{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:VUWVKNG6F553G3SNUOGL2D253P","short_pith_number":"pith:VUWVKNG6","canonical_record":{"source":{"id":"2507.13927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-18T14:03:17Z","cross_cats_sorted":[],"title_canon_sha256":"ce198348dc0bf2a491b23065e6391a4d95081864c1608050f0b34ec9829e26c1","abstract_canon_sha256":"3ea9664448e2a4ef3eb3f49aff6ed3c0ac28314ff9fab9e7daa1d38c55360051"},"schema_version":"1.0"},"canonical_sha256":"ad2d5534de2f7bb36e4da38cbd0f5ddbc8d51aca1e06d26eeb22cffb0e6e53a9","source":{"kind":"arxiv","id":"2507.13927","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13927","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13927v1","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13927","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"pith_short_12","alias_value":"VUWVKNG6F553","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"pith_short_16","alias_value":"VUWVKNG6F553G3SN","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"pith_short_8","alias_value":"VUWVKNG6","created_at":"2026-07-05T11:39:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:VUWVKNG6F553G3SNUOGL2D253P","target":"record","payload":{"canonical_record":{"source":{"id":"2507.13927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-18T14:03:17Z","cross_cats_sorted":[],"title_canon_sha256":"ce198348dc0bf2a491b23065e6391a4d95081864c1608050f0b34ec9829e26c1","abstract_canon_sha256":"3ea9664448e2a4ef3eb3f49aff6ed3c0ac28314ff9fab9e7daa1d38c55360051"},"schema_version":"1.0"},"canonical_sha256":"ad2d5534de2f7bb36e4da38cbd0f5ddbc8d51aca1e06d26eeb22cffb0e6e53a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:25.665977Z","signature_b64":"zsMvRmzatT7zE1fbPCA34DBXRJUmWxVMh95K7bHOK8dWrMBCg7RdfawMCbF6CaCPrRutz4LOIyZwjbb5QmeLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad2d5534de2f7bb36e4da38cbd0f5ddbc8d51aca1e06d26eeb22cffb0e6e53a9","last_reissued_at":"2026-07-05T11:39:25.665312Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:25.665312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.13927","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:39:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JfvsUIhL5dAZqAC83PAUPnzdNoAHSGkTCoKG5xLqwE9nZZ8ROG3eNLYvPbWjQ6oO+rJgubJH6WUvKDph3sf0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:44:07.240274Z"},"content_sha256":"5950613d0b894c2a815872524a4db6f5c13e38bb82156e6e6e5b1347554365a8","schema_version":"1.0","event_id":"sha256:5950613d0b894c2a815872524a4db6f5c13e38bb82156e6e6e5b1347554365a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:VUWVKNG6F553G3SNUOGL2D253P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Restricted tangent bundle of rational curves on projective hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lucas Mioranci","submitted_at":"2025-07-18T14:03:17Z","abstract_excerpt":"We determine all triples $(e,d,n)$ for which a general degree $d$ hypersurface $X\\subset \\mathbb{P}^n$ contains a degree $e$ rational curve $C$ with balanced restricted tangent bundle $T_X|_C$. In addition, we show how to compute explicit examples of hypersurfaces with balanced $T_X|_C$ when $C$ is a rational normal curve."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13927","kind":"arxiv","version":1},"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/2507.13927/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":"2026-07-05T11:39:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rU87PQGkb5hzPS5LOvf58lJjrA0Am8Jv4o/jg20En+aG8VamwV71MEIY0Zt32SNC+MRa2eyUDqjzGXLuQZSODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:44:07.240650Z"},"content_sha256":"f7f4f3b1f8e7477eb03cbc83f7c815a0d5c79ef9174196820d5245b91e695929","schema_version":"1.0","event_id":"sha256:f7f4f3b1f8e7477eb03cbc83f7c815a0d5c79ef9174196820d5245b91e695929"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VUWVKNG6F553G3SNUOGL2D253P/bundle.json","state_url":"https://pith.science/