{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WQUDRZ7BBFLBS6SWF7HYBWRJQS","short_pith_number":"pith:WQUDRZ7B","canonical_record":{"source":{"id":"2312.03504","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2023-12-06T14:01:45Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"3ff1ec7e9c6fb774b2885d7047edd7802b72df4febc6a1a5f3b4e88805d884fb","abstract_canon_sha256":"dcbb358319c775681181fbf5397ceb1c0642e3f18f110fce51577f7391a6b979"},"schema_version":"1.0"},"canonical_sha256":"b42838e7e10956197a562fcf80da298495e0b9636ec66609fa480a9498779530","source":{"kind":"arxiv","id":"2312.03504","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.03504","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"arxiv_version","alias_value":"2312.03504v2","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.03504","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"pith_short_12","alias_value":"WQUDRZ7BBFLB","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"pith_short_16","alias_value":"WQUDRZ7BBFLBS6SW","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"pith_short_8","alias_value":"WQUDRZ7B","created_at":"2026-06-19T16:10:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WQUDRZ7BBFLBS6SWF7HYBWRJQS","target":"record","payload":{"canonical_record":{"source":{"id":"2312.03504","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2023-12-06T14:01:45Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"3ff1ec7e9c6fb774b2885d7047edd7802b72df4febc6a1a5f3b4e88805d884fb","abstract_canon_sha256":"dcbb358319c775681181fbf5397ceb1c0642e3f18f110fce51577f7391a6b979"},"schema_version":"1.0"},"canonical_sha256":"b42838e7e10956197a562fcf80da298495e0b9636ec66609fa480a9498779530","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:27.746504Z","signature_b64":"4yAFslZ3VM9BYseWXaQGBFjU2Znf4XofxkRBPXzpLm13lzbh+LsEJIqmE4BjXyPMNJzT7sGfa9NHgZ3DzUt3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b42838e7e10956197a562fcf80da298495e0b9636ec66609fa480a9498779530","last_reissued_at":"2026-06-19T16:10:27.746115Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:27.746115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.03504","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":"2026-06-19T16:10:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3W2im2TthRrcFdqA1G49srDLS7M3MuLeZgZvBnX+JMyp+/PlVNNvC6/4iWgDYLaKce2xNSenMhvHYPJwYeQmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:01:22.091093Z"},"content_sha256":"68abbef3558ac6fb069b81b1f4abc4c7865740aa2fd245c070b1b76da19cca8f","schema_version":"1.0","event_id":"sha256:68abbef3558ac6fb069b81b1f4abc4c7865740aa2fd245c070b1b76da19cca8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WQUDRZ7BBFLBS6SWF7HYBWRJQS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three counterexamples to a conjecture of Colin de Verdi\\`ere on multiplicity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SP","authors_text":"Bram Petri, \\'Emile Gruda-Mediavilla, Mathieu Pineault, Maxime Fortier Bourque","submitted_at":"2023-12-06T14:01:45Z","abstract_excerpt":"We exhibit closed hyperbolic surfaces of genus $10$, $17$, and $37$ such that the multiplicity of the first nonzero eigenvalue of their Laplacian is larger than the maximum conjectured by Yves Colin de Verdi\\`ere in 1986. In order to determine these multiplicities, we apply the twisted Selberg trace formula to the representations induced by the isometry groups of these surfaces on corresponding triangle groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.03504","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.03504/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":"2026-06-19T16:10:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/tgy0yggo49dRn/C7S3Z74Qu9IXYKt2eHvOMlkUoUxzs61Cluh2aLzxs7mpZfXnvf3IHk7xNLQ/Nov20netAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T10:01:22.091483Z"},"content_sha256":"57f2a9b61f65147dd243f0d0a4d4c865c89540eaf154fcfda9add398cbe0e9c5","schema_version":"1.0","event_id":"sha256:57f2a9b61f65147dd243f0d0a4d4c865c89540eaf154fcfda9add398cbe0e9c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQUDRZ7BBFLBS6SWF7HYBWRJQS/bundle.json","state_url":"https://