{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ER4XFYZ2HD6EU4WJWFJM27Y2NK","short_pith_number":"pith:ER4XFYZ2","canonical_record":{"source":{"id":"1308.4422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-08-20T20:05:45Z","cross_cats_sorted":[],"title_canon_sha256":"8105215aadbcbc43ff46f66e6e16319f9c4cad070a5a886c18675f6967352fa1","abstract_canon_sha256":"b1cedc85d855a82a1d5101dee9bf56d321c1c5d7cfb33a48b758bb3970634827"},"schema_version":"1.0"},"canonical_sha256":"247972e33a38fc4a72c9b152cd7f1a6a9c5f169521ebd7f735337a34034fce63","source":{"kind":"arxiv","id":"1308.4422","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4422","created_at":"2026-05-18T03:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4422v1","created_at":"2026-05-18T03:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4422","created_at":"2026-05-18T03:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"ER4XFYZ2HD6E","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ER4XFYZ2HD6EU4WJ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ER4XFYZ2","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ER4XFYZ2HD6EU4WJWFJM27Y2NK","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-08-20T20:05:45Z","cross_cats_sorted":[],"title_canon_sha256":"8105215aadbcbc43ff46f66e6e16319f9c4cad070a5a886c18675f6967352fa1","abstract_canon_sha256":"b1cedc85d855a82a1d5101dee9bf56d321c1c5d7cfb33a48b758bb3970634827"},"schema_version":"1.0"},"canonical_sha256":"247972e33a38fc4a72c9b152cd7f1a6a9c5f169521ebd7f735337a34034fce63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:31.887165Z","signature_b64":"UZaF1+XDF8oB0o1mScyHZMAaMefvJwQXWC+pC+clziHXTZ5Bj05UKXwwV5DCjz+t+JzCf/kN50tWFSSproRYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"247972e33a38fc4a72c9b152cd7f1a6a9c5f169521ebd7f735337a34034fce63","last_reissued_at":"2026-05-18T03:15:31.886568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:31.886568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4422","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":"2026-05-18T03:15:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kTQFPTHytNFam8eJYyK1rZIhJVLGv9AhaNOoF1lplXxqKHZ2/GMQ94DUvk/m8HHWEOtilwWbDnPHx5mHbtNfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:30:50.874969Z"},"content_sha256":"a84342e86e95e3271b4ce30a13d19d2425e45d8af32c745ce3e440237f758fcd","schema_version":"1.0","event_id":"sha256:a84342e86e95e3271b4ce30a13d19d2425e45d8af32c745ce3e440237f758fcd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ER4XFYZ2HD6EU4WJWFJM27Y2NK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Pleijel's nodal domain theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Jean Bourgain","submitted_at":"2013-08-20T20:05:45Z","abstract_excerpt":"A slight improvement of Pleijel's estimate on the number of nodal domains is obtained, exploiting a refinement of the Faber-Krahn inequality and packing density of discs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4422","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":"2026-05-18T03:15:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rjyvX7lQKymOWJyoYP9kfJUOMF6sWY+apl6S2KgBTvKror+MMgFOUx13f4jXL9rWSYyqnX/S9dn4yFA9WDJwBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:30:50.875336Z"},"content_sha256":"d6626e05a314aaaea5f8cdc04d758378c2019935c1bf38c331111503f144b992","schema_version":"1.0","event_id":"sha256:d6626e05a314aaaea5f8cdc04d758378c2019935c1bf38c331111503f144b992"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ER4XFYZ2HD6EU4WJWFJM27Y2NK/bundle.json","state_url":"https://pith.science/pith/ER4XFYZ2HD6EU4WJWFJM27Y2NK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ER4XFYZ2HD6EU4WJWFJM27Y2NK/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":"2026-05-28T06:30:50Z","links":{"resolver":"https://pith.science/pith/ER4XFYZ2HD6EU4WJWFJM27Y2NK","bundle":"https://pith.science/pith/ER4XFYZ2HD6EU4WJWFJM27Y2NK/bundle.json","state":"https://pith.science/pith/ER4XFYZ2HD6EU4WJWFJM27Y2NK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ER4XFYZ2HD6EU4WJWFJM27Y2NK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ER4XFYZ2HD6EU4WJWFJM27Y2NK","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":"b1cedc85d855a82a1d5101dee9bf56d321c1c5d7cfb33a48b758bb3970634827","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-08-20T20:05:45Z","title_canon_sha256":"8105215aadbcbc43ff46f66e6e16319f9c4cad070a5a886c18675f6967352fa1"},"schema_version":"1.0","source":{"id":"1308.4422","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4422","created_at":"2026-05-18T03:15:31Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4422v1","created_at":"2026-05-18T03:15:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4422","created_at":"2026-05-18T03:15:31Z"},{"alias_kind":"pith_short_12","alias_value":"ER4XFYZ2HD6E","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ER4XFYZ2HD6EU4WJ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ER4XFYZ2","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:d6626e05a314aaaea5f8cdc04d758378c2019935c1bf38c331111503f144b992","target":"graph","created_at":"2026-05-18T03:15:31Z","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":"A slight improvement of Pleijel's estimate on the number of nodal domains is obtained, exploiting a refinement of the Faber-Krahn inequality and packing density of discs.","authors_text":"Jean Bourgain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-08-20T20:05:45Z","title":"On Pleijel's nodal domain theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4422","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:a84342e86e95e3271b4ce30a13d19d2425e45d8af32c745ce3e440237f758fcd","target":"record","created_at":"2026-05-18T03:15:31Z","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":"b1cedc85d855a82a1d5101dee9bf56d321c1c5d7cfb33a48b758bb3970634827","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-08-20T20:05:45Z","title_canon_sha256":"8105215aadbcbc43ff46f66e6e16319f9c4cad070a5a886c18675f6967352fa1"},"schema_version":"1.0","source":{"id":"1308.4422","kind":"arxiv","version":1}},"canonical_sha256":"247972e33a38fc4a72c9b152cd7f1a6a9c5f169521ebd7f735337a34034fce63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"247972e33a38fc4a72c9b152cd7f1a6a9c5f169521ebd7f735337a34034fce63","first_computed_at":"2026-05-18T03:15:31.886568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:31.886568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UZaF1+XDF8oB0o1mScyHZMAaMefvJwQXWC+pC+clziHXTZ5Bj05UKXwwV5DCjz+t+JzCf/kN50tWFSSproRYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:31.887165Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4422","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a84342e86e95e3271b4ce30a13d19d2425e45d8af32c745ce3e440237f758fcd","sha256:d6626e05a314aaaea5f8cdc04d758378c2019935c1bf38c331111503f144b992"],"state_sha256":"f2d0ea4e6b97e17fdffd3cfb98174ceb6ad98d8f755440b7d408105ab4c79ff6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HMomoN7Kaw5FzbiB0Mj3Jkd81qhxC55Io33V7c3WFKIEAwlz1tcnGgVzg/Ytm5yrb+gv47d3s/yHNIBJ+GWbCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:30:50.877380Z","bundle_sha256":"9349c32eeee0928caa75ce277503f5960766a6e6efe9d3a7ab5054e310700e25"}}