{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:4J6Y5IZDEUDABN2TKUIIAPWTCV","short_pith_number":"pith:4J6Y5IZD","canonical_record":{"source":{"id":"1403.2840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-12T08:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"b6a82f7e25a60046af226b65372cd753c36f5df9232a70546dd666b6d44e302d","abstract_canon_sha256":"684d2956421d48e1f360cb167fcbaa8fab821d5d2d9fc73b26459d92a366c9cd"},"schema_version":"1.0"},"canonical_sha256":"e27d8ea323250600b7535510803ed3154296cf53b97be4d14adbcee2d5b28038","source":{"kind":"arxiv","id":"1403.2840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2840","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2840v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2840","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"4J6Y5IZDEUDA","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4J6Y5IZDEUDABN2T","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4J6Y5IZD","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:4J6Y5IZDEUDABN2TKUIIAPWTCV","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-12T08:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"b6a82f7e25a60046af226b65372cd753c36f5df9232a70546dd666b6d44e302d","abstract_canon_sha256":"684d2956421d48e1f360cb167fcbaa8fab821d5d2d9fc73b26459d92a366c9cd"},"schema_version":"1.0"},"canonical_sha256":"e27d8ea323250600b7535510803ed3154296cf53b97be4d14adbcee2d5b28038","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:33.844857Z","signature_b64":"KYhzQOW+Csn6gmzGIfeLs4zLxHpXU5zIwtwZ9t3J24mXKzeGEFi2olTaTtr6p8ijkKMGh3gynAIyCiQjSyP6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e27d8ea323250600b7535510803ed3154296cf53b97be4d14adbcee2d5b28038","last_reissued_at":"2026-05-18T02:56:33.844072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:33.844072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2840","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":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X1cjYeKybq38IS/n/JThh7vVsVWi+o+h8RdQgC7mVfNwRi+UhjJahM5YZpI9wkGzWOJ3MSgYzqQiyLNDRt5uDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:02:29.635518Z"},"content_sha256":"68c2da2f718f037361f096ba9db0b0aab899e4817cd54ba197914e1f62d1c22b","schema_version":"1.0","event_id":"sha256:68c2da2f718f037361f096ba9db0b0aab899e4817cd54ba197914e1f62d1c22b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:4J6Y5IZDEUDABN2TKUIIAPWTCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the intersection of ACM curves in $\\PP^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"R. Hartshorne, R.M. Mir\\'o-Roig","submitted_at":"2014-03-12T08:18:24Z","abstract_excerpt":"Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in P^3 never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in P^3. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2840","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":""},"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":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UZSUIylbFVyhCKo1NyC697yKSkzCOUmjBuYV2T8xFmePA53HWmW0r6yG830RbwzO/DhurMSFhmjiCmoaRyQ4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:02:29.635856Z"},"content_sha256":"d1f0f567dc8ac2b9375d4336780535e9cbce1193731c3d61d778d258c24fde84","schema_version":"1.0","event_id":"sha256:d1f0f567dc8ac2b9375d4336780535e9cbce1193731c3d61d778d258c24fde84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4J6Y5IZDEUDABN2TKUIIAPWTCV/bundle.json","state_url":"https://pith.science/pith/4J6Y5IZDEUDABN2TKUIIAPWTCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4J6Y5IZDEUDABN2TKUIIAPWTCV/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":"2026-06-01T23:02:29Z","links":{"resolver":"https://pith.science/pith/4J6Y5IZDEUDABN2TKUIIAPWTCV","bundle":"https://pith.science/pith/4J6Y5IZDEUDABN2TKUIIAPWTCV/bundle.json","state":"https://pith.science/pith/4J6Y5IZDEUDABN2TKUIIAPWTCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4J6Y5IZDEUDABN2TKUIIAPWTCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4J6Y5IZDEUDABN2TKUIIAPWTCV","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":"684d2956421d48e1f360cb167fcbaa8fab821d5d2d9fc73b26459d92a366c9cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-12T08:18:24Z","title_canon_sha256":"b6a82f7e25a60046af226b65372cd753c36f5df9232a70546dd666b6d44e302d"},"schema_version":"1.0","source":{"id":"1403.2840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2840","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2840v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2840","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"4J6Y5IZDEUDA","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4J6Y5IZDEUDABN2T","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4J6Y5IZD","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:d1f0f567dc8ac2b9375d4336780535e9cbce1193731c3d61d778d258c24fde84","target":"graph","created_at":"2026-05-18T02:56:33Z","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":"Bezout's theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in P^3 never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in P^3. The bound that we give is in many cases optimal as a function of only the degrees and the initial degrees of the curves.","authors_text":"R. Hartshorne, R.M. Mir\\'o-Roig","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-12T08:18:24Z","title":"On the intersection of ACM curves in $\\PP^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2840","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":"sha256:68c2da2f718f037361f096ba9db0b0aab899e4817cd54ba197914e1f62d1c22b","target":"record","created_at":"2026-05-18T02:56:33Z","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":"684d2956421d48e1f360cb167fcbaa8fab821d5d2d9fc73b26459d92a366c9cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-12T08:18:24Z","title_canon_sha256":"b6a82f7e25a60046af226b65372cd753c36f5df9232a70546dd666b6d44e302d"},"schema_version":"1.0","source":{"id":"1403.2840","kind":"arxiv","version":1}},"canonical_sha256":"e27d8ea323250600b7535510803ed3154296cf53b97be4d14adbcee2d5b28038","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e27d8ea323250600b7535510803ed3154296cf53b97be4d14adbcee2d5b28038","first_computed_at":"2026-05-18T02:56:33.844072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:33.844072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KYhzQOW+Csn6gmzGIfeLs4zLxHpXU5zIwtwZ9t3J24mXKzeGEFi2olTaTtr6p8ijkKMGh3gynAIyCiQjSyP6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:33.844857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68c2da2f718f037361f096ba9db0b0aab899e4817cd54ba197914e1f62d1c22b","sha256:d1f0f567dc8ac2b9375d4336780535e9cbce1193731c3d61d778d258c24fde84"],"state_sha256":"aba26c35c8ac49861d77d4a5e158538021a0bf295e3816773da2f57dd73939e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RoRqqCqV1pqFW1NWy2X3mksEFMyy0Ilz3JaZNYahA6nvDxOLm9nhJIOE8KMdYtdZZng0udgC/GYjlG849s8pBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:02:29.637746Z","bundle_sha256":"1164e7067def84c40c2796badc411698797c0401a383d6289533d52cdc6c9ddf"}}