{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:N7VV7F2FG7PSI6COMDFYEXAGN3","short_pith_number":"pith:N7VV7F2F","canonical_record":{"source":{"id":"alg-geom/9501009","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1995-01-17T15:27:37Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ded406e34d5c96c06bf4296bc9797653ce20bf8728857a1d8cf13b34cf7d556b","abstract_canon_sha256":"1b02fb17b961fa6e1936f3dfb0a0cba1612e0d92726a68003fbfd88804bf621a"},"schema_version":"1.0"},"canonical_sha256":"6feb5f974537df24784e60cb825c066eda5c33af32955dcf950ad58b97df7b84","source":{"kind":"arxiv","id":"alg-geom/9501009","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9501009","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9501009v1","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9501009","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"N7VV7F2FG7PS","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"N7VV7F2FG7PSI6CO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"N7VV7F2F","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:N7VV7F2FG7PSI6COMDFYEXAGN3","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9501009","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1995-01-17T15:27:37Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ded406e34d5c96c06bf4296bc9797653ce20bf8728857a1d8cf13b34cf7d556b","abstract_canon_sha256":"1b02fb17b961fa6e1936f3dfb0a0cba1612e0d92726a68003fbfd88804bf621a"},"schema_version":"1.0"},"canonical_sha256":"6feb5f974537df24784e60cb825c066eda5c33af32955dcf950ad58b97df7b84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:43.031441Z","signature_b64":"zIQjE55yzoyKK8DuBOwqsd4lyPcLy8pIV1uz3XQ+iBAyAKkx6ipWWmpTTrqX4pMrHxwK/8eCOdXKiqQm97bWCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6feb5f974537df24784e60cb825c066eda5c33af32955dcf950ad58b97df7b84","last_reissued_at":"2026-05-18T01:37:43.031022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:43.031022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9501009","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":"2026-05-18T01:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lOtAk3hbRXoIz18TuLTB0IZv2wrGwvVipafgubcsY5MPkMiQJmtdRz/twkq2/iS63muQsq08s2PsO7pXF5cPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:38:26.732740Z"},"content_sha256":"f58ee385a1472c369c2b9bc67e681e35bf8603f5968a7151cde1ce738b206017","schema_version":"1.0","event_id":"sha256:f58ee385a1472c369c2b9bc67e681e35bf8603f5968a7151cde1ce738b206017"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:N7VV7F2FG7PSI6COMDFYEXAGN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Hilbert scheme of curves in higher-dimensional projective space","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Barbara Fantechi, Rita Pardini","submitted_at":"1995-01-17T15:27:37Z","abstract_excerpt":"In this paper we prove that, for any $n\\ge 3$, there exist infinitely many $r\\in \\N$ and for each of them a smooth, connected curve $C_r$ in $\\P^r$ such that $C_r$ lies on  exactly $n$ irreducible components of the Hilbert scheme $\\hilb(\\P^r)$. This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9501009","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":"2026-05-18T01:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0i+XDE1YOKGux3xECT+LVYyTS2pjwlugiqqSONlUwYSwzKC5PPsDvsZgGrhKAymkLrSjC3zSOlXAqQfpRlEXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:38:26.733096Z"},"content_sha256":"735df2bef5ce0b03c79863c9a792ffadd0a414bc98f91c777072eaaa13796614","schema_version":"1.0","event_id":"sha256:735df2bef5ce0b03c79863c9a792ffadd0a414bc98f91c777072eaaa13796614"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7VV7F2FG7PSI6COMDFYEXAGN3/bundle.json","state_url":"https://pith.science/pith/N7VV7F2FG7PSI6COMDFYEXAGN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7VV7F2FG7PSI6COMDFYEXAGN3/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":"2026-06-02T15:38:26Z","links":{"resolver":"https://pith.science/pith/N7VV7F2FG7PSI6COMDFYEXAGN3","bundle":"https://pith.science/pith/N7VV7F2FG7PSI6COMDFYEXAGN3/bundle.json","state":"https://pith.science/pith/N7VV7F2FG7PSI6COMDFYEXAGN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7VV7F2FG7PSI6COMDFYEXAGN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:N7VV7F2FG7PSI6COMDFYEXAGN3","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":"1b02fb17b961fa6e1936f3dfb0a0cba1612e0d92726a68003fbfd88804bf621a","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1995-01-17T15:27:37Z","title_canon_sha256":"ded406e34d5c96c06bf4296bc9797653ce20bf8728857a1d8cf13b34cf7d556b"},"schema_version":"1.0","source":{"id":"alg-geom/9501009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9501009","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9501009v1","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9501009","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"N7VV7F2FG7PS","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"N7VV7F2FG7PSI6CO","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"N7VV7F2F","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:735df2bef5ce0b03c79863c9a792ffadd0a414bc98f91c777072eaaa13796614","target":"graph","created_at":"2026-05-18T01:37:43Z","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":"In this paper we prove that, for any $n\\ge 3$, there exist infinitely many $r\\in \\N$ and for each of them a smooth, connected curve $C_r$ in $\\P^r$ such that $C_r$ lies on  exactly $n$ irreducible components of the Hilbert scheme $\\hilb(\\P^r)$. This is proven by reducing the problem to an analogous statement for the moduli of surfaces of general type.","authors_text":"Barbara Fantechi, Rita Pardini","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1995-01-17T15:27:37Z","title":"On the Hilbert scheme of curves in higher-dimensional projective space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9501009","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:f58ee385a1472c369c2b9bc67e681e35bf8603f5968a7151cde1ce738b206017","target":"record","created_at":"2026-05-18T01:37:43Z","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":"1b02fb17b961fa6e1936f3dfb0a0cba1612e0d92726a68003fbfd88804bf621a","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1995-01-17T15:27:37Z","title_canon_sha256":"ded406e34d5c96c06bf4296bc9797653ce20bf8728857a1d8cf13b34cf7d556b"},"schema_version":"1.0","source":{"id":"alg-geom/9501009","kind":"arxiv","version":1}},"canonical_sha256":"6feb5f974537df24784e60cb825c066eda5c33af32955dcf950ad58b97df7b84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6feb5f974537df24784e60cb825c066eda5c33af32955dcf950ad58b97df7b84","first_computed_at":"2026-05-18T01:37:43.031022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:43.031022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zIQjE55yzoyKK8DuBOwqsd4lyPcLy8pIV1uz3XQ+iBAyAKkx6ipWWmpTTrqX4pMrHxwK/8eCOdXKiqQm97bWCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:43.031441Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9501009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f58ee385a1472c369c2b9bc67e681e35bf8603f5968a7151cde1ce738b206017","sha256:735df2bef5ce0b03c79863c9a792ffadd0a414bc98f91c777072eaaa13796614"],"state_sha256":"a77693fa49a275ead8ffd985868e325c1ce7e54bb5a2b68eae1750e3f95bcd7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TazOhUTPbOHK+BslCvwVZQvuM318jJD99hHluwJDqb9OH9M2lA/bO+zyGAesP6w+WndDFpRIwW6goSUt6P5jCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:38:26.735055Z","bundle_sha256":"f3ea3d31fb6e55097e43a253f726f344ab05984035d645dd8772312ca85a3104"}}