{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BVFF4CO6L3ZTB47YWESPIRV6TH","short_pith_number":"pith:BVFF4CO6","canonical_record":{"source":{"id":"2512.14817","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-16T19:00:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bbad22d6763aa8390f15fa5cd43e8ddb8127729e79c5074d63ab229cee805cf3","abstract_canon_sha256":"8bcf656dad2aea450ef658d1b230bbfd9b9c17a7d69ed32aa0d32212d106f7fe"},"schema_version":"1.0"},"canonical_sha256":"0d4a5e09de5ef330f3f8b124f446be99e43fc75bf54abf1691f94bccf8186474","source":{"kind":"arxiv","id":"2512.14817","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.14817","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"2512.14817v2","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.14817","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"BVFF4CO6L3ZT","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"BVFF4CO6L3ZTB47Y","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"BVFF4CO6","created_at":"2026-05-27T01:04:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BVFF4CO6L3ZTB47YWESPIRV6TH","target":"record","payload":{"canonical_record":{"source":{"id":"2512.14817","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-16T19:00:01Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bbad22d6763aa8390f15fa5cd43e8ddb8127729e79c5074d63ab229cee805cf3","abstract_canon_sha256":"8bcf656dad2aea450ef658d1b230bbfd9b9c17a7d69ed32aa0d32212d106f7fe"},"schema_version":"1.0"},"canonical_sha256":"0d4a5e09de5ef330f3f8b124f446be99e43fc75bf54abf1691f94bccf8186474","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:04:53.882192Z","signature_b64":"mJI3LWZu/Vyu55fkRisBbL+tCoE34+a8ZgUfhlVMhpp9quTgO+zJEkJ8I8BI3e4tDSLPi1ZGD35adfi9+jUeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d4a5e09de5ef330f3f8b124f446be99e43fc75bf54abf1691f94bccf8186474","last_reissued_at":"2026-05-27T01:04:53.881632Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:04:53.881632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.14817","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-27T01:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3DckxvcQl5wQhWI6Efcgwxgmrbspaa7Wnpk79g3XWMFguu+xL/5B5fcNv4hrfCbdKD2BrUqRWi8bc3hnSj5GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:42:41.675305Z"},"content_sha256":"af836e965af3c74af39b9611b8fbce997d906e7db51c4ffa2495864aa08c01fa","schema_version":"1.0","event_id":"sha256:af836e965af3c74af39b9611b8fbce997d906e7db51c4ffa2495864aa08c01fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BVFF4CO6L3ZTB47YWESPIRV6TH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calabi-Yau Threefolds from Vex Triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Elijah Sheridan, Nate MacFadden","submitted_at":"2025-12-16T19:00:01Z","abstract_excerpt":"We study the birational geometry (i.e., K\\\"ahler moduli space) of Calabi--Yau (CY) threefold hypersurfaces in toric varieties arising from four-dimensional reflexive polytopes. In particular, it has been observed that the birational classes of these geometries are not exhausted by toric hypersurfaces arising from fine, regular, star triangulations (FRSTs). We begin by introducing a classification problem: enumeration of birational classes of toric varieties, which is equivalent to enumeration of certain triangulations/fans. We consider this problem from the complementary perspectives of triang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.14817","kind":"arxiv","version":2},"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/2512.14817/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":"2026-05-27T01:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g8mSkaTRIGn8KpRXFHNLWGp1Du/6qQPlbIJ4TpRaCxOcYiegMIfo5cbw63pCRuojmnhJYRFvh/m66/lyX5HvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:42:41.676000Z"},"content_sha256":"fc2ae8c814f5bf22b3bf94f2bd5ff1e36860db09f930296b2b6443b279de174a","schema_version":"1.0","event_id":"sha256:fc2ae8c814f5bf22b3bf94f2bd5ff1e36860db09f930296b2b6443b279de174a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVFF4CO6L3ZTB47YWESPIRV6TH/bundle.json","state_url":"https://pith.science/pith/BVFF4CO6L3