2c600aa2f857e721caec2788badbb7dfa9afa069"},"schema_version":"1.0"},"canonical_sha256":"5cec8afb89102a02574d8e1a74a8d3875b093d92fd06c35a6578d4715d0b65df","source":{"kind":"arxiv","id":"1308.4247","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4247","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4247v3","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4247","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"LTWIV64JCAVA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LTWIV64JCAVAEV2N","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LTWIV64J","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LTWIV64JCAVAEV2NRYNHJKGTQ5","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4247","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-20T07:51:34Z","cross_cats_sorted":["math-ph","math.MP","math.NT"],"title_canon_sha256":"5dc5ed02c54bd1794e0df2311ce11f1380de0d478ba1a425b739107b74742945","abstract_canon_sha256":"fb71a95d1a3588f88d8f338a2c600aa2f857e721caec2788badbb7dfa9afa069"},"schema_version":"1.0"},"canonical_sha256":"5cec8afb89102a02574d8e1a74a8d3875b093d92fd06c35a6578d4715d0b65df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:12.653654Z","signature_b64":"KNq9Fp0A+o+G7FsDPrURJFWgr3sXz9aeFmS7v3K4MRLt+Fp6FOZw6LJkEeQ4Bp1LomSvRdia59a/ML1Lqst5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cec8afb89102a02574d8e1a74a8d3875b093d92fd06c35a6578d4715d0b65df","last_reissued_at":"2026-05-18T03:00:12.652876Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:12.652876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4247","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":"2026-05-18T03:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hfbdi9A5GfQTFRjc46tWkF7cYLqmNWh4AatLMbEBNPSvdNFnQgUmVEbKTPt8DIGX7c3BIINJNvolLIg7rg32DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:25:10.394279Z"},"content_sha256":"4d4da21c27f1dd47f1d434aff98b9e4a0c3da297940684b00af13d8667e4c9d5","schema_version":"1.0","event_id":"sha256:4d4da21c27f1dd47f1d434aff98b9e4a0c3da297940684b00af13d8667e4c9d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LTWIV64JCAVAEV2NRYNHJKGTQ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nodal intersections and Lp restriction theorems on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NT"],"primary_cat":"math.AP","authors_text":"Jean Bourgain, Zeev Rudnick","submitted_at":"2013-08-20T07:51:34Z","abstract_excerpt":"We study the number of intersections of the nodal lines of an eigenfunction of the Laplacian on the standard torus with a fixed reference curve, that is, the number of zeros of the eigenfunction restricted to the curve. An upper bound is the wave number k. When the curve has nowhere zero curvature, we conjecture that, up to a constant multiple, this should also be the correct a lower bound. We give a lower bound which differs from this by an arithmetic quantity, given in terms of the maximal number of lattice points in arcs of size square root of the wave number k on a circle of radius k. Acco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4247","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":"2026-05-18T03:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F8nIlBi2zRTHI5KxdhiYHi6wpUkxxwbedMZCOXK2/M0POqzvAbWBqdcDKbA/ZSr7UPbpbAwNyyzscfZ1JZIACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:25:10.394958Z"},"content_sha256":"22fc3d78112f5d9495ce8f04a88d0d271934ff2e32ee254bc0d687e5e55d695f","schema_version":"1.0","event_id":"sha256:22fc3d78112f5d9495ce8f04a88d0d271934ff2e32ee254bc0d687e5e55d695f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTWIV64JCAVAEV2NRYNHJKGTQ5/bundle.json","state_url":"https://pith.science/pith/LTWIV64JCAVAEV2NRYNHJKGTQ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTWIV64JCAVAEV2NRYNHJKGTQ5/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":"2026-05-27T23:25:10Z","links":{"resolver":"https://pith.science/pith/LTWIV64JCAVAEV2NRYNHJKGTQ5","bundle":"https://pith.science/pith/LTWIV64JCAVAEV2NRYNHJKGTQ5/bundle.json","state":"https://pith.science/pith/LTWIV64JCAVAEV2NRYNHJKGTQ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTWIV64JCAVAEV2NRYNHJKGTQ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LTWIV64JCAVAEV2NRYNHJKGTQ5","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":"fb71a95d1a3588f88d8f338a2c600aa2f857e721caec2788badbb7dfa9afa069","cross_cats_sorted":["math-ph","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-20T07:51:34Z","title_canon_sha256":"5dc5ed02c54bd1794e0df2311ce11f1380de0d478ba1a425b739107b74742945"},"schema_version":"1.0","source":{"id":"1308.4247","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4247","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4247v3","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4247","created_at":"2026-05-18T03:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"LTWIV64JCAVA","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LTWIV64JCAVAEV2N","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LTWIV64J","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:22fc3d78112f5d9495ce8f04a88d0d271934ff2e32ee254bc0d687e5e55d695f","target":"graph","created_at":"2026-05-18T03:00:12Z","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 study the number of intersections of the nodal lines of an eigenfunction of the Laplacian on the standard torus with a fixed reference curve, that is, the number of zeros of the eigenfunction restricted to the curve. An upper bound is the wave number k. When the curve has nowhere zero curvature, we conjecture that, up to a constant multiple, this should also be the correct a lower bound. We give a lower bound which differs from this by an arithmetic quantity, given in terms of the maximal number of lattice points in arcs of size square root of the wave number k on a circle of radius k. Acco","authors_text":"Jean Bourgain, Zeev Rudnick","cross_cats":["math-ph","math.MP","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-20T07:51:34Z","title":"Nodal intersections and Lp restriction theorems on the torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4247","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":"sha256:4d4da21c27f1dd47f1d434aff98b9e4a0c3da297940684b00af13d8667e4c9d5","target":"record","created_at":"2026-05-18T03:00:12Z","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":"fb71a95d1a3588f88d8f338a2c600aa2f857e721caec2788badbb7dfa9afa069","cross_cats_sorted":["math-ph","math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-20T07:51:34Z","title_canon_sha256":"5dc5ed02c54bd1794e0df2311ce11f1380de0d478ba1a425b739107b74742945"},"schema_version":"1.0","source":{"id":"1308.4247","kind":"arxiv","version":3}},"canonical_sha256":"5cec8afb89102a02574d8e1a74a8d3875b093d92fd06c35a6578d4715d0b65df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cec8afb89102a02574d8e1a74a8d3875b093d92fd06c35a6578d4715d0b65df","first_computed_at":"2026-05-18T03:00:12.652876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:12.652876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KNq9Fp0A+o+G7FsDPrURJFWgr3sXz9aeFmS7v3K4MRLt+Fp6FOZw6LJkEeQ4Bp1LomSvRdia59a/ML1Lqst5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:12.653654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4247","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d4da21c27f1dd47f1d434aff98b9e4a0c3da297940684b00af13d8667e4c9d5","sha256:22fc3d78112f5d9495ce8f04a88d0d271934ff2e32ee254bc0d687e5e55d695f"],"state_sha256":"bbd028108e957846bea890f5fa99b3586a57ff5b2a051810269b677051695016"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"naZdyMGe0FvlzL4uGL2MnQC3A9o6bU6pdMcKFEf2qxXUbCO8w+dIVsTsKOu0jEKOruMd0A8ALg1HrR/g6K5dCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:25:10.398598Z","bundle_sha256":"5e4318d07c7341385c3182873f37bd680e875650191a2195b1731b19e517ba36"}}