{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:GLZ5BBNILTVFS272BG6JV3S4WW","short_pith_number":"pith:GLZ5BBNI","canonical_record":{"source":{"id":"math/0405448","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2004-05-24T14:53:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5ad3fa02a28592c598d8719e84d40c9cab6a6c5cc3fa121f0f9e4927a729360b","abstract_canon_sha256":"10a509a3ef618330c254721051eaa61494f5eeeef78f3f8e91262b1ebbfd2084"},"schema_version":"1.0"},"canonical_sha256":"32f3d085a85cea596bfa09bc9aee5cb5b1f2b106983ef49d5bd2120e147d149c","source":{"kind":"arxiv","id":"math/0405448","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0405448","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0405448v1","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0405448","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"GLZ5BBNILTVF","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"pith_short_16","alias_value":"GLZ5BBNILTVFS272","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"pith_short_8","alias_value":"GLZ5BBNI","created_at":"2026-07-04T14:38:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:GLZ5BBNILTVFS272BG6JV3S4WW","target":"record","payload":{"canonical_record":{"source":{"id":"math/0405448","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2004-05-24T14:53:36Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5ad3fa02a28592c598d8719e84d40c9cab6a6c5cc3fa121f0f9e4927a729360b","abstract_canon_sha256":"10a509a3ef618330c254721051eaa61494f5eeeef78f3f8e91262b1ebbfd2084"},"schema_version":"1.0"},"canonical_sha256":"32f3d085a85cea596bfa09bc9aee5cb5b1f2b106983ef49d5bd2120e147d149c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:38.785709Z","signature_b64":"0gXwXrlgR3j0uL3BUf7801S3jsSz+kUWB0FOMYqGOx00mCEuucioqOF3AY/Yzc59qPPiEJ1sgYShyodtao9kAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32f3d085a85cea596bfa09bc9aee5cb5b1f2b106983ef49d5bd2120e147d149c","last_reissued_at":"2026-07-04T14:38:38.785239Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:38.785239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0405448","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":"2026-07-04T14:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+XjcFAx993jIuzhTQq31mtQX+Rk08ZOrA/WQs/Yw5p64hcV52OV3E5Qze53t2C1qbUDVzSCa1aD5B1zXn++PDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:06:14.754634Z"},"content_sha256":"e9696f1b44f5fd39a990ea4644c48bdc2b1dbae39176018342ec43c1b7fb21f2","schema_version":"1.0","event_id":"sha256:e9696f1b44f5fd39a990ea4644c48bdc2b1dbae39176018342ec43c1b7fb21f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:GLZ5BBNILTVFS272BG6JV3S4WW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gorenstein toric Fano varieties","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Benjamin Nill","submitted_at":"2004-05-24T14:53:36Z","abstract_excerpt":"We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for nonsingular toric Fano varieties. As applications we obtain new classification results, bounds of invariants and formulate conjectures concerning combinatorial and geometrical properties of reflexive polytopes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405448","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/math/0405448/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":"2026-07-04T14:38:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGN4emmxFvJorYAvAKHoJjTKUkXU4sGg3jN1DC53N7PuYg8Peb2yqJfZ4JzzSlfHpi2IuXJc6W2lacPW6ZINDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:06:14.755030Z"},"content_sha256":"274dbda18cbf1903adf6e027ea685763d72e46c4b6010152ad24030d911105da","schema_version":"1.0","event_id":"sha256:274dbda18cbf1903adf6e027ea685763d72e46c4b6010152ad24030d911105da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLZ5BBNILTVFS272BG6JV3S4WW/bundle.json","state_url":"https://pith.science/pith/GLZ5BBNILTVFS272BG6JV3S4WW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLZ5BBNILTVFS272BG6JV3S4WW/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":"2026-08-13T14:06:14Z","links":{"resolver":"https://pith.science/pith/GLZ5BBNILTVFS272BG6JV3S4WW","bundle":"https://pith.science/pith/GLZ5BBNILTVFS272BG6JV3S4WW/bundle.json","state":"https://pith.science/pith/GLZ5BBNILTVFS272BG6JV3S4WW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLZ5BBNILTVFS272BG6JV3S4WW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:GLZ5BBNILTVFS272BG6JV3S4WW","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":"10a509a3ef618330c254721051eaa61494f5eeeef78f3f8e91262b1ebbfd2084","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AG","submitted_at":"2004-05-24T14:53:36Z","title_canon_sha256":"5ad3fa02a28592c598d8719e84d40c9cab6a6c5cc3fa121f0f9e4927a729360b"},"schema_version":"1.0","source":{"id":"math/0405448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0405448","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0405448v1","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0405448","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"pith_short_12","alias_value":"GLZ5BBNILTVF","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"pith_short_16","alias_value":"GLZ5BBNILTVFS272","created_at":"2026-07-04T14:38:38Z"},{"alias_kind":"pith_short_8","alias_value":"GLZ5BBNI","created_at":"2026-07-04T14:38:38Z"}],"graph_snapshots":[{"event_id":"sha256:274dbda18cbf1903adf6e027ea685763d72e46c4b6010152ad24030d911105da","target":"graph","created_at":"2026-07-04T14:38:38Z","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/math/0405448/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for nonsingular toric Fano varieties. As applications we obtain new classification results, bounds of invariants and formulate conjectures concerning combinatorial and geometrical properties of reflexive polytopes.","authors_text":"Benjamin Nill","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2004-05-24T14:53:36Z","title":"Gorenstein toric Fano varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0405448","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:e9696f1b44f5fd39a990ea4644c48bdc2b1dbae39176018342ec43c1b7fb21f2","target":"record","created_at":"2026-07-04T14:38:38Z","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":"10a509a3ef618330c254721051eaa61494f5eeeef78f3f8e91262b1ebbfd2084","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AG","submitted_at":"2004-05-24T14:53:36Z","title_canon_sha256":"5ad3fa02a28592c598d8719e84d40c9cab6a6c5cc3fa121f0f9e4927a729360b"},"schema_version":"1.0","source":{"id":"math/0405448","kind":"arxiv","version":1}},"canonical_sha256":"32f3d085a85cea596bfa09bc9aee5cb5b1f2b106983ef49d5bd2120e147d149c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32f3d085a85cea596bfa09bc9aee5cb5b1f2b106983ef49d5bd2120e147d149c","first_computed_at":"2026-07-04T14:38:38.785239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:38.785239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0gXwXrlgR3j0uL3BUf7801S3jsSz+kUWB0FOMYqGOx00mCEuucioqOF3AY/Yzc59qPPiEJ1sgYShyodtao9kAg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:38.785709Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0405448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9696f1b44f5fd39a990ea4644c48bdc2b1dbae39176018342ec43c1b7fb21f2","sha256:274dbda18cbf1903adf6e027ea685763d72e46c4b6010152ad24030d911105da"],"state_sha256":"e86fb0030a5d257708877990e786da2437fbd4d2664e0f853d0561bc5c223617"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2tu/XScas9fwZYhTChm3yfK9raJPttugXkOekqVQJEQj3bBR+G0VoBZ9iQfOz9TjBQj6/cGZkOkoULTj9J5NBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T14:06:14.760919Z","bundle_sha256":"10332e76ce4968336fabe9e9e88a4cea4f47885013f77c13fc037a391127b145"}}