{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OC4WQ25ITXL4POZVS65WQQRUSF","short_pith_number":"pith:OC4WQ25I","canonical_record":{"source":{"id":"2603.11022","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-11T17:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"afd5c8e847a243f4a2190c5326b51675c0e992715e5803872d0a1a2f051fd00b","abstract_canon_sha256":"9e07b4358f304defd12172e11e3ac4dd6a42bdfe4dd470566af2354b1f8e09c4"},"schema_version":"1.0"},"canonical_sha256":"70b9686ba89dd7c7bb3597bb684234915ca437a65d26cc57f13605cdbfe44117","source":{"kind":"arxiv","id":"2603.11022","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.11022","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"2603.11022v2","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.11022","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"OC4WQ25ITXL4","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"pith_short_16","alias_value":"OC4WQ25ITXL4POZV","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"pith_short_8","alias_value":"OC4WQ25I","created_at":"2026-06-02T01:04:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OC4WQ25ITXL4POZVS65WQQRUSF","target":"record","payload":{"canonical_record":{"source":{"id":"2603.11022","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-11T17:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"afd5c8e847a243f4a2190c5326b51675c0e992715e5803872d0a1a2f051fd00b","abstract_canon_sha256":"9e07b4358f304defd12172e11e3ac4dd6a42bdfe4dd470566af2354b1f8e09c4"},"schema_version":"1.0"},"canonical_sha256":"70b9686ba89dd7c7bb3597bb684234915ca437a65d26cc57f13605cdbfe44117","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:16.056976Z","signature_b64":"wjABA87qtybDNWPOF3LPOhh58Oln+QnbbPREfNcykOP2Oov67zDt5KhdbvzHsGB9T5tMPA+EsDLm2+iCLndABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70b9686ba89dd7c7bb3597bb684234915ca437a65d26cc57f13605cdbfe44117","last_reissued_at":"2026-06-02T01:04:16.056511Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:16.056511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.11022","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":"2026-06-02T01:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLCNPtpJ8gZ3MqN3+73mWjl1ofWk4AHqPUgO0iEJXuyqslFJtW1EwcPiRnP5CIEAYqeluC4Jyw/DJceNFHLkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T23:28:43.909502Z"},"content_sha256":"ad9b5a092f89dd861e023701b72813e59a5c9a0085f88c94754f13a624d24480","schema_version":"1.0","event_id":"sha256:ad9b5a092f89dd861e023701b72813e59a5c9a0085f88c94754f13a624d24480"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OC4WQ25ITXL4POZVS65WQQRUSF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nondegenerate neck pinches along the mean curvature flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"G\\'abor Sz\\'ekelyhidi","submitted_at":"2026-03-11T17:48:48Z","abstract_excerpt":"We show that for generic smooth compact initial surfaces the mean curvature flow in $\\mathbb{R}^3$ has spherical or nondegenerate neck pinch singularities at the first singular time. In particular the singularities at the first singular time are isolated in spacetime. As an application we give a new approach to constructing a mean curvature flow with surgery for smooth compact initial surfaces in $\\mathbb{R}^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.11022","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/2603.11022/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":"2026-06-02T01:04:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TAexvHXFwOl/6tqkB4GZZxhrl6zZw/vzqgR9NV2D36Xf3SZ3RYbnU4SSjm9+U1qb5cuQ+i5OimnNTJ5aqMbYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T23:28:43.909881Z"},"content_sha256":"128f4e6fb86f8d9e8af31d24a8ce795d797e72524ace58c9511f43dea7c77fe2","schema_version":"1.0","event_id":"sha256:128f4e6fb86f8d9e8af31d24a8ce795d797e72524ace58c9511f43dea7c77fe2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OC4WQ25ITXL4POZVS65WQQRUSF/bundle.json","state_url":"https