{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AKCL7KCXJUM3YUIESROKTMSNDR","short_pith_number":"pith:AKCL7KCX","canonical_record":{"source":{"id":"1008.1316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-08-07T09:50:50Z","cross_cats_sorted":[],"title_canon_sha256":"91665482467e56d74b79557a0f3645c30fa4336fa2d91a4c4aad502cab8e43a3","abstract_canon_sha256":"19bea4fab400a4a8ad63f2e26a08ae6233612f65c046e9f12d26a24704072992"},"schema_version":"1.0"},"canonical_sha256":"0284bfa8574d19bc5104945ca9b24d1c5d6de4ce86c7e352b8deace07feb58d5","source":{"kind":"arxiv","id":"1008.1316","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1316","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1316v1","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1316","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"AKCL7KCXJUM3","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AKCL7KCXJUM3YUIE","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AKCL7KCX","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AKCL7KCXJUM3YUIESROKTMSNDR","target":"record","payload":{"canonical_record":{"source":{"id":"1008.1316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-08-07T09:50:50Z","cross_cats_sorted":[],"title_canon_sha256":"91665482467e56d74b79557a0f3645c30fa4336fa2d91a4c4aad502cab8e43a3","abstract_canon_sha256":"19bea4fab400a4a8ad63f2e26a08ae6233612f65c046e9f12d26a24704072992"},"schema_version":"1.0"},"canonical_sha256":"0284bfa8574d19bc5104945ca9b24d1c5d6de4ce86c7e352b8deace07feb58d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:33.327421Z","signature_b64":"yDa9YmH3xeHTqbaxZk5p6ukhq2s6fnJReNSciKCf6saG7IjCeV5YuICCyXFaUIpxUFahmUJoC3C9bFPx1XVMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0284bfa8574d19bc5104945ca9b24d1c5d6de4ce86c7e352b8deace07feb58d5","last_reissued_at":"2026-05-18T04:42:33.326862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:33.326862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.1316","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":"2026-05-18T04:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SY4ro8RWiw3l/bdUedEitp7unygbsVWeIvjvQ59VjwUlAMA1X13V+Q3yr6jLxuz/LvzyyDEM8+sW7hhBZHd3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:29:40.232913Z"},"content_sha256":"6d1589fb7b139ef5c48edca9c3712e1eeef74b193b53b8b7a6a3b0c26c665ade","schema_version":"1.0","event_id":"sha256:6d1589fb7b139ef5c48edca9c3712e1eeef74b193b53b8b7a6a3b0c26c665ade"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AKCL7KCXJUM3YUIESROKTMSNDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirichlet eigenvalue sums on triangles are minimal for equilaterals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Bartlomiej Siudeja, Richard Laugesen","submitted_at":"2010-08-07T09:50:50Z","abstract_excerpt":"Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first $n$ eigenvalues of the Dirichlet Laplacian, for each $n \\geq 1$. In addition, the first, second and third eigenvalues are each proved to be minimal for the equilateral triangle. The disk is conjectured to be the minimizer among general domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1316","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":"2026-05-18T04:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HkyZN12nVWpI5q9v6YP9EkqFVZrc54hDyuVearhKPpjk+4q3NivEx2l7Eeo+1imjTP9pb2r7vCf3hdxZZ0EWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:29:40.233621Z"},"content_sha256":"e75f488bdee68a9910545c777498f404daa2e9af8ea17937ce027d7f078381be","schema_version":"1.0","event_id":"sha256:e75f488bdee68a9910545c777498f404daa2e9af8ea17937ce027d7f078381be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AKCL7KCXJUM3YUIESROKTMSNDR/bundle.json","state_url":"https://pith.science/pith/AKCL7KCXJUM3YUIESROKTMSNDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AKCL7KCXJUM3YUIESROKTMSNDR/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":"2026-05-26T16:29:40Z","links":{"resolver":"https://pith.science/pith/AKCL7KCXJUM3YUIESROKTMSNDR","bundle":"https://pith.science/pith/AKCL7KCXJUM3YUIESROKTMSNDR/bundle.json","state":"https://pith.science/pith/AKCL7KCXJUM3YUIESROKTMSNDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AKCL7KCXJUM3YUIESROKTMSNDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AKCL7KCXJUM3YUIESROKTMSNDR","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":"19bea4fab400a4a8ad63f2e26a08ae6233612f65c046e9f12d26a24704072992","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-08-07T09:50:50Z","title_canon_sha256":"91665482467e56d74b79557a0f3645c30fa4336fa2d91a4c4aad502cab8e43a3"},"schema_version":"1.0","source":{"id":"1008.1316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.1316","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1008.1316v1","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.1316","created_at":"2026-05-18T04:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"AKCL7KCXJUM3","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AKCL7KCXJUM3YUIE","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AKCL7KCX","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:e75f488bdee68a9910545c777498f404daa2e9af8ea17937ce027d7f078381be","target":"graph","created_at":"2026-05-18T04:42:33Z","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":"Among all triangles of given diameter, the equilateral triangle is shown to minimize the sum of the first $n$ eigenvalues of the Dirichlet Laplacian, for each $n \\geq 1$. In addition, the first, second and third eigenvalues are each proved to be minimal for the equilateral triangle. The disk is conjectured to be the minimizer among general domains.","authors_text":"Bartlomiej Siudeja, Richard Laugesen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-08-07T09:50:50Z","title":"Dirichlet eigenvalue sums on triangles are minimal for equilaterals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1316","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":"sha256:6d1589fb7b139ef5c48edca9c3712e1eeef74b193b53b8b7a6a3b0c26c665ade","target":"record","created_at":"2026-05-18T04:42:33Z","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":"19bea4fab400a4a8ad63f2e26a08ae6233612f65c046e9f12d26a24704072992","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2010-08-07T09:50:50Z","title_canon_sha256":"91665482467e56d74b79557a0f3645c30fa4336fa2d91a4c4aad502cab8e43a3"},"schema_version":"1.0","source":{"id":"1008.1316","kind":"arxiv","version":1}},"canonical_sha256":"0284bfa8574d19bc5104945ca9b24d1c5d6de4ce86c7e352b8deace07feb58d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0284bfa8574d19bc5104945ca9b24d1c5d6de4ce86c7e352b8deace07feb58d5","first_computed_at":"2026-05-18T04:42:33.326862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:33.326862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yDa9YmH3xeHTqbaxZk5p6ukhq2s6fnJReNSciKCf6saG7IjCeV5YuICCyXFaUIpxUFahmUJoC3C9bFPx1XVMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:33.327421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.1316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d1589fb7b139ef5c48edca9c3712e1eeef74b193b53b8b7a6a3b0c26c665ade","sha256:e75f488bdee68a9910545c777498f404daa2e9af8ea17937ce027d7f078381be"],"state_sha256":"e0004e049f5e7a8b3774ed2125726fff02a804cf204893205e380bd57942f840"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L2xMX8DgqTEqEBx9Wgx5TuGdrt2dUYYTyGDS/79gQh+4EA0+H1jAzE9OnkF5uqtT0u4wSjaajDlrTYLPzZ12AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:29:40.237340Z","bundle_sha256":"594fe5b6adbab57635015b7999f538f756e95f98734c7b3fe353dfed913b907a"}}