{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:4DZXV3QJRKIKFBSBCM4GQ3EQWW","short_pith_number":"pith:4DZXV3QJ","canonical_record":{"source":{"id":"hep-th/9704129","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1997-04-16T21:54:34Z","cross_cats_sorted":[],"title_canon_sha256":"9f69a10f6921d1fb1822098dcb6861b0fa1ea2359c6640e88da8e4e095bf00da","abstract_canon_sha256":"288573b3daa32b96c6061d9f3d448c17e1b9cb75f774cc4203be48cc440973ae"},"schema_version":"1.0"},"canonical_sha256":"e0f37aee098a90a286411338686c90b5b1175d94ea799abf4d97fb8c2d342247","source":{"kind":"arxiv","id":"hep-th/9704129","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9704129","created_at":"2026-05-18T02:36:02Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9704129v2","created_at":"2026-05-18T02:36:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9704129","created_at":"2026-05-18T02:36:02Z"},{"alias_kind":"pith_short_12","alias_value":"4DZXV3QJRKIK","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"4DZXV3QJRKIKFBSB","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"4DZXV3QJ","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:4DZXV3QJRKIKFBSBCM4GQ3EQWW","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9704129","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1997-04-16T21:54:34Z","cross_cats_sorted":[],"title_canon_sha256":"9f69a10f6921d1fb1822098dcb6861b0fa1ea2359c6640e88da8e4e095bf00da","abstract_canon_sha256":"288573b3daa32b96c6061d9f3d448c17e1b9cb75f774cc4203be48cc440973ae"},"schema_version":"1.0"},"canonical_sha256":"e0f37aee098a90a286411338686c90b5b1175d94ea799abf4d97fb8c2d342247","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:36:02.444678Z","signature_b64":"f0HPpp//VLeRinjVPf7LCLFmgahPEEoRSSLFh/bQXV2XSnxzoxVitwNSIhd0Oi0c+yMYmm9wlPmDNrNkEkJZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0f37aee098a90a286411338686c90b5b1175d94ea799abf4d97fb8c2d342247","last_reissued_at":"2026-05-18T02:36:02.443966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:36:02.443966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9704129","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":"2026-05-18T02:36:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szzsa6iAWnWCotyP+rHtBOZ/+8wuRdpmNOq1HLIW+veuxxXy4lreAqRCLtdYpgQjKggNFRYzn1NPJyVt93RtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:30:59.416527Z"},"content_sha256":"b312ef40c69a80b734eae2eae69853813e958cd0fb5060fc4b728dc4b4479c9f","schema_version":"1.0","event_id":"sha256:b312ef40c69a80b734eae2eae69853813e958cd0fb5060fc4b728dc4b4479c9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:4DZXV3QJRKIKFBSBCM4GQ3EQWW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enhanced Gauge Symmetry in Type II and F-Theory Compactifications: Dynkin Diagrams from Polyhedra","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Eugene Perevalov, Harald Skarke","submitted_at":"1997-04-16T21:54:34Z","abstract_excerpt":"We explain the observation by Candelas and Font that the Dynkin diagrams of nonabelian gauge groups occurring in type IIA and F-theory can be read off from the polyhedron $\\Delta^*$ that provides the toric description of the Calabi-Yau manifold used for compacification. We show how the intersection pattern of toric divisors corresponding to the degeneration of elliptic fibers follows the ADE classification of singularities and the Kodaira classification of degenerations. We treat in detail the cases of elliptic K3 surfaces and K3 fibered threefolds where the fiber is again elliptic. We also ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9704129","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":""},"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":"2026-05-18T02:36:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uA2nlmn+vvz4M4B0r9duGbWEDnXZIVXCYp1wn42djsjmZ71whZzKyvZD3x379lKvuNAFalqdrdXNJIAB/eynBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:30:59.416884Z"},"content_sha256":"32febb9f6f4863c11cfab14eb89a650d0e692ea75052f55a4a6fbc90991624fa","schema_version":"1.0","event_id":"sha256:32febb9f6f4863c11cfab14eb89a650d0e692ea75052f55a4a6fbc90991624fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4DZXV3QJRKIKFBSBCM4GQ3EQWW/bundle.json","state_url