{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4YG32T2BD3Y7AIOGUIF23QZTTK","short_pith_number":"pith:4YG32T2B","canonical_record":{"source":{"id":"2608.01611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-03T02:36:27Z","cross_cats_sorted":["math-ph","math.AP","math.MP","math.SP"],"title_canon_sha256":"4fd39f28cdedf00e9411f862e8372c296618655fdc39dd1274c8b3ef7d4712cd","abstract_canon_sha256":"3f92d167bd831a84281a739bbd4a6ac78f879361a57f5c1d11cf1d767838d371"},"schema_version":"1.0"},"canonical_sha256":"e60dbd4f411ef1f021c6a20badc3339abb2dab67138b55b4d094c4d500079a6b","source":{"kind":"arxiv","id":"2608.01611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01611","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01611v1","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01611","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"4YG32T2BD3Y7","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"4YG32T2BD3Y7AIOG","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"4YG32T2B","created_at":"2026-08-04T02:06:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4YG32T2BD3Y7AIOGUIF23QZTTK","target":"record","payload":{"canonical_record":{"source":{"id":"2608.01611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-03T02:36:27Z","cross_cats_sorted":["math-ph","math.AP","math.MP","math.SP"],"title_canon_sha256":"4fd39f28cdedf00e9411f862e8372c296618655fdc39dd1274c8b3ef7d4712cd","abstract_canon_sha256":"3f92d167bd831a84281a739bbd4a6ac78f879361a57f5c1d11cf1d767838d371"},"schema_version":"1.0"},"canonical_sha256":"e60dbd4f411ef1f021c6a20badc3339abb2dab67138b55b4d094c4d500079a6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-04T02:06:07.489928Z","signature_b64":"MJhbF8+kppxGBmrlnKxtn5WDz1VrqUry1DqWvQvAWbuq2QL5GvOoLqLM7N+m+MmKMBPNeKQON5MQtywxU6iqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e60dbd4f411ef1f021c6a20badc3339abb2dab67138b55b4d094c4d500079a6b","last_reissued_at":"2026-08-04T02:06:07.488375Z","signature_status":"signed_v1","first_computed_at":"2026-08-04T02:06:07.488375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.01611","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":"2026-08-04T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1VSddj3tYobkBdMsYBJgxrP0jKOhqSAnTe9iWjZ1jBY8aMqzhQfAOEhlfymk8ITES5rnvAbRvVZsxeGw39sCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:17:41.301556Z"},"content_sha256":"7bc64f4b25aef5b5797025c515b8ac77d242f9961ef4b0deaeddc83e192fdd26","schema_version":"1.0","event_id":"sha256:7bc64f4b25aef5b5797025c515b8ac77d242f9961ef4b0deaeddc83e192fdd26"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4YG32T2BD3Y7AIOGUIF23QZTTK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral determinants of the Bolza surface and the Klein quartic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","math.SP"],"primary_cat":"math.DG","authors_text":"Victor Kalvin","submitted_at":"2026-08-03T02:36:27Z","abstract_excerpt":"We obtain closed explicit formulas for the spectral determinants of the smooth hyperbolic Bolza surface and the Klein quartic. In each case, a multiplicative relation expresses the determinant of the surface in terms of determinants of singular quotient orbifolds of genera zero and one. The elliptic factors are evaluated by applying the singular Polyakov anomaly formula to explicit Belyi maps on CM elliptic curves of discriminants -8 and -7, while the genus-zero factors are evaluated by explicit determinant formulas for constant-curvature spheres with conical singularities. The same multiplica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01611","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/2608.01611/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":"2026-08-04T02:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UQDvoN88QU7TnQ7z6v4go35s6tk/Zn1o+jSANZpv4yMKP9mLVDhiEXaioiIK+lluAITOKY2u+Zwiqy8EcSAHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:17:41.302103Z"},"content_sha256":"ea4e40e49708a17141a3e3122c79c296a3af71392706636d24d53b2fb73f646d","schema_version":"1.0","event_id":"sha256:ea4e40e49708a17141a3e3122c79c296a3af71392706636d24d53b2fb73f646d"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:4YG32T2BD3Y7AIOGUIF23QZTTK","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s11005-024-01809-9) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"L.A.TakhtajanandP.G.Zograf,Correction to: Local index theorem for orbifold Riemann surfaces, Lett. Math. Phys.114(2024), no. 3, Paper No. 60; doi:10.1007/s11005-024- 