{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:34ZKRHETNO3VYTCBSMBFFVLVHK","short_pith_number":"pith:34ZKRHET","canonical_record":{"source":{"id":"alg-geom/9611010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1996-11-08T21:01:14Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c428adfd0e8a77f60d566009b32c96b5b0201d681105022062157890ef5d4395","abstract_canon_sha256":"131c5b6f4d4897857929aaf082a270fbdf2289af8dcac4bf588ea0fb967d0c29"},"schema_version":"1.0"},"canonical_sha256":"df32a89c936bb75c4c41930252d5753a872730317fe0695677a777859314da09","source":{"kind":"arxiv","id":"alg-geom/9611010","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9611010","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9611010v1","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9611010","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"34ZKRHETNO3V","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"34ZKRHETNO3VYTCB","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"34ZKRHET","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:34ZKRHETNO3VYTCBSMBFFVLVHK","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9611010","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1996-11-08T21:01:14Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c428adfd0e8a77f60d566009b32c96b5b0201d681105022062157890ef5d4395","abstract_canon_sha256":"131c5b6f4d4897857929aaf082a270fbdf2289af8dcac4bf588ea0fb967d0c29"},"schema_version":"1.0"},"canonical_sha256":"df32a89c936bb75c4c41930252d5753a872730317fe0695677a777859314da09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:47.142864Z","signature_b64":"38EKlfZVfT0P3+MgVwgQxGMb6uTkmdM+zmhMJ35cUFRa145gY/m1MAoAqulwmXYQoD6igW6GwfpllVGMji0eBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df32a89c936bb75c4c41930252d5753a872730317fe0695677a777859314da09","last_reissued_at":"2026-05-18T01:07:47.142355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:47.142355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9611010","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":"2026-05-18T01:07:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmAxqR5kWROfBbBi9uzZmSuqA8a8njvQHX1gIasWY2RTd+pKtH5plX3J2g5Iif2lD0u/GY/oZi9/ujY0xjwyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:04:52.456853Z"},"content_sha256":"ce0bf35482e4b3670a144b2c8c3e87100e701f091bd6c11621b0119d2cd6ec74","schema_version":"1.0","event_id":"sha256:ce0bf35482e4b3670a144b2c8c3e87100e701f091bd6c11621b0119d2cd6ec74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:34ZKRHETNO3VYTCBSMBFFVLVHK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Complexity of Smooth Projective Toric Varieties","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Serkan Hosten","submitted_at":"1996-11-08T21:01:14Z","abstract_excerpt":"In this paper we answer a question posed by V.V. Batyrev. The question asked if there exists a complete regular fan with more than quadratically many primitive collections. We construct a smooth projective toric variety associated to a complete regular fan $\\Delta$ in R^d with $n$ generators where the number of primitive collections of $\\Delta$ is at least exponential in $n-d$. We also exhibit the connection between the number of primitive collections of $\\Delta$ and the facet complexity of the Gr\\\"obner fan of the associated integer program."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9611010","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":"2026-05-18T01:07:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d3sOZttHyWPegqy/B6lvTEbYEGKS4SeoE3RCvbugVV7ZKM6JNeV7uePKCVB4H9UqlbeDxd6SZ9VpE/AWwiSdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T02:04:52.457190Z"},"content_sha256":"168155d64a8eeb603b40430b4193a1f5c1a91be3b4dbc3dc6cf9f4d0a408bd03","schema_version":"1.0","event_id":"sha256:168155d64a8eeb603b40430b4193a1f5c1a91be3b4dbc3dc6cf9f4d0a408bd03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/34ZKRHETNO3VYTCBSMBFFVLVHK/bundle.json","state_url":"https://pith.science/pith/34ZKRHETNO3VYTCBSMBFFVLVHK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/34ZKRHETNO3VYTCBSMBFFVLVHK/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":"2026-06-05T02:04:52Z","links":{"resolver":"https://pith.science/pith/34ZKRHETNO3VYTCBSMBFFVLVHK","bundle":"https://pith.science/pith/34ZKRHETNO3VYTCBSMBFFVLVHK/bundle.json","state":"https://pith.science/pith/34ZKRHETNO3VYTCBSMBFFVLVHK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/34ZKRHETNO3VYTCBSMBFFVLVHK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:34ZKRHETNO3VYTCBSMBFFVLVHK","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":"131c5b6f4d4897857929aaf082a270fbdf2289af8dcac4bf588ea0fb967d0c29","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-11-08T21:01:14Z","title_canon_sha256":"c428adfd0e8a77f60d566009b32c96b5b0201d681105022062157890ef5d4395"},"schema_version":"1.0","source":{"id":"alg-geom/9611010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9611010","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9611010v1","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9611010","created_at":"2026-05-18T01:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"34ZKRHETNO3V","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"34ZKRHETNO3VYTCB","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"34ZKRHET","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:168155d64a8eeb603b40430b4193a1f5c1a91be3b4dbc3dc6cf9f4d0a408bd03","target":"graph","created_at":"2026-05-18T01:07:47Z","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 answer a question posed by V.V. Batyrev. The question asked if there exists a complete regular fan with more than quadratically many primitive collections. We construct a smooth projective toric variety associated to a complete regular fan $\\Delta$ in R^d with $n$ generators where the number of primitive collections of $\\Delta$ is at least exponential in $n-d$. We also exhibit the connection between the number of primitive collections of $\\Delta$ and the facet complexity of the Gr\\\"obner fan of the associated integer program.","authors_text":"Serkan Hosten","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1996-11-08T21:01:14Z","title":"On the Complexity of Smooth Projective Toric Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9611010","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:ce0bf35482e4b3670a144b2c8c3e87100e701f091bd6c11621b0119d2cd6ec74","target":"record","created_at":"2026-05-18T01:07:47Z","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":"131c5b6f4d4897857929aaf082a270fbdf2289af8dcac4bf588ea0fb967d0c29","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1996-11-08T21:01:14Z","title_canon_sha256":"c428adfd0e8a77f60d566009b32c96b5b0201d681105022062157890ef5d4395"},"schema_version":"1.0","source":{"id":"alg-geom/9611010","kind":"arxiv","version":1}},"canonical_sha256":"df32a89c936bb75c4c41930252d5753a872730317fe0695677a777859314da09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df32a89c936bb75c4c41930252d5753a872730317fe0695677a777859314da09","first_computed_at":"2026-05-18T01:07:47.142355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:47.142355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"38EKlfZVfT0P3+MgVwgQxGMb6uTkmdM+zmhMJ35cUFRa145gY/m1MAoAqulwmXYQoD6igW6GwfpllVGMji0eBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:47.142864Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9611010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce0bf35482e4b3670a144b2c8c3e87100e701f091bd6c11621b0119d2cd6ec74","sha256:168155d64a8eeb603b40430b4193a1f5c1a91be3b4dbc3dc6cf9f4d0a408bd03"],"state_sha256":"1a52617c957dcb942ae113756522f322e4ab98865f7f8e2d1034e739fd0f13dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tM7r7gsowCPL0WF0wYYKPnrJE56oUvLfjuJ1A9S54aGOCzgwbZBewEifJrpDtrSPZZJkYGn2l+TDnJUuQnUzAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T02:04:52.462343Z","bundle_sha256":"b28e320529ab0a5fe41d92570a97008a70f54839ff1aa76fc0a145ae131c6c55"}}