ZTB47YWESPIRV6TH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVFF4CO6L3ZTB47YWESPIRV6TH/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":"2026-06-10T12:42:41Z","links":{"resolver":"https://pith.science/pith/BVFF4CO6L3ZTB47YWESPIRV6TH","bundle":"https://pith.science/pith/BVFF4CO6L3ZTB47YWESPIRV6TH/bundle.json","state":"https://pith.science/pith/BVFF4CO6L3ZTB47YWESPIRV6TH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVFF4CO6L3ZTB47YWESPIRV6TH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BVFF4CO6L3ZTB47YWESPIRV6TH","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":"8bcf656dad2aea450ef658d1b230bbfd9b9c17a7d69ed32aa0d32212d106f7fe","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-16T19:00:01Z","title_canon_sha256":"bbad22d6763aa8390f15fa5cd43e8ddb8127729e79c5074d63ab229cee805cf3"},"schema_version":"1.0","source":{"id":"2512.14817","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.14817","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"2512.14817v2","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.14817","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"BVFF4CO6L3ZT","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"BVFF4CO6L3ZTB47Y","created_at":"2026-05-27T01:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"BVFF4CO6","created_at":"2026-05-27T01:04:53Z"}],"graph_snapshots":[{"event_id":"sha256:fc2ae8c814f5bf22b3bf94f2bd5ff1e36860db09f930296b2b6443b279de174a","target":"graph","created_at":"2026-05-27T01:04:53Z","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/2512.14817/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the birational geometry (i.e., K\\\"ahler moduli space) of Calabi--Yau (CY) threefold hypersurfaces in toric varieties arising from four-dimensional reflexive polytopes. In particular, it has been observed that the birational classes of these geometries are not exhausted by toric hypersurfaces arising from fine, regular, star triangulations (FRSTs). We begin by introducing a classification problem: enumeration of birational classes of toric varieties, which is equivalent to enumeration of certain triangulations/fans. We consider this problem from the complementary perspectives of triang","authors_text":"Elijah Sheridan, Nate MacFadden","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-16T19:00:01Z","title":"Calabi-Yau Threefolds from Vex Triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.14817","kind":"arxiv","version":2},"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:af836e965af3c74af39b9611b8fbce997d906e7db51c4ffa2495864aa08c01fa","target":"record","created_at":"2026-05-27T01:04:53Z","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":"8bcf656dad2aea450ef658d1b230bbfd9b9c17a7d69ed32aa0d32212d106f7fe","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2025-12-16T19:00:01Z","title_canon_sha256":"bbad22d6763aa8390f15fa5cd43e8ddb8127729e79c5074d63ab229cee805cf3"},"schema_version":"1.0","source":{"id":"2512.14817","kind":"arxiv","version":2}},"canonical_sha256":"0d4a5e09de5ef330f3f8b124f446be99e43fc75bf54abf1691f94bccf8186474","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d4a5e09de5ef330f3f8b124f446be99e43fc75bf54abf1691f94bccf8186474","first_computed_at":"2026-05-27T01:04:53.881632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:04:53.881632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mJI3LWZu/Vyu55fkRisBbL+tCoE34+a8ZgUfhlVMhpp9quTgO+zJEkJ8I8BI3e4tDSLPi1ZGD35adfi9+jUeDQ==","signature_status":"signed_v1","signed_at":"2026-05-27T01:04:53.882192Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.14817","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af836e965af3c74af39b9611b8fbce997d906e7db51c4ffa2495864aa08c01fa","sha256:fc2ae8c814f5bf22b3bf94f2bd5ff1e36860db09f930296b2b6443b279de174a"],"state_sha256":"f3f85b59a9b4f1c1d114d46ce9e24d300032c3fdf9d1d63f454aa580a2c833a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TS3pmMCtcswZ+i44M45WLxK0WWKQp9pzNw+L1Anczmg0uyBYEI/xBnHRBe+w4/bHdDwBmXkRl22UejbUkWfcDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:42:41.680042Z","bundle_sha256":"c5512816670eb5fed6b20bf385e98efd270052a621f764a23ea8e8fa1d51ae69"}}