01809-9","arxiv_id":"2608.01611","detector":"doi_compliance","evidence":{"ref_index":36,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s11005-024-","reconstructed_doi":"10.1007/s11005-024-01809-9"},"severity":"advisory","ref_index":36,"audited_at":"2026-08-05T00:28:09.021092Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s11005-024-01809-9","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"a270b97ea5a2d43a0e2595fd7e305a6764e616367320e39c076bf836ef20f89c","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":17970,"payload_sha256":"09b0144c398c11f38cc04b7dc32c5d67bc64f4297120e9839abc5c671ca09d8b","signature_b64":"vb9///ejU1ni3C5em59+XOwKpIETFh6+TLXR6mrfeKfNZpEY9b3ebtIBUiyzewZLBiHubYErnSHjLP6HopvVBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-05T00:28:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GaE5gLjdtou4EJPiAvV4Z/0ZBagf85JmfBPvK6jj6A2S9mOMHnw6zvAqnCLbasmaqbo+GYOKGe3sCleQBgFnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T12:17:41.305138Z"},"content_sha256":"3c789262d8b295aa17959bf14dfeb93e1325695d4742c3e7c1fa3cf831c0e2c0","schema_version":"1.0","event_id":"sha256:3c789262d8b295aa17959bf14dfeb93e1325695d4742c3e7c1fa3cf831c0e2c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YG32T2BD3Y7AIOGUIF23QZTTK/bundle.json","state_url":"https://pith.science/pith/4YG32T2BD3Y7AIOGUIF23QZTTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YG32T2BD3Y7AIOGUIF23QZTTK/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":"2026-08-07T12:17:41Z","links":{"resolver":"https://pith.science/pith/4YG32T2BD3Y7AIOGUIF23QZTTK","bundle":"https://pith.science/pith/4YG32T2BD3Y7AIOGUIF23QZTTK/bundle.json","state":"https://pith.science/pith/4YG32T2BD3Y7AIOGUIF23QZTTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YG32T2BD3Y7AIOGUIF23QZTTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4YG32T2BD3Y7AIOGUIF23QZTTK","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3f92d167bd831a84281a739bbd4a6ac78f879361a57f5c1d11cf1d767838d371","cross_cats_sorted":["math-ph","math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-03T02:36:27Z","title_canon_sha256":"4fd39f28cdedf00e9411f862e8372c296618655fdc39dd1274c8b3ef7d4712cd"},"schema_version":"1.0","source":{"id":"2608.01611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.01611","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"2608.01611v1","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.01611","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"4YG32T2BD3Y7","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"pith_short_16","alias_value":"4YG32T2BD3Y7AIOG","created_at":"2026-08-04T02:06:07Z"},{"alias_kind":"pith_short_8","alias_value":"4YG32T2B","created_at":"2026-08-04T02:06:07Z"}],"graph_snapshots":[{"event_id":"sha256:ea4e40e49708a17141a3e3122c79c296a3af71392706636d24d53b2fb73f646d","target":"graph","created_at":"2026-08-04T02:06:07Z","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/2608.01611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We obtain closed explicit formulas for the spectral determinants of the smooth hyperbolic Bolza surface and the Klein quartic. In each case, a multiplicative relation expresses the determinant of the surface in terms of determinants of singular quotient orbifolds of genera zero and one. The elliptic factors are evaluated by applying the singular Polyakov anomaly formula to explicit Belyi maps on CM elliptic curves of discriminants -8 and -7, while the genus-zero factors are evaluated by explicit determinant formulas for constant-curvature spheres with conical singularities. The same multiplica","authors_text":"Victor Kalvin","cross_cats":["math-ph","math.AP","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-03T02:36:27Z","title":"Spectral determinants of the Bolza surface and the Klein quartic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01611","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":"sha256:7bc64f4b25aef5b5797025c515b8ac77d242f9961ef4b0deaeddc83e192fdd26","target":"record","created_at":"2026-08-04T02:06:07Z","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":"3f92d167bd831a84281a739bbd4a6ac78f879361a57f5c1d11cf1d767838d371","cross_cats_sorted":["math-ph","math.AP","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-08-03T02:36:27Z","title_canon_sha256":"4fd39f28cdedf00e9411f862e8372c296618655fdc39dd1274c8b3ef7d4712cd"},"schema_version":"1.0","source":{"id":"2608.01611","kind":"arxiv","version":1}},"canonical_sha256":"e60dbd4f411ef1f021c6a20badc3339abb2dab67138b55b4d094c4d500079a6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e60dbd4f411ef1f021c6a20badc3339abb2dab67138b55b4d094c4d500079a6b","first_computed_at":"2026-08-04T02:06:07.488375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-04T02:06:07.488375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MJhbF8+kppxGBmrlnKxtn5WDz1VrqUry1DqWvQvAWbuq2QL5GvOoLqLM7N+m+MmKMBPNeKQON5MQtywxU6iqBg==","signature_status":"signed_v1","signed_at":"2026-08-04T02:06:07.489928Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.01611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bc64f4b25aef5b5797025c515b8ac77d242f9961ef4b0deaeddc83e192fdd26","sha256:ea4e40e49708a17141a3e3122c79c296a3af71392706636d24d53b2fb73f646d","sha256:3c789262d8b295aa17959bf14dfeb93e1325695d4742c3e7c1fa3cf831c0e2c0"],"state_sha256":"caffd858b44551b11e2caa29707c3411f0b307b4ff896789a3d6988f62b326a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4zgiOItqsJzPCK0r8AyUpESbBu/ECjvrGdaN7S3r7d2uQ2/xRqn16oGM0vp4ra87Hyg9ImRLwVg/rTjFsd5gCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T12:17:41.307414Z","bundle_sha256":"1f9a10ee7640b90e12032163a24315222e7531d2fd15b84d1ba6241581d0bb31"}}