{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KEXK5JVPPWUGMCBQFSMV5N2QPM","short_pith_number":"pith:KEXK5JVP","canonical_record":{"source":{"id":"2510.00576","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-10-01T06:56:40Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"f7c6e163ea0f019269183ec75317a9bd6d94908f63be36765c7e267074fb3908","abstract_canon_sha256":"7b934e0577452cb1736fd9841533fd119379c4de3f35b8e250d17c9812a07df0"},"schema_version":"1.0"},"canonical_sha256":"512eaea6af7da86608302c995eb7507b3054c9c19b6d5b1124304d04136d6e52","source":{"kind":"arxiv","id":"2510.00576","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.00576","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"2510.00576v3","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.00576","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"KEXK5JVPPWUG","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"KEXK5JVPPWUGMCBQ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"KEXK5JVP","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KEXK5JVPPWUGMCBQFSMV5N2QPM","target":"record","payload":{"canonical_record":{"source":{"id":"2510.00576","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-10-01T06:56:40Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"f7c6e163ea0f019269183ec75317a9bd6d94908f63be36765c7e267074fb3908","abstract_canon_sha256":"7b934e0577452cb1736fd9841533fd119379c4de3f35b8e250d17c9812a07df0"},"schema_version":"1.0"},"canonical_sha256":"512eaea6af7da86608302c995eb7507b3054c9c19b6d5b1124304d04136d6e52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:12.295913Z","signature_b64":"blof4MRTsdUcHAujZutgt9dCxoIon2SUvRskrvWz8Ki7CCKbzvt6VTNepTzrhhfjs/zotUqFPW5TsHYjyhKfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"512eaea6af7da86608302c995eb7507b3054c9c19b6d5b1124304d04136d6e52","last_reissued_at":"2026-05-18T02:45:12.295245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:12.295245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.00576","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":"2026-05-18T02:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v9IIN+8tYspS9QygsvhyTd5xoOWKZ3Q0AugNb+nw5l3WwferrlzYxb/eunf9oFOs1XO5OjPoh68iTpjUgNePBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T09:08:07.130559Z"},"content_sha256":"5690432397277ebed1f61aefb39b2420bba869049081b14aaa3f50efe4bc684a","schema_version":"1.0","event_id":"sha256:5690432397277ebed1f61aefb39b2420bba869049081b14aaa3f50efe4bc684a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KEXK5JVPPWUGMCBQFSMV5N2QPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A transversality theorem for multiple-point crossings under generic linear perturbations with Hausdorff measure estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.GT","authors_text":"Shunsuke Ichiki","submitted_at":"2025-10-01T06:56:40Z","abstract_excerpt":"We establish a transversality theorem for multiple-point crossings under generic linear perturbations with explicit Hausdorff measure estimates for the exceptional parameter set, and hence explicit upper bounds on its Hausdorff dimension. This strengthens our earlier result, which showed only that the exceptional parameter set has Lebesgue measure zero. As applications, we obtain results on normal crossings, injectivity, and embeddings under generic linear perturbations. The embedding result yields a refinement of Mather's stability theorem for generic projections when the target dimension is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.00576","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":""},"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":"2026-05-18T02:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IgIDuZ1ZnK2edhhq9lJK36CX0oa8fXQ72Md9LWU0VuSru9Ur8Y7tdJ/dxaz91O9tOv/a+wj4UMtfjx4fXDLqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T09:08:07.131112Z"},"content_sha256":"e696bc905c4fa17a6147b5e61e86d1f4196e93d4097dc2156d8f7699617001ae","schema_version":"1.0","event_id":"sha256:e696bc905c4fa17a6147b5e61e86d1f4196e93d4097dc2156d8f7699617001ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEXK5JVPPWUGMCBQFSMV5N2QPM/bundle.json","state_url":"https://pith.science/pith/KEXK5JVPPWUGMCBQFSMV5N2QPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEXK5JVPPWUGMCBQFSMV5N2QPM/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":"2026-05-21T09:08:07Z","links":{"resolver":"https://pith.science/pith/KEXK5JVPPWUGMCBQFSMV5N2QPM","bundle":"https://pith.science/pith/KEXK5JVPPWUGMCBQFSMV5N2QPM/bundle.json","state":"https://pith.science/pith/KEXK5JVPPWUGMCBQFSMV5N2QPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEXK5JVPPWUGMCBQFSMV5N2QPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KEXK5JVPPWUGMCBQFSMV5N2QPM","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":"7b934e0577452cb1736fd9841533fd119379c4de3f35b8e250d17c9812a07df0","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-10-01T06:56:40Z","title_canon_sha256":"f7c6e163ea0f019269183ec75317a9bd6d94908f63be36765c7e267074fb3908"},"schema_version":"1.0","source":{"id":"2510.00576","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.00576","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"2510.00576v3","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.00576","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"KEXK5JVPPWUG","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"KEXK5JVPPWUGMCBQ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"KEXK5JVP","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:e696bc905c4fa17a6147b5e61e86d1f4196e93d4097dc2156d8f7699617001ae","target":"graph","created_at":"2026-05-18T02:45:12Z","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"},"paper":{"abstract_excerpt":"We establish a transversality theorem for multiple-point crossings under generic linear perturbations with explicit Hausdorff measure estimates for the exceptional parameter set, and hence explicit upper bounds on its Hausdorff dimension. This strengthens our earlier result, which showed only that the exceptional parameter set has Lebesgue measure zero. As applications, we obtain results on normal crossings, injectivity, and embeddings under generic linear perturbations. The embedding result yields a refinement of Mather's stability theorem for generic projections when the target dimension is ","authors_text":"Shunsuke Ichiki","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-10-01T06:56:40Z","title":"A transversality theorem for multiple-point crossings under generic linear perturbations with Hausdorff measure estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.00576","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":"sha256:5690432397277ebed1f61aefb39b2420bba869049081b14aaa3f50efe4bc684a","target":"record","created_at":"2026-05-18T02:45:12Z","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":"7b934e0577452cb1736fd9841533fd119379c4de3f35b8e250d17c9812a07df0","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-10-01T06:56:40Z","title_canon_sha256":"f7c6e163ea0f019269183ec75317a9bd6d94908f63be36765c7e267074fb3908"},"schema_version":"1.0","source":{"id":"2510.00576","kind":"arxiv","version":3}},"canonical_sha256":"512eaea6af7da86608302c995eb7507b3054c9c19b6d5b1124304d04136d6e52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"512eaea6af7da86608302c995eb7507b3054c9c19b6d5b1124304d04136d6e52","first_computed_at":"2026-05-18T02:45:12.295245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:12.295245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"blof4MRTsdUcHAujZutgt9dCxoIon2SUvRskrvWz8Ki7CCKbzvt6VTNepTzrhhfjs/zotUqFPW5TsHYjyhKfCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:12.295913Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.00576","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5690432397277ebed1f61aefb39b2420bba869049081b14aaa3f50efe4bc684a","sha256:e696bc905c4fa17a6147b5e61e86d1f4196e93d4097dc2156d8f7699617001ae"],"state_sha256":"3dcda171f88afe2030bdbab74a9d23abfa29446339be5814fe201e18952725be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KE57Jtvg0svjY4cBIupk3KnDvtFF9Ug8Oi/elnJOlirv6AH2CYNOkCXyEHq3rorZ8UoglnTUP7p2kptmQj3rBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T09:08:07.134071Z","bundle_sha256":"b3deb55fe80c2c93cd28bb5a4a0d247062183ff6caa7c4c0ea12d407fc315d13"}}