{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:TDFGIPIE5BTY7PHCBBIFXUYCFM","short_pith_number":"pith:TDFGIPIE","canonical_record":{"source":{"id":"1906.02556","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-06T12:53:29Z","cross_cats_sorted":[],"title_canon_sha256":"c4a27c103a74eca49917eca9cb0b845d5e0aa835179cbe72189a6b42a76c3a87","abstract_canon_sha256":"9c95d3759477bafc3ce055cfa471a4648a4ecfaeb267f3fc89283eb191f56c5e"},"schema_version":"1.0"},"canonical_sha256":"98ca643d04e8678fbce208505bd3022b2bc317be28d020b1be6f43dd7bd053aa","source":{"kind":"arxiv","id":"1906.02556","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.02556","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1906.02556v5","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02556","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"TDFGIPIE5BTY","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"pith_short_16","alias_value":"TDFGIPIE5BTY7PHC","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"pith_short_8","alias_value":"TDFGIPIE","created_at":"2026-07-05T01:23:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:TDFGIPIE5BTY7PHCBBIFXUYCFM","target":"record","payload":{"canonical_record":{"source":{"id":"1906.02556","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-06T12:53:29Z","cross_cats_sorted":[],"title_canon_sha256":"c4a27c103a74eca49917eca9cb0b845d5e0aa835179cbe72189a6b42a76c3a87","abstract_canon_sha256":"9c95d3759477bafc3ce055cfa471a4648a4ecfaeb267f3fc89283eb191f56c5e"},"schema_version":"1.0"},"canonical_sha256":"98ca643d04e8678fbce208505bd3022b2bc317be28d020b1be6f43dd7bd053aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:23:08.468069Z","signature_b64":"uBjboJ6SiMHUQuwq+GsIEymkX/arVBZAloxCRzRmLRFvpItn9kGi3i/lFWVu/WsuBdVUdu+ppT24OnVj25XKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98ca643d04e8678fbce208505bd3022b2bc317be28d020b1be6f43dd7bd053aa","last_reissued_at":"2026-07-05T01:23:08.467652Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:23:08.467652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.02556","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zPQmfYvLjxUFVmzCPB73+xkKTBl+eu5+QEkR0QApuRr2E8jME1mPOeJp38fk/+LQRk9/4EnOx+UpPQA0tlV2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:05:44.482410Z"},"content_sha256":"022afdc7eb164cfd6341d8ffa8301d34b50396c99aa724380abd741a24f54c96","schema_version":"1.0","event_id":"sha256:022afdc7eb164cfd6341d8ffa8301d34b50396c99aa724380abd741a24f54c96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:TDFGIPIE5BTY7PHCBBIFXUYCFM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duality on generalized cuspidal edges preserving singular set images and first fundamental forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Atsufumi Honda, Kentaro Saji, Kosuke Naokawa, Kotaro Yamada, Masaaki Umehara","submitted_at":"2019-06-06T12:53:29Z","abstract_excerpt":"In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space $\\boldsymbol R^3$ preserving their singular set images and first fundamental forms, was given. Here, we call this an `isometric duality'. When the singular set image has no symmetries and does not lie in a plane, the dual cuspidal edge is not congruent to the original one. In this paper, we show that this duality extends to generalized cuspidal edges in $\\boldsymbol R^3$, including cuspidal cross caps, and $5/2$-cuspidal edges. Moreover, we give several new geometr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02556","kind":"arxiv","version":5},"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/1906.02556/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":"2026-07-05T01:23:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mmbz3LrGw38+D8pyTjV9jUOorDZP4fBCoUv3QzFBVAqjk4l34AMJ6NPBiSgeylMyDuJqU5poIBPbvHLGzIVYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:05:44.482961Z"},"content_sha256":"ace2f30b1a68202938721421eed182c1dfdffb7891cb159b0ffcf100be390f7f","schema_version":"1.0","event_id":"sha256:ace2f30b1a68202938721421eed182c1dfdffb7891cb159b0ffcf100be390f7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TDFGIPIE5BTY7PHCBBIFXUYCFM/bundle.json","state_url":"https://pith.science/pith/TDFGIPIE5BTY7PHCBBIFXUYCFM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TDFGIPIE5BTY7PHCBBIFXUYCFM/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":"2026-08-16T13:05:44Z","links":{"resolver":"https://pith.science/pith/TDFGIPIE5BTY7PHCBBIFXUYCFM","bundle":"https://pith.science/pith/TDFGIPIE5BTY7PHCBBIFXUYCFM/bundle.json","state":"https://pith.science/pith/TDFGIPIE5BTY7PHCBBIFXUYCFM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TDFGIPIE5BTY7PHCBBIFXUYCFM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TDFGIPIE5BTY7PHCBBIFXUYCFM","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":"9c95d3759477bafc3ce055cfa471a4648a4ecfaeb267f3fc89283eb191f56c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-06T12:53:29Z","title_canon_sha256":"c4a27c103a74eca49917eca9cb0b845d5e0aa835179cbe72189a6b42a76c3a87"},"schema_version":"1.0","source":{"id":"1906.02556","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.02556","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"arxiv_version","alias_value":"1906.02556v5","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.02556","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"pith_short_12","alias_value":"TDFGIPIE5BTY","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"pith_short_16","alias_value":"TDFGIPIE5BTY7PHC","created_at":"2026-07-05T01:23:08Z"},{"alias_kind":"pith_short_8","alias_value":"TDFGIPIE","created_at":"2026-07-05T01:23:08Z"}],"graph_snapshots":[{"event_id":"sha256:ace2f30b1a68202938721421eed182c1dfdffb7891cb159b0ffcf100be390f7f","target":"graph","created_at":"2026-07-05T01:23:08Z","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/1906.02556/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the second, fourth and fifth authors' previous work, a duality on generic real analytic cuspidal edges in the Euclidean 3-space $\\boldsymbol R^3$ preserving their singular set images and first fundamental forms, was given. Here, we call this an `isometric duality'. When the singular set image has no symmetries and does not lie in a plane, the dual cuspidal edge is not congruent to the original one. In this paper, we show that this duality extends to generalized cuspidal edges in $\\boldsymbol R^3$, including cuspidal cross caps, and $5/2$-cuspidal edges. Moreover, we give several new geometr","authors_text":"Atsufumi Honda, Kentaro Saji, Kosuke Naokawa, Kotaro Yamada, Masaaki Umehara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-06T12:53:29Z","title":"Duality on generalized cuspidal edges preserving singular set images and first fundamental forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.02556","kind":"arxiv","version":5},"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":"sha256:022afdc7eb164cfd6341d8ffa8301d34b50396c99aa724380abd741a24f54c96","target":"record","created_at":"2026-07-05T01:23:08Z","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":"9c95d3759477bafc3ce055cfa471a4648a4ecfaeb267f3fc89283eb191f56c5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-06-06T12:53:29Z","title_canon_sha256":"c4a27c103a74eca49917eca9cb0b845d5e0aa835179cbe72189a6b42a76c3a87"},"schema_version":"1.0","source":{"id":"1906.02556","kind":"arxiv","version":5}},"canonical_sha256":"98ca643d04e8678fbce208505bd3022b2bc317be28d020b1be6f43dd7bd053aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98ca643d04e8678fbce208505bd3022b2bc317be28d020b1be6f43dd7bd053aa","first_computed_at":"2026-07-05T01:23:08.467652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:23:08.467652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uBjboJ6SiMHUQuwq+GsIEymkX/arVBZAloxCRzRmLRFvpItn9kGi3i/lFWVu/WsuBdVUdu+ppT24OnVj25XKDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:23:08.468069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.02556","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:022afdc7eb164cfd6341d8ffa8301d34b50396c99aa724380abd741a24f54c96","sha256:ace2f30b1a68202938721421eed182c1dfdffb7891cb159b0ffcf100be390f7f"],"state_sha256":"26b692c120d856168e8ac4d2979c4764d7923afb89293f0f6a9d1a653777b672"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2e6YvUs0EXbDISGfgPDKuRRNM1RZEquEEyWEYDyHUGZyatyme0uN/g41Y/M4EnOR6S4OBJYo/Zzkn5ZCGOZvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:05:44.488255Z","bundle_sha256":"58aacfe44313b6dca665dbb6d358e617f7157c1473e520987dcdc801538812fb"}}