{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:H5HKI2TZH4XSO54YCJPVJEBKJT","short_pith_number":"pith:H5HKI2TZ","canonical_record":{"source":{"id":"1309.5057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-19T17:35:30Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"9314c87ce0211ee566d268a29f15418b40b17e81b4f47c48418680a17dbf071d","abstract_canon_sha256":"758dfcde70077c86cfc02e1e602e4af3c2d8182d4d16181fe8d0bc5a4d7d2954"},"schema_version":"1.0"},"canonical_sha256":"3f4ea46a793f2f277798125f54902a4cc598451add27b2bf3fda43f7172e896d","source":{"kind":"arxiv","id":"1309.5057","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5057","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5057v2","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5057","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"H5HKI2TZH4XS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"H5HKI2TZH4XSO54Y","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"H5HKI2TZ","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:H5HKI2TZH4XSO54YCJPVJEBKJT","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5057","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-19T17:35:30Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"9314c87ce0211ee566d268a29f15418b40b17e81b4f47c48418680a17dbf071d","abstract_canon_sha256":"758dfcde70077c86cfc02e1e602e4af3c2d8182d4d16181fe8d0bc5a4d7d2954"},"schema_version":"1.0"},"canonical_sha256":"3f4ea46a793f2f277798125f54902a4cc598451add27b2bf3fda43f7172e896d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:31.919333Z","signature_b64":"ZbytPuyoybm1kzPlG+5C+xWTl+fRcqwK8ss9kqTakJfbDoUL3Zzg1GQ8pzC8fVTUJAY3LE0TqX8OHp3F9W3iCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f4ea46a793f2f277798125f54902a4cc598451add27b2bf3fda43f7172e896d","last_reissued_at":"2026-05-18T02:45:31.918682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:31.918682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5057","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":"2026-05-18T02:45:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"57DwyaNM9LHYCGTL8SxT2C6aKtyLkNQ+b/nBDW1RNyMlBc/flQAin9xzATJOdHCVNJrfQRK6tPj3PE8wMZTEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:32:05.167819Z"},"content_sha256":"fac8bef21e7c6b80e684b6efd8df23d897009f95e939611577796f6b5fefeac7","schema_version":"1.0","event_id":"sha256:fac8bef21e7c6b80e684b6efd8df23d897009f95e939611577796f6b5fefeac7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:H5HKI2TZH4XSO54YCJPVJEBKJT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximization of the first nontrivial eigenvalue on the surface of genus two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DG","authors_text":"Mikhail A. Karpukhin","submitted_at":"2013-09-19T17:35:30Z","abstract_excerpt":"The first nontrivial eigenvalue of the Laplacian can be considered as a functional on the space of all Riemannian metrics of unit volume on a fixed surface. In this paper we prove that for the surface of genus 2 the supremum of this functional is equal to $16\\pi$. This provides a positive answer to the conjecture by Jakobson, Levitin, Nadirashvili, Nigam and Polterovich."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5057","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":"2026-05-18T02:45:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nx2sOPlkXaQdnPnYWrQYhbQ42ud+eFVzNyXDr+X7jJYZ2h91uEGRpnRUmw6/rPa/sN/OJp4kC4nBUGocIAd2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:32:05.168170Z"},"content_sha256":"43c29085d9e87bd5ecce18016155086f7dc70d357ae48e57bf2ad12a425d1232","schema_version":"1.0","event_id":"sha256:43c29085d9e87bd5ecce18016155086f7dc70d357ae48e57bf2ad12a425d1232"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5HKI2TZH4XSO54YCJPVJEBKJT/bundle.json","state_url":"https://pith.science/pith/H5HKI2TZH4XSO54YCJPVJEBKJT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5HKI2TZH4XSO54YCJPVJEBKJT/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":"2026-06-02T04:32:05Z","links":{"resolver":"https://pith.science/pith/H5HKI2TZH4XSO54YCJPVJEBKJT","bundle":"https://pith.science/pith/H5HKI2TZH4XSO54YCJPVJEBKJT/bundle.json","state":"https://pith.science/pith/H5HKI2TZH4XSO54YCJPVJEBKJT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5HKI2TZH4XSO54YCJPVJEBKJT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:H5HKI2TZH4XSO54YCJPVJEBKJT","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":"758dfcde70077c86cfc02e1e602e4af3c2d8182d4d16181fe8d0bc5a4d7d2954","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-19T17:35:30Z","title_canon_sha256":"9314c87ce0211ee566d268a29f15418b40b17e81b4f47c48418680a17dbf071d"},"schema_version":"1.0","source":{"id":"1309.5057","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5057","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5057v2","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5057","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"H5HKI2TZH4XS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"H5HKI2TZH4XSO54Y","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"H5HKI2TZ","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:43c29085d9e87bd5ecce18016155086f7dc70d357ae48e57bf2ad12a425d1232","target":"graph","created_at":"2026-05-18T02:45:31Z","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":"The first nontrivial eigenvalue of the Laplacian can be considered as a functional on the space of all Riemannian metrics of unit volume on a fixed surface. In this paper we prove that for the surface of genus 2 the supremum of this functional is equal to $16\\pi$. This provides a positive answer to the conjecture by Jakobson, Levitin, Nadirashvili, Nigam and Polterovich.","authors_text":"Mikhail A. Karpukhin","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-19T17:35:30Z","title":"Maximization of the first nontrivial eigenvalue on the surface of genus two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5057","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:fac8bef21e7c6b80e684b6efd8df23d897009f95e939611577796f6b5fefeac7","target":"record","created_at":"2026-05-18T02:45:31Z","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":"758dfcde70077c86cfc02e1e602e4af3c2d8182d4d16181fe8d0bc5a4d7d2954","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-19T17:35:30Z","title_canon_sha256":"9314c87ce0211ee566d268a29f15418b40b17e81b4f47c48418680a17dbf071d"},"schema_version":"1.0","source":{"id":"1309.5057","kind":"arxiv","version":2}},"canonical_sha256":"3f4ea46a793f2f277798125f54902a4cc598451add27b2bf3fda43f7172e896d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f4ea46a793f2f277798125f54902a4cc598451add27b2bf3fda43f7172e896d","first_computed_at":"2026-05-18T02:45:31.918682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:31.918682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZbytPuyoybm1kzPlG+5C+xWTl+fRcqwK8ss9kqTakJfbDoUL3Zzg1GQ8pzC8fVTUJAY3LE0TqX8OHp3F9W3iCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:31.919333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5057","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fac8bef21e7c6b80e684b6efd8df23d897009f95e939611577796f6b5fefeac7","sha256:43c29085d9e87bd5ecce18016155086f7dc70d357ae48e57bf2ad12a425d1232"],"state_sha256":"adad0f5464897cf16cbb704adbcde092ba7f37573e83e9674493003778763245"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kh8E2arKaNhLapQgMy6/TWaajhOQvXFhEMWPlxfq42o3w40ouWeZU10uh9ezQA/NEEpUPhFpsuQU5/qUv3xsBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:32:05.170155Z","bundle_sha256":"b6604ec83b6bb96f36b46c1b39776af03547f5827793f88bec5e1ff2b7ad5663"}}