":"https://pith.science/pith/4DZXV3QJRKIKFBSBCM4GQ3EQWW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4DZXV3QJRKIKFBSBCM4GQ3EQWW/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":"2026-05-31T22:30:59Z","links":{"resolver":"https://pith.science/pith/4DZXV3QJRKIKFBSBCM4GQ3EQWW","bundle":"https://pith.science/pith/4DZXV3QJRKIKFBSBCM4GQ3EQWW/bundle.json","state":"https://pith.science/pith/4DZXV3QJRKIKFBSBCM4GQ3EQWW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4DZXV3QJRKIKFBSBCM4GQ3EQWW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:4DZXV3QJRKIKFBSBCM4GQ3EQWW","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":"288573b3daa32b96c6061d9f3d448c17e1b9cb75f774cc4203be48cc440973ae","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1997-04-16T21:54:34Z","title_canon_sha256":"9f69a10f6921d1fb1822098dcb6861b0fa1ea2359c6640e88da8e4e095bf00da"},"schema_version":"1.0","source":{"id":"hep-th/9704129","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9704129","created_at":"2026-05-18T02:36:02Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9704129v2","created_at":"2026-05-18T02:36:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9704129","created_at":"2026-05-18T02:36:02Z"},{"alias_kind":"pith_short_12","alias_value":"4DZXV3QJRKIK","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"4DZXV3QJRKIKFBSB","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"4DZXV3QJ","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:32febb9f6f4863c11cfab14eb89a650d0e692ea75052f55a4a6fbc90991624fa","target":"graph","created_at":"2026-05-18T02:36:02Z","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":"We explain the observation by Candelas and Font that the Dynkin diagrams of nonabelian gauge groups occurring in type IIA and F-theory can be read off from the polyhedron $\\Delta^*$ that provides the toric description of the Calabi-Yau manifold used for compacification. We show how the intersection pattern of toric divisors corresponding to the degeneration of elliptic fibers follows the ADE classification of singularities and the Kodaira classification of degenerations. We treat in detail the cases of elliptic K3 surfaces and K3 fibered threefolds where the fiber is again elliptic. We also ex","authors_text":"Eugene Perevalov, Harald Skarke","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1997-04-16T21:54:34Z","title":"Enhanced Gauge Symmetry in Type II and F-Theory Compactifications: Dynkin Diagrams from Polyhedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9704129","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:b312ef40c69a80b734eae2eae69853813e958cd0fb5060fc4b728dc4b4479c9f","target":"record","created_at":"2026-05-18T02:36:02Z","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":"288573b3daa32b96c6061d9f3d448c17e1b9cb75f774cc4203be48cc440973ae","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1997-04-16T21:54:34Z","title_canon_sha256":"9f69a10f6921d1fb1822098dcb6861b0fa1ea2359c6640e88da8e4e095bf00da"},"schema_version":"1.0","source":{"id":"hep-th/9704129","kind":"arxiv","version":2}},"canonical_sha256":"e0f37aee098a90a286411338686c90b5b1175d94ea799abf4d97fb8c2d342247","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0f37aee098a90a286411338686c90b5b1175d94ea799abf4d97fb8c2d342247","first_computed_at":"2026-05-18T02:36:02.443966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:36:02.443966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f0HPpp//VLeRinjVPf7LCLFmgahPEEoRSSLFh/bQXV2XSnxzoxVitwNSIhd0Oi0c+yMYmm9wlPmDNrNkEkJZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:36:02.444678Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9704129","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b312ef40c69a80b734eae2eae69853813e958cd0fb5060fc4b728dc4b4479c9f","sha256:32febb9f6f4863c11cfab14eb89a650d0e692ea75052f55a4a6fbc90991624fa"],"state_sha256":"4ceb5c81f62929c21f6b0460abf2661ebfecc4fe86d5e72c8ccce0c55861b5a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XmVIQLZ8D0GmSgCPIboJNBgw5I+aN0tZUhTJ9VybV0oXTeotfJIMNelfjH+Q1vLMwqiq2kBKQ67yQtFkgteRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:30:59.419387Z","bundle_sha256":"25542f18b472b92e81548a588bd78a6a4763c0a62c1014d041ae1fe0d7ea38de"}}