{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QBO456XWRMP3ZFMSD73GBTZPF2","short_pith_number":"pith:QBO456XW","canonical_record":{"source":{"id":"1602.08376","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-26T15:58:58Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"4c93554c41f152e3cd31429c30b3687260347683286c1a3046c5795c2fd45805","abstract_canon_sha256":"a56d442f14c7275d1c70a24a91b2641e04bad14b2a4fcf8662fa0aa0c11c037f"},"schema_version":"1.0"},"canonical_sha256":"805dcefaf68b1fbc95921ff660cf2f2eb2f123dea4140d6a1b49b638b194c8f7","source":{"kind":"arxiv","id":"1602.08376","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08376","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08376v3","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08376","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"pith_short_12","alias_value":"QBO456XWRMP3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QBO456XWRMP3ZFMS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QBO456XW","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QBO456XWRMP3ZFMSD73GBTZPF2","target":"record","payload":{"canonical_record":{"source":{"id":"1602.08376","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-26T15:58:58Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"4c93554c41f152e3cd31429c30b3687260347683286c1a3046c5795c2fd45805","abstract_canon_sha256":"a56d442f14c7275d1c70a24a91b2641e04bad14b2a4fcf8662fa0aa0c11c037f"},"schema_version":"1.0"},"canonical_sha256":"805dcefaf68b1fbc95921ff660cf2f2eb2f123dea4140d6a1b49b638b194c8f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:38.285207Z","signature_b64":"5JA23yKGsUIcH+9Nnb85cu6jU3+BiDktQD843h7aGTklwdjTpSm0pSODq/jjEyrtHPC1sDIxQA6Wxj2+bvKhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"805dcefaf68b1fbc95921ff660cf2f2eb2f123dea4140d6a1b49b638b194c8f7","last_reissued_at":"2026-05-18T00:47:38.284588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:38.284588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.08376","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":"2026-05-18T00:47:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hCszgukZ6NNtkubBoOVSjOznv8vvkqk1DujlGP2vW05ukwVf7Lf9YRHPgEiMz9yC8jTzG8HSXIECy9UDINYcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T10:44:48.107086Z"},"content_sha256":"6be31779fc2ebf68bf128982d4d9ac75843f0a839a6999f772957cccf0bd908a","schema_version":"1.0","event_id":"sha256:6be31779fc2ebf68bf128982d4d9ac75843f0a839a6999f772957cccf0bd908a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QBO456XWRMP3ZFMSD73GBTZPF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the number of Courant-sharp Dirichlet eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Katie Gittins, Michiel van den Berg","submitted_at":"2016-02-26T15:58:58Z","abstract_excerpt":"We consider arbitrary open sets $\\Omega$ in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of $\\Omega$, (ii) the number of Courant-sharp Dirichlet eigenvalues of $\\Omega$. This extends recent results of P. B\\'erard and B. Helffer."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08376","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":"2026-05-18T00:47:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qZXMRjLyvxxLxu6h8eXPNFKKgU0xayZK6KrqIVPW624sqQykPweHemBa1hohFdGLW0/d55iUADSGj5bLy4yiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T10:44:48.107701Z"},"content_sha256":"965a4c2ca145f38e3e5ace1691360fbab954e60dfcab279b572bfb17449d0708","schema_version":"1.0","event_id":"sha256:965a4c2ca145f38e3e5ace1691360fbab954e60dfcab279b572bfb17449d0708"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBO456XWRMP3ZFMSD73GBTZPF2/bundle.json","state_url":"https://pith.science/pith/QBO456XWRMP3ZFMSD73GBTZPF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBO456XWRMP3ZFMSD73GBTZPF2/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":"2026-05-20T10:44:48Z","links":{"resolver":"https://pith.science/pith/QBO456XWRMP3ZFMSD73GBTZPF2","bundle":"https://pith.science/pith/QBO456XWRMP3ZFMSD73GBTZPF2/bundle.json","state":"https://pith.science/pith/QBO456XWRMP3ZFMSD73GBTZPF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBO456XWRMP3ZFMSD73GBTZPF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QBO456XWRMP3ZFMSD73GBTZPF2","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":"a56d442f14c7275d1c70a24a91b2641e04bad14b2a4fcf8662fa0aa0c11c037f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-26T15:58:58Z","title_canon_sha256":"4c93554c41f152e3cd31429c30b3687260347683286c1a3046c5795c2fd45805"},"schema_version":"1.0","source":{"id":"1602.08376","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08376","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08376v3","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08376","created_at":"2026-05-18T00:47:38Z"},{"alias_kind":"pith_short_12","alias_value":"QBO456XWRMP3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QBO456XWRMP3ZFMS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QBO456XW","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:965a4c2ca145f38e3e5ace1691360fbab954e60dfcab279b572bfb17449d0708","target":"graph","created_at":"2026-05-18T00:47:38Z","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 consider arbitrary open sets $\\Omega$ in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of $\\Omega$, (ii) the number of Courant-sharp Dirichlet eigenvalues of $\\Omega$. This extends recent results of P. B\\'erard and B. Helffer.","authors_text":"Katie Gittins, Michiel van den Berg","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-26T15:58:58Z","title":"On the number of Courant-sharp Dirichlet eigenvalues"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08376","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":"sha256:6be31779fc2ebf68bf128982d4d9ac75843f0a839a6999f772957cccf0bd908a","target":"record","created_at":"2026-05-18T00:47:38Z","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":"a56d442f14c7275d1c70a24a91b2641e04bad14b2a4fcf8662fa0aa0c11c037f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-26T15:58:58Z","title_canon_sha256":"4c93554c41f152e3cd31429c30b3687260347683286c1a3046c5795c2fd45805"},"schema_version":"1.0","source":{"id":"1602.08376","kind":"arxiv","version":3}},"canonical_sha256":"805dcefaf68b1fbc95921ff660cf2f2eb2f123dea4140d6a1b49b638b194c8f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"805dcefaf68b1fbc95921ff660cf2f2eb2f123dea4140d6a1b49b638b194c8f7","first_computed_at":"2026-05-18T00:47:38.284588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:38.284588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5JA23yKGsUIcH+9Nnb85cu6jU3+BiDktQD843h7aGTklwdjTpSm0pSODq/jjEyrtHPC1sDIxQA6Wxj2+bvKhBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:38.285207Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08376","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6be31779fc2ebf68bf128982d4d9ac75843f0a839a6999f772957cccf0bd908a","sha256:965a4c2ca145f38e3e5ace1691360fbab954e60dfcab279b572bfb17449d0708"],"state_sha256":"9bf12f51188a840a326ff6a49d00af0bb76e7d9d664f59088e98b0cf64714a93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ttfeZ+P8dYHU44OI6UN5+ZqDZVG9jomWtuQYjlgqnySaX7QJcimDa8u/P1Y2f4JxW6aeeXvH1on9DCFdFtPADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T10:44:48.110367Z","bundle_sha256":"205259b1f13af728b8ccea2fcbffdbf96eb3695fc3f5bd14e58fbc6b297fe83d"}}