pith/VUWVKNG6F553G3SNUOGL2D253P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VUWVKNG6F553G3SNUOGL2D253P/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":"2026-07-07T14:44:07Z","links":{"resolver":"https://pith.science/pith/VUWVKNG6F553G3SNUOGL2D253P","bundle":"https://pith.science/pith/VUWVKNG6F553G3SNUOGL2D253P/bundle.json","state":"https://pith.science/pith/VUWVKNG6F553G3SNUOGL2D253P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VUWVKNG6F553G3SNUOGL2D253P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:VUWVKNG6F553G3SNUOGL2D253P","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":"3ea9664448e2a4ef3eb3f49aff6ed3c0ac28314ff9fab9e7daa1d38c55360051","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-18T14:03:17Z","title_canon_sha256":"ce198348dc0bf2a491b23065e6391a4d95081864c1608050f0b34ec9829e26c1"},"schema_version":"1.0","source":{"id":"2507.13927","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13927","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13927v1","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13927","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"pith_short_12","alias_value":"VUWVKNG6F553","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"pith_short_16","alias_value":"VUWVKNG6F553G3SN","created_at":"2026-07-05T11:39:25Z"},{"alias_kind":"pith_short_8","alias_value":"VUWVKNG6","created_at":"2026-07-05T11:39:25Z"}],"graph_snapshots":[{"event_id":"sha256:f7f4f3b1f8e7477eb03cbc83f7c815a0d5c79ef9174196820d5245b91e695929","target":"graph","created_at":"2026-07-05T11:39:25Z","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/2507.13927/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine all triples $(e,d,n)$ for which a general degree $d$ hypersurface $X\\subset \\mathbb{P}^n$ contains a degree $e$ rational curve $C$ with balanced restricted tangent bundle $T_X|_C$. In addition, we show how to compute explicit examples of hypersurfaces with balanced $T_X|_C$ when $C$ is a rational normal curve.","authors_text":"Lucas Mioranci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-18T14:03:17Z","title":"Restricted tangent bundle of rational curves on projective hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13927","kind":"arxiv","version":1},"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":"sha256:5950613d0b894c2a815872524a4db6f5c13e38bb82156e6e6e5b1347554365a8","target":"record","created_at":"2026-07-05T11:39:25Z","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":"3ea9664448e2a4ef3eb3f49aff6ed3c0ac28314ff9fab9e7daa1d38c55360051","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-07-18T14:03:17Z","title_canon_sha256":"ce198348dc0bf2a491b23065e6391a4d95081864c1608050f0b34ec9829e26c1"},"schema_version":"1.0","source":{"id":"2507.13927","kind":"arxiv","version":1}},"canonical_sha256":"ad2d5534de2f7bb36e4da38cbd0f5ddbc8d51aca1e06d26eeb22cffb0e6e53a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad2d5534de2f7bb36e4da38cbd0f5ddbc8d51aca1e06d26eeb22cffb0e6e53a9","first_computed_at":"2026-07-05T11:39:25.665312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:25.665312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zsMvRmzatT7zE1fbPCA34DBXRJUmWxVMh95K7bHOK8dWrMBCg7RdfawMCbF6CaCPrRutz4LOIyZwjbb5QmeLCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:25.665977Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13927","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5950613d0b894c2a815872524a4db6f5c13e38bb82156e6e6e5b1347554365a8","sha256:f7f4f3b1f8e7477eb03cbc83f7c815a0d5c79ef9174196820d5245b91e695929"],"state_sha256":"46207e1b75eef6eb0245b37f0d10fb7850cbeb9ce5b9fe3e0cd7d7b2c14c1dbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J5FI8Y5BPOd4Ugs5pJRpMW1qi1kIA6qQQAn9yXL/hHe40dbVs446IW7xfaoZbhwEjTyhKOwGie7d2XZyxxgMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:44:07.242573Z","bundle_sha256":"7906a3735d25383f9fdb9f39a85c9c1d7b3e60a2c572f06feee4d20ed8c24b85"}}