://pith.science/pith/OC4WQ25ITXL4POZVS65WQQRUSF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OC4WQ25ITXL4POZVS65WQQRUSF/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":"2026-07-02T23:28:43Z","links":{"resolver":"https://pith.science/pith/OC4WQ25ITXL4POZVS65WQQRUSF","bundle":"https://pith.science/pith/OC4WQ25ITXL4POZVS65WQQRUSF/bundle.json","state":"https://pith.science/pith/OC4WQ25ITXL4POZVS65WQQRUSF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OC4WQ25ITXL4POZVS65WQQRUSF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OC4WQ25ITXL4POZVS65WQQRUSF","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":"9e07b4358f304defd12172e11e3ac4dd6a42bdfe4dd470566af2354b1f8e09c4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-11T17:48:48Z","title_canon_sha256":"afd5c8e847a243f4a2190c5326b51675c0e992715e5803872d0a1a2f051fd00b"},"schema_version":"1.0","source":{"id":"2603.11022","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.11022","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"2603.11022v2","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.11022","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"OC4WQ25ITXL4","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"pith_short_16","alias_value":"OC4WQ25ITXL4POZV","created_at":"2026-06-02T01:04:16Z"},{"alias_kind":"pith_short_8","alias_value":"OC4WQ25I","created_at":"2026-06-02T01:04:16Z"}],"graph_snapshots":[{"event_id":"sha256:128f4e6fb86f8d9e8af31d24a8ce795d797e72524ace58c9511f43dea7c77fe2","target":"graph","created_at":"2026-06-02T01:04:16Z","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/2603.11022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that for generic smooth compact initial surfaces the mean curvature flow in $\\mathbb{R}^3$ has spherical or nondegenerate neck pinch singularities at the first singular time. In particular the singularities at the first singular time are isolated in spacetime. As an application we give a new approach to constructing a mean curvature flow with surgery for smooth compact initial surfaces in $\\mathbb{R}^3$.","authors_text":"G\\'abor Sz\\'ekelyhidi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-11T17:48:48Z","title":"Nondegenerate neck pinches along the mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.11022","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:ad9b5a092f89dd861e023701b72813e59a5c9a0085f88c94754f13a624d24480","target":"record","created_at":"2026-06-02T01:04:16Z","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":"9e07b4358f304defd12172e11e3ac4dd6a42bdfe4dd470566af2354b1f8e09c4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-03-11T17:48:48Z","title_canon_sha256":"afd5c8e847a243f4a2190c5326b51675c0e992715e5803872d0a1a2f051fd00b"},"schema_version":"1.0","source":{"id":"2603.11022","kind":"arxiv","version":2}},"canonical_sha256":"70b9686ba89dd7c7bb3597bb684234915ca437a65d26cc57f13605cdbfe44117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70b9686ba89dd7c7bb3597bb684234915ca437a65d26cc57f13605cdbfe44117","first_computed_at":"2026-06-02T01:04:16.056511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:04:16.056511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjABA87qtybDNWPOF3LPOhh58Oln+QnbbPREfNcykOP2Oov67zDt5KhdbvzHsGB9T5tMPA+EsDLm2+iCLndABA==","signature_status":"signed_v1","signed_at":"2026-06-02T01:04:16.056976Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.11022","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad9b5a092f89dd861e023701b72813e59a5c9a0085f88c94754f13a624d24480","sha256:128f4e6fb86f8d9e8af31d24a8ce795d797e72524ace58c9511f43dea7c77fe2"],"state_sha256":"d44beb349164348f4916ccca81ab6583efdc3b77b66ed6b914347fe83322bade"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Np5z93pwiEevqG0GnDUfDi5KXCV8I4MixNQaI20LihzzieFmXBjs2QyHVml/jx9ierLtC2rU+TOVErhX9EdyCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T23:28:43.911866Z","bundle_sha256":"f10a99d5459b833d3cbb4ad35bd47e5a294c20f8b81e2d8575f30f786ba52985"}}