pith.science/pith/WQUDRZ7BBFLBS6SWF7HYBWRJQS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQUDRZ7BBFLBS6SWF7HYBWRJQS/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":"2026-07-03T10:01:22Z","links":{"resolver":"https://pith.science/pith/WQUDRZ7BBFLBS6SWF7HYBWRJQS","bundle":"https://pith.science/pith/WQUDRZ7BBFLBS6SWF7HYBWRJQS/bundle.json","state":"https://pith.science/pith/WQUDRZ7BBFLBS6SWF7HYBWRJQS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQUDRZ7BBFLBS6SWF7HYBWRJQS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WQUDRZ7BBFLBS6SWF7HYBWRJQS","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":"dcbb358319c775681181fbf5397ceb1c0642e3f18f110fce51577f7391a6b979","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2023-12-06T14:01:45Z","title_canon_sha256":"3ff1ec7e9c6fb774b2885d7047edd7802b72df4febc6a1a5f3b4e88805d884fb"},"schema_version":"1.0","source":{"id":"2312.03504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.03504","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"arxiv_version","alias_value":"2312.03504v2","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.03504","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"pith_short_12","alias_value":"WQUDRZ7BBFLB","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"pith_short_16","alias_value":"WQUDRZ7BBFLBS6SW","created_at":"2026-06-19T16:10:27Z"},{"alias_kind":"pith_short_8","alias_value":"WQUDRZ7B","created_at":"2026-06-19T16:10:27Z"}],"graph_snapshots":[{"event_id":"sha256:57f2a9b61f65147dd243f0d0a4d4c865c89540eaf154fcfda9add398cbe0e9c5","target":"graph","created_at":"2026-06-19T16:10:27Z","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/2312.03504/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We exhibit closed hyperbolic surfaces of genus $10$, $17$, and $37$ such that the multiplicity of the first nonzero eigenvalue of their Laplacian is larger than the maximum conjectured by Yves Colin de Verdi\\`ere in 1986. In order to determine these multiplicities, we apply the twisted Selberg trace formula to the representations induced by the isometry groups of these surfaces on corresponding triangle groups.","authors_text":"Bram Petri, \\'Emile Gruda-Mediavilla, Mathieu Pineault, Maxime Fortier Bourque","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2023-12-06T14:01:45Z","title":"Three counterexamples to a conjecture of Colin de Verdi\\`ere on multiplicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.03504","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":"sha256:68abbef3558ac6fb069b81b1f4abc4c7865740aa2fd245c070b1b76da19cca8f","target":"record","created_at":"2026-06-19T16:10:27Z","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":"dcbb358319c775681181fbf5397ceb1c0642e3f18f110fce51577f7391a6b979","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2023-12-06T14:01:45Z","title_canon_sha256":"3ff1ec7e9c6fb774b2885d7047edd7802b72df4febc6a1a5f3b4e88805d884fb"},"schema_version":"1.0","source":{"id":"2312.03504","kind":"arxiv","version":2}},"canonical_sha256":"b42838e7e10956197a562fcf80da298495e0b9636ec66609fa480a9498779530","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b42838e7e10956197a562fcf80da298495e0b9636ec66609fa480a9498779530","first_computed_at":"2026-06-19T16:10:27.746115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:27.746115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4yAFslZ3VM9BYseWXaQGBFjU2Znf4XofxkRBPXzpLm13lzbh+LsEJIqmE4BjXyPMNJzT7sGfa9NHgZ3DzUt3CQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:27.746504Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.03504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68abbef3558ac6fb069b81b1f4abc4c7865740aa2fd245c070b1b76da19cca8f","sha256:57f2a9b61f65147dd243f0d0a4d4c865c89540eaf154fcfda9add398cbe0e9c5"],"state_sha256":"42a300d4478bda97a65b7519d5de55301978e2147a9f98aad207383ee4d35d43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TFGjdM9ynCtmrTs6nPfwUzHWkzl1340mmNwKd9a8sJ/HWUrjQtDsQLzhsLtiOljbZ0gSOGgFWzWvpFgQJE5sDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T10:01:22.093425Z","bundle_sha256":"bc8f9435168ae9a8d7cb0e8170d649f559a5d7f0c45b3f1f3e792d325972ade3"}}