{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:DPTHX6JAJ6SVXRKG5XAE3A4NV4","short_pith_number":"pith:DPTHX6JA","canonical_record":{"source":{"id":"2509.00860","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T14:06:52Z","cross_cats_sorted":[],"title_canon_sha256":"03df59f08108ff5098873264bcea353dfc73fa76c420ee183ae817755f5da18c","abstract_canon_sha256":"9696660a8c3f109d3dc3adb8c8c5bf7dfcff3582847b51ecd1a9888ea307b177"},"schema_version":"1.0"},"canonical_sha256":"1be67bf9204fa55bc546edc04d838daf0e2f7d743ac8b7fbfe2fcf5bed922a56","source":{"kind":"arxiv","id":"2509.00860","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.00860","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.00860v3","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.00860","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"DPTHX6JAJ6SV","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"pith_short_16","alias_value":"DPTHX6JAJ6SVXRKG","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"pith_short_8","alias_value":"DPTHX6JA","created_at":"2026-05-20T00:04:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:DPTHX6JAJ6SVXRKG5XAE3A4NV4","target":"record","payload":{"canonical_record":{"source":{"id":"2509.00860","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T14:06:52Z","cross_cats_sorted":[],"title_canon_sha256":"03df59f08108ff5098873264bcea353dfc73fa76c420ee183ae817755f5da18c","abstract_canon_sha256":"9696660a8c3f109d3dc3adb8c8c5bf7dfcff3582847b51ecd1a9888ea307b177"},"schema_version":"1.0"},"canonical_sha256":"1be67bf9204fa55bc546edc04d838daf0e2f7d743ac8b7fbfe2fcf5bed922a56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:12.860915Z","signature_b64":"XkSZnXcjR8yoicXJ+i0xqfX/kuG361xwoVtKXEuEfPceBaev4D5HLmVCyoEguPxipGnHKVOLFkn5s7j1eD8SAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1be67bf9204fa55bc546edc04d838daf0e2f7d743ac8b7fbfe2fcf5bed922a56","last_reissued_at":"2026-05-20T00:04:12.860067Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:12.860067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.00860","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":"2026-05-20T00:04:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRjTreCrJdVD+lvG1LzIBXW6iclUPAJu9ENMivMReAkF5MOS+Ojz1O8KVKlaDvj2BVBwP9jo/zTkJdwJiadbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:36:42.515659Z"},"content_sha256":"90e9d653b12d192b6562e3d065c044ce4d0217274233bd3585b3fdb62f4767e6","schema_version":"1.0","event_id":"sha256:90e9d653b12d192b6562e3d065c044ce4d0217274233bd3585b3fdb62f4767e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:DPTHX6JAJ6SVXRKG5XAE3A4NV4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cuspidal edges on focal surfaces of regular surfaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Keisuke Teramoto","submitted_at":"2025-08-31T14:06:52Z","abstract_excerpt":"We investigate geometric invariants of cuspidal edges on focal surfaces of regular surface. In particular, we shall clarify the sign of the singular curvature at a cuspidal edge on a focal surface using singularities of parallel surface of a given surface satisfying certain conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00860","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.00860/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":"2026-05-20T00:04:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"24uHFvN6udL3Gn5rlfX2G3ie8S/BYUclbBRawpuoK6YYVhfof56M2pGQlRO2PkQXdqm+RVe8sv9onEL9eaXHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:36:42.516476Z"},"content_sha256":"1bf0cd0b5966eb4af49bb9c26af40d83eab5d0b308c2709b4775cd092d7bad31","schema_version":"1.0","event_id":"sha256:1bf0cd0b5966eb4af49bb9c26af40d83eab5d0b308c2709b4775cd092d7bad31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPTHX6JAJ6SVXRKG5XAE3A4NV4/bundle.json","state_url":"https://pith.science/pith/DPTHX6JAJ6SVXRKG5XAE3A4NV4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPTHX6JAJ6SVXRKG5XAE3A4NV4/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":"2026-05-31T22:36:42Z","links":{"resolver":"https://pith.science/pith/DPTHX6JAJ6SVXRKG5XAE3A4NV4","bundle":"https://pith.science/pith/DPTHX6JAJ6SVXRKG5XAE3A4NV4/bundle.json","state":"https://pith.science/pith/DPTHX6JAJ6SVXRKG5XAE3A4NV4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPTHX6JAJ6SVXRKG5XAE3A4NV4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DPTHX6JAJ6SVXRKG5XAE3A4NV4","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":"9696660a8c3f109d3dc3adb8c8c5bf7dfcff3582847b51ecd1a9888ea307b177","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T14:06:52Z","title_canon_sha256":"03df59f08108ff5098873264bcea353dfc73fa76c420ee183ae817755f5da18c"},"schema_version":"1.0","source":{"id":"2509.00860","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.00860","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.00860v3","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.00860","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"pith_short_12","alias_value":"DPTHX6JAJ6SV","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"pith_short_16","alias_value":"DPTHX6JAJ6SVXRKG","created_at":"2026-05-20T00:04:12Z"},{"alias_kind":"pith_short_8","alias_value":"DPTHX6JA","created_at":"2026-05-20T00:04:12Z"}],"graph_snapshots":[{"event_id":"sha256:1bf0cd0b5966eb4af49bb9c26af40d83eab5d0b308c2709b4775cd092d7bad31","target":"graph","created_at":"2026-05-20T00:04:12Z","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/2509.00860/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate geometric invariants of cuspidal edges on focal surfaces of regular surface. In particular, we shall clarify the sign of the singular curvature at a cuspidal edge on a focal surface using singularities of parallel surface of a given surface satisfying certain conditions.","authors_text":"Keisuke Teramoto","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T14:06:52Z","title":"Cuspidal edges on focal surfaces of regular surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00860","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":"sha256:90e9d653b12d192b6562e3d065c044ce4d0217274233bd3585b3fdb62f4767e6","target":"record","created_at":"2026-05-20T00:04:12Z","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":"9696660a8c3f109d3dc3adb8c8c5bf7dfcff3582847b51ecd1a9888ea307b177","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-08-31T14:06:52Z","title_canon_sha256":"03df59f08108ff5098873264bcea353dfc73fa76c420ee183ae817755f5da18c"},"schema_version":"1.0","source":{"id":"2509.00860","kind":"arxiv","version":3}},"canonical_sha256":"1be67bf9204fa55bc546edc04d838daf0e2f7d743ac8b7fbfe2fcf5bed922a56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1be67bf9204fa55bc546edc04d838daf0e2f7d743ac8b7fbfe2fcf5bed922a56","first_computed_at":"2026-05-20T00:04:12.860067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:12.860067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XkSZnXcjR8yoicXJ+i0xqfX/kuG361xwoVtKXEuEfPceBaev4D5HLmVCyoEguPxipGnHKVOLFkn5s7j1eD8SAg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:12.860915Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.00860","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e9d653b12d192b6562e3d065c044ce4d0217274233bd3585b3fdb62f4767e6","sha256:1bf0cd0b5966eb4af49bb9c26af40d83eab5d0b308c2709b4775cd092d7bad31"],"state_sha256":"f5ab3cb4ceb8c134e5d54ce1c9cddbb447af1a3a0de6611a1e88601604610bdf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbA40OeoHR7CFH5YJyy8bYXo32a+xxUh2czJGXwyyhwIpGG+9kBGfY2GTmLmTHGua4zoaYgyPO2aBgmx9Y21BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:36:42.520835Z","bundle_sha256":"6d15b9fcbb7a338a114d650a9d0d79b737a3ae143675e354368980eb4067cfa3"}}