{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T5PRBI6WYC2EJ5JF2IWSHBZVXN","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":"84952c63ae509c44a7df62f4643feb77932c931c1f311a5f9d4fda11b8387c10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T06:34:22Z","title_canon_sha256":"1b794ac56e4c7be14a6da180c99ada5f7aa23ebb569f3d23b4d9934dcf590103"},"schema_version":"1.0","source":{"id":"1908.06609","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06609","created_at":"2026-07-05T00:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06609v3","created_at":"2026-07-05T00:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06609","created_at":"2026-07-05T00:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"T5PRBI6WYC2E","created_at":"2026-07-05T00:58:23Z"},{"alias_kind":"pith_short_16","alias_value":"T5PRBI6WYC2EJ5JF","created_at":"2026-07-05T00:58:23Z"},{"alias_kind":"pith_short_8","alias_value":"T5PRBI6W","created_at":"2026-07-05T00:58:23Z"}],"graph_snapshots":[{"event_id":"sha256:1379ab2aa928968f3cf06fec2be591cf1336d8fbc11e35571ca811a3f5beb9a4","target":"graph","created_at":"2026-07-05T00:58:23Z","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/1908.06609/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Letting $C$ be a compact $C^\\omega$-curve embedded in $\\boldsymbol R^3$ ($C^\\omega$ means real analyticity), we consider a $C^\\omega$-cuspidal edge $f$ along $C$. When $C$ is non-closed, in the authors' previous works, the local existence of three distinct cuspidal edges along $C$ whose first fundamental forms coincide with that of $f$ was shown, under a certain reasonable assumption on $f$. In this paper, if $C$ is closed, that is, $C$ is a knot, we show that there exist infinitely many cuspidal edges along $C$ having the same first fundamental form as that of $f$ such that their images are n","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":"2019-08-19T06:34:22Z","title":"Cuspidal edges with the same first fundamental forms along a knot"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06609","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":"sha256:4eb822baced44dd9b10ec74d611497be7f5907bba389c7da287ae2ee0a54086e","target":"record","created_at":"2026-07-05T00:58:23Z","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":"84952c63ae509c44a7df62f4643feb77932c931c1f311a5f9d4fda11b8387c10","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-08-19T06:34:22Z","title_canon_sha256":"1b794ac56e4c7be14a6da180c99ada5f7aa23ebb569f3d23b4d9934dcf590103"},"schema_version":"1.0","source":{"id":"1908.06609","kind":"arxiv","version":3}},"canonical_sha256":"9f5f10a3d6c0b444f525d22d238735bb74acb4f54557059fe130e0300a7b1836","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f5f10a3d6c0b444f525d22d238735bb74acb4f54557059fe130e0300a7b1836","first_computed_at":"2026-07-05T00:58:23.999369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:58:23.999369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CLvIq1U1jJWS3ZyHGLxbLKV5hUZkzTrfQ1/HQdYsX8fqLRCZqD6a+jejXHj2viPa+GUPXzKb0r6/eeYpuJTCDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:58:23.999786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06609","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eb822baced44dd9b10ec74d611497be7f5907bba389c7da287ae2ee0a54086e","sha256:1379ab2aa928968f3cf06fec2be591cf1336d8fbc11e35571ca811a3f5beb9a4"],"state_sha256":"18de9869383fd92caa65357bac82adfe95cf3ff0b7ac209dc04e310d2301f7d0"}