{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:T46ARMMFNHR3ZMXSYGBQGLFW6M","short_pith_number":"pith:T46ARMMF","canonical_record":{"source":{"id":"1108.5160","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-08-25T19:08:56Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b9b0601bef73cd83b2f825be2738301238591fac859824c1d3864633c895bdf1","abstract_canon_sha256":"7e0345e234429bb9775503fcb02474dbf67125d82a591d7c03824ec53a1aec81"},"schema_version":"1.0"},"canonical_sha256":"9f3c08b18569e3bcb2f2c183032cb6f3049125851979090c9debea216443b4c3","source":{"kind":"arxiv","id":"1108.5160","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5160","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5160v3","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5160","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"pith_short_12","alias_value":"T46ARMMFNHR3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T46ARMMFNHR3ZMXS","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T46ARMMF","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:T46ARMMFNHR3ZMXSYGBQGLFW6M","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5160","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-08-25T19:08:56Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b9b0601bef73cd83b2f825be2738301238591fac859824c1d3864633c895bdf1","abstract_canon_sha256":"7e0345e234429bb9775503fcb02474dbf67125d82a591d7c03824ec53a1aec81"},"schema_version":"1.0"},"canonical_sha256":"9f3c08b18569e3bcb2f2c183032cb6f3049125851979090c9debea216443b4c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:59.045677Z","signature_b64":"Vu5SYt2QeceHGLE1B/6GPHCpsQoX0ZLO+vcUSG00DI4ie2fCfHPDuo0it+h7JGdg1vGFCrhAcIfn+E6l8GbBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f3c08b18569e3bcb2f2c183032cb6f3049125851979090c9debea216443b4c3","last_reissued_at":"2026-05-18T03:32:59.044883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:59.044883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5160","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":"2026-05-18T03:32:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6nF+6DlrZX8i6Bk/YIZF9RFY51BRijVxk7SHLgUs8LAD4Tp5wfnI54PtPPxSWT7aBQneTQ2WjU8knZGHOqojBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T01:13:39.607298Z"},"content_sha256":"b62aa588ebe06f7c110bb9332f59dfd075ce76b30ccc7fc58f4e2b5ac860afc4","schema_version":"1.0","event_id":"sha256:b62aa588ebe06f7c110bb9332f59dfd075ce76b30ccc7fc58f4e2b5ac860afc4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:T46ARMMFNHR3ZMXSYGBQGLFW6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremal spectral properties of Otsuki tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Alexei V. Penskoi","submitted_at":"2011-08-25T19:08:56Z","abstract_excerpt":"Otsuki tori form a countable family of immersed minimal two-dimensional tori in the unitary three-dimensional sphere. According to El Soufi-Ilias theorem, the metrics on the Otsuki tori are extremal for some unknown eigenvalues of the Laplace-Beltrami operator. Despite the fact that the Otsuki tori are defined in quite an implicit way, we find explicitly the numbers of the corresponding extremal eigenvalues. In particular we provide an extremal metric for the third eigenvalue of the torus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5160","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":"2026-05-18T03:32:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zQ3ecgiQ65qF/g2Skow22kD3A0rsRahhh9XnNFGeOQCe4/H4xKee9O3HtEUenVQP0N3n63SOjgRFbRg/l8/SBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T01:13:39.607657Z"},"content_sha256":"180f2a724eab5e26efa9c4c211bf85503b4ff21f1ed2a1eaf6aef872a0c20547","schema_version":"1.0","event_id":"sha256:180f2a724eab5e26efa9c4c211bf85503b4ff21f1ed2a1eaf6aef872a0c20547"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T46ARMMFNHR3ZMXSYGBQGLFW6M/bundle.json","state_url":"https://pith.science/pith/T46ARMMFNHR3ZMXSYGBQGLFW6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T46ARMMFNHR3ZMXSYGBQGLFW6M/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":"2026-06-28T01:13:39Z","links":{"resolver":"https://pith.science/pith/T46ARMMFNHR3ZMXSYGBQGLFW6M","bundle":"https://pith.science/pith/T46ARMMFNHR3ZMXSYGBQGLFW6M/bundle.json","state":"https://pith.science/pith/T46ARMMFNHR3ZMXSYGBQGLFW6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T46ARMMFNHR3ZMXSYGBQGLFW6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T46ARMMFNHR3ZMXSYGBQGLFW6M","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":"7e0345e234429bb9775503fcb02474dbf67125d82a591d7c03824ec53a1aec81","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-08-25T19:08:56Z","title_canon_sha256":"b9b0601bef73cd83b2f825be2738301238591fac859824c1d3864633c895bdf1"},"schema_version":"1.0","source":{"id":"1108.5160","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5160","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5160v3","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5160","created_at":"2026-05-18T03:32:59Z"},{"alias_kind":"pith_short_12","alias_value":"T46ARMMFNHR3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T46ARMMFNHR3ZMXS","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T46ARMMF","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:180f2a724eab5e26efa9c4c211bf85503b4ff21f1ed2a1eaf6aef872a0c20547","target":"graph","created_at":"2026-05-18T03:32:59Z","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":"Otsuki tori form a countable family of immersed minimal two-dimensional tori in the unitary three-dimensional sphere. According to El Soufi-Ilias theorem, the metrics on the Otsuki tori are extremal for some unknown eigenvalues of the Laplace-Beltrami operator. Despite the fact that the Otsuki tori are defined in quite an implicit way, we find explicitly the numbers of the corresponding extremal eigenvalues. In particular we provide an extremal metric for the third eigenvalue of the torus.","authors_text":"Alexei V. Penskoi","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-08-25T19:08:56Z","title":"Extremal spectral properties of Otsuki tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5160","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:b62aa588ebe06f7c110bb9332f59dfd075ce76b30ccc7fc58f4e2b5ac860afc4","target":"record","created_at":"2026-05-18T03:32:59Z","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":"7e0345e234429bb9775503fcb02474dbf67125d82a591d7c03824ec53a1aec81","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2011-08-25T19:08:56Z","title_canon_sha256":"b9b0601bef73cd83b2f825be2738301238591fac859824c1d3864633c895bdf1"},"schema_version":"1.0","source":{"id":"1108.5160","kind":"arxiv","version":3}},"canonical_sha256":"9f3c08b18569e3bcb2f2c183032cb6f3049125851979090c9debea216443b4c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f3c08b18569e3bcb2f2c183032cb6f3049125851979090c9debea216443b4c3","first_computed_at":"2026-05-18T03:32:59.044883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:59.044883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vu5SYt2QeceHGLE1B/6GPHCpsQoX0ZLO+vcUSG00DI4ie2fCfHPDuo0it+h7JGdg1vGFCrhAcIfn+E6l8GbBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:59.045677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5160","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b62aa588ebe06f7c110bb9332f59dfd075ce76b30ccc7fc58f4e2b5ac860afc4","sha256:180f2a724eab5e26efa9c4c211bf85503b4ff21f1ed2a1eaf6aef872a0c20547"],"state_sha256":"321bd900b9b06164b92d272ba815488e2b8ce830cecaa5a59aac37df7710aabe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jyi+8RdGn0LaWXD6EEI98XxC3yVEy1os0EJ/cfxZErr1asir+aqnM6gkDsbErh8bHNZzQxQVKn11Toq78B2rAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T01:13:39.609484Z","bundle_sha256":"680cc2f1792afd7caa38c2f4ccbbcd46fbae1120fd52ac2fbb5e352452a5cae5"}}