{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:3J7VIYTDZTWIPXE4JTIKWB37E2","short_pith_number":"pith:3J7VIYTD","canonical_record":{"source":{"id":"2211.15636","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-11-28T18:42:25Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"883c272092118e0643e3338c772a9e67ec25da097b105ff1a67a5a6571d692dd","abstract_canon_sha256":"144f73b470fdffa939ebfb59ab34ffca76559accada91a1a5000c9081d61ce6b"},"schema_version":"1.0"},"canonical_sha256":"da7f546263ccec87dc9c4cd0ab077f26a281906335c09f3804940e10b39501ad","source":{"kind":"arxiv","id":"2211.15636","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.15636","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"2211.15636v1","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.15636","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"3J7VIYTDZTWI","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_16","alias_value":"3J7VIYTDZTWIPXE4","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_8","alias_value":"3J7VIYTD","created_at":"2026-07-05T05:20:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:3J7VIYTDZTWIPXE4JTIKWB37E2","target":"record","payload":{"canonical_record":{"source":{"id":"2211.15636","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-11-28T18:42:25Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"883c272092118e0643e3338c772a9e67ec25da097b105ff1a67a5a6571d692dd","abstract_canon_sha256":"144f73b470fdffa939ebfb59ab34ffca76559accada91a1a5000c9081d61ce6b"},"schema_version":"1.0"},"canonical_sha256":"da7f546263ccec87dc9c4cd0ab077f26a281906335c09f3804940e10b39501ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:20:06.257712Z","signature_b64":"aebUX0Vrbv01PmFOzIz5ltHW5orHp5BI8D6KKPnO4eevYPzE3gaG8IdTu/UtnYmA9oUQ5I/hd/USLTWfmHPCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da7f546263ccec87dc9c4cd0ab077f26a281906335c09f3804940e10b39501ad","last_reissued_at":"2026-07-05T05:20:06.257216Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:20:06.257216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.15636","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":"2026-07-05T05:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aVCUhPx4KsRRHOQGAqyd6bSa5hRZ6Rbje/4egUzMI5MhqcuOuMCHBxU+nPHWFeHu1Xv7GBta8s/kdlnTqvN1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T08:00:23.123961Z"},"content_sha256":"33582482a3103b790ef8faf9350fa3c79acb638b431cc54e21a9c608ef9b8208","schema_version":"1.0","event_id":"sha256:33582482a3103b790ef8faf9350fa3c79acb638b431cc54e21a9c608ef9b8208"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:3J7VIYTDZTWIPXE4JTIKWB37E2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximizing one Laplace eigenvalue on n-dimensional manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Romain Petrides","submitted_at":"2022-11-28T18:42:25Z","abstract_excerpt":"We prove existence and regularity results for the problem of maximization of one Laplace eigenvalue with respect to metrics of same volume lying in a conformal class of a Riemannian manifold of dimension $n\\geq 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.15636","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.15636/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:20:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ykGd5auq77n4bg36XbA+7Gegr6AFh8RWGVWQY04WJTo1vAuX8FoYxXWCo4vQ4jbCZePbuBQYO3Eu2e0jCHpzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T08:00:23.124460Z"},"content_sha256":"e3efcdbf9b78265dca5e59ab7663140c436cff10e901dc77e960a99c83083eac","schema_version":"1.0","event_id":"sha256:e3efcdbf9b78265dca5e59ab7663140c436cff10e901dc77e960a99c83083eac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3J7VIYTDZTWIPXE4JTIKWB37E2/bundle.json","state_url":"https://pith.science/pith/3J7VIYTDZTWIPXE4JTIKWB37E2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3J7VIYTDZTWIPXE4JTIKWB37E2/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":"2026-08-19T08:00:23Z","links":{"resolver":"https://pith.science/pith/3J7VIYTDZTWIPXE4JTIKWB37E2","bundle":"https://pith.science/pith/3J7VIYTDZTWIPXE4JTIKWB37E2/bundle.json","state":"https://pith.science/pith/3J7VIYTDZTWIPXE4JTIKWB37E2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3J7VIYTDZTWIPXE4JTIKWB37E2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3J7VIYTDZTWIPXE4JTIKWB37E2","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":"144f73b470fdffa939ebfb59ab34ffca76559accada91a1a5000c9081d61ce6b","cross_cats_sorted":["math.DG","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-11-28T18:42:25Z","title_canon_sha256":"883c272092118e0643e3338c772a9e67ec25da097b105ff1a67a5a6571d692dd"},"schema_version":"1.0","source":{"id":"2211.15636","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.15636","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"arxiv_version","alias_value":"2211.15636v1","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.15636","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_12","alias_value":"3J7VIYTDZTWI","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_16","alias_value":"3J7VIYTDZTWIPXE4","created_at":"2026-07-05T05:20:06Z"},{"alias_kind":"pith_short_8","alias_value":"3J7VIYTD","created_at":"2026-07-05T05:20:06Z"}],"graph_snapshots":[{"event_id":"sha256:e3efcdbf9b78265dca5e59ab7663140c436cff10e901dc77e960a99c83083eac","target":"graph","created_at":"2026-07-05T05:20:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.15636/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove existence and regularity results for the problem of maximization of one Laplace eigenvalue with respect to metrics of same volume lying in a conformal class of a Riemannian manifold of dimension $n\\geq 3$.","authors_text":"Romain Petrides","cross_cats":["math.DG","math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-11-28T18:42:25Z","title":"Maximizing one Laplace eigenvalue on n-dimensional manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.15636","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":"sha256:33582482a3103b790ef8faf9350fa3c79acb638b431cc54e21a9c608ef9b8208","target":"record","created_at":"2026-07-05T05:20:06Z","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":"144f73b470fdffa939ebfb59ab34ffca76559accada91a1a5000c9081d61ce6b","cross_cats_sorted":["math.DG","math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-11-28T18:42:25Z","title_canon_sha256":"883c272092118e0643e3338c772a9e67ec25da097b105ff1a67a5a6571d692dd"},"schema_version":"1.0","source":{"id":"2211.15636","kind":"arxiv","version":1}},"canonical_sha256":"da7f546263ccec87dc9c4cd0ab077f26a281906335c09f3804940e10b39501ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da7f546263ccec87dc9c4cd0ab077f26a281906335c09f3804940e10b39501ad","first_computed_at":"2026-07-05T05:20:06.257216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:20:06.257216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aebUX0Vrbv01PmFOzIz5ltHW5orHp5BI8D6KKPnO4eevYPzE3gaG8IdTu/UtnYmA9oUQ5I/hd/USLTWfmHPCBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:20:06.257712Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.15636","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33582482a3103b790ef8faf9350fa3c79acb638b431cc54e21a9c608ef9b8208","sha256:e3efcdbf9b78265dca5e59ab7663140c436cff10e901dc77e960a99c83083eac"],"state_sha256":"f2e816cfa38031dc215b73c57b1f4338fc89cd718f545e8dd83497dd09eb09bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nrVHEYhEDkAuOOvYTIXSltAfxmnamyCSCPLfvNHxggIRbPehi9y3MZs4Aea9X48fI/yaIXNue1CPuabnq3lDAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T08:00:23.130139Z","bundle_sha256":"ffe31864f96654a62404d021cfa9829ceaf5c5250a8ecc05bcb188c537f27037"}}