{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KZ5AZ6V4CJCRPEXLQHVZ5YTITJ","short_pith_number":"pith:KZ5AZ6V4","canonical_record":{"source":{"id":"1906.08196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-19T16:16:26Z","cross_cats_sorted":[],"title_canon_sha256":"e433413027e0c9d16924b0f755dfbe03b5bda10ebd52c3d1b04c0ddca7c94017","abstract_canon_sha256":"6c210203d8e390cb6c4b2152bd8eccdba694bc0a8dc1ded7c8b8ef9729af99f5"},"schema_version":"1.0"},"canonical_sha256":"567a0cfabc12451792eb81eb9ee2689a5d23aa82c170839ffe5092c551c6ffdd","source":{"kind":"arxiv","id":"1906.08196","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08196","created_at":"2026-05-17T23:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08196v1","created_at":"2026-05-17T23:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08196","created_at":"2026-05-17T23:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"KZ5AZ6V4CJCR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KZ5AZ6V4CJCRPEXL","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KZ5AZ6V4","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KZ5AZ6V4CJCRPEXLQHVZ5YTITJ","target":"record","payload":{"canonical_record":{"source":{"id":"1906.08196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-19T16:16:26Z","cross_cats_sorted":[],"title_canon_sha256":"e433413027e0c9d16924b0f755dfbe03b5bda10ebd52c3d1b04c0ddca7c94017","abstract_canon_sha256":"6c210203d8e390cb6c4b2152bd8eccdba694bc0a8dc1ded7c8b8ef9729af99f5"},"schema_version":"1.0"},"canonical_sha256":"567a0cfabc12451792eb81eb9ee2689a5d23aa82c170839ffe5092c551c6ffdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:54.338901Z","signature_b64":"rdVfyky+Z+xWLfbjUPCgfNwC0WIS8sB/TyH2in48eQB48nc1HFZqcMo+LAOKu+y+CZgstAdYb1zrYz1xCC1FAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"567a0cfabc12451792eb81eb9ee2689a5d23aa82c170839ffe5092c551c6ffdd","last_reissued_at":"2026-05-17T23:42:54.338263Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:54.338263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.08196","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":"2026-05-17T23:42:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goK1ecgh+t3JdwZWZXLfs5CHxYI5udla9YALlqwFgJ/rEFlFXAgVjo2p/91UsOVfoidh51LFJXUoUfs8tzEdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:15:35.365968Z"},"content_sha256":"8a24a813ea15cf11116ce31f5ba75adc2a044a3944bfa06fabbe55c2e82bf44c","schema_version":"1.0","event_id":"sha256:8a24a813ea15cf11116ce31f5ba75adc2a044a3944bfa06fabbe55c2e82bf44c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KZ5AZ6V4CJCRPEXLQHVZ5YTITJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anticanonical tropical cubic del Pezzos contain exactly 27 lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Anand Deopurkar, Maria Angelica Cueto","submitted_at":"2019-06-19T16:16:26Z","abstract_excerpt":"The classical statement of Cayley-Salmon that there are 27 lines on every smooth cubic surface in P^3 fails to hold under tropicalization: a tropical cubic surface in TP^3 often contains infinitely many tropical lines. Under mild genericity assumptions, we show that when embedded using the Eckardt triangles in the anticanonical system, tropical cubic del Pezzo surfaces contain exactly 27 tropical lines. In the non-generic case, which we identify explicitly, we find up to 27 extra lines, no multiple of which lifts to a curve on the cubic surface.\n  We realize the moduli space of stable anticano"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08196","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":"2026-05-17T23:42:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rqws2O9waq3h3WzosR3U9SWjFzsrBPnyZEok0TYR60YtuHhqcrU4WnbrRQyw+ezong4WSXSyD5rHjurDku9nDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:15:35.366674Z"},"content_sha256":"2c7d1d3b41bee01081a176e5d316e6dbea60d664633ea18cd36ad3025d631b95","schema_version":"1.0","event_id":"sha256:2c7d1d3b41bee01081a176e5d316e6dbea60d664633ea18cd36ad3025d631b95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KZ5AZ6V4CJCRPEXLQHVZ5YTITJ/bundle.json","state_url":"https://pith.science/pith/KZ5AZ6V4CJCRPEXLQHVZ5YTITJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KZ5AZ6V4CJCRPEXLQHVZ5YTITJ/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":"2026-06-08T06:15:35Z","links":{"resolver":"https://pith.science/pith/KZ5AZ6V4CJCRPEXLQHVZ5YTITJ","bundle":"https://pith.science/pith/KZ5AZ6V4CJCRPEXLQHVZ5YTITJ/bundle.json","state":"https://pith.science/pith/KZ5AZ6V4CJCRPEXLQHVZ5YTITJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KZ5AZ6V4CJCRPEXLQHVZ5YTITJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KZ5AZ6V4CJCRPEXLQHVZ5YTITJ","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":"6c210203d8e390cb6c4b2152bd8eccdba694bc0a8dc1ded7c8b8ef9729af99f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-19T16:16:26Z","title_canon_sha256":"e433413027e0c9d16924b0f755dfbe03b5bda10ebd52c3d1b04c0ddca7c94017"},"schema_version":"1.0","source":{"id":"1906.08196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08196","created_at":"2026-05-17T23:42:54Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08196v1","created_at":"2026-05-17T23:42:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08196","created_at":"2026-05-17T23:42:54Z"},{"alias_kind":"pith_short_12","alias_value":"KZ5AZ6V4CJCR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KZ5AZ6V4CJCRPEXL","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KZ5AZ6V4","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:2c7d1d3b41bee01081a176e5d316e6dbea60d664633ea18cd36ad3025d631b95","target":"graph","created_at":"2026-05-17T23:42:54Z","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":"The classical statement of Cayley-Salmon that there are 27 lines on every smooth cubic surface in P^3 fails to hold under tropicalization: a tropical cubic surface in TP^3 often contains infinitely many tropical lines. Under mild genericity assumptions, we show that when embedded using the Eckardt triangles in the anticanonical system, tropical cubic del Pezzo surfaces contain exactly 27 tropical lines. In the non-generic case, which we identify explicitly, we find up to 27 extra lines, no multiple of which lifts to a curve on the cubic surface.\n  We realize the moduli space of stable anticano","authors_text":"Anand Deopurkar, Maria Angelica Cueto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-19T16:16:26Z","title":"Anticanonical tropical cubic del Pezzos contain exactly 27 lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08196","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":"sha256:8a24a813ea15cf11116ce31f5ba75adc2a044a3944bfa06fabbe55c2e82bf44c","target":"record","created_at":"2026-05-17T23:42:54Z","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":"6c210203d8e390cb6c4b2152bd8eccdba694bc0a8dc1ded7c8b8ef9729af99f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-19T16:16:26Z","title_canon_sha256":"e433413027e0c9d16924b0f755dfbe03b5bda10ebd52c3d1b04c0ddca7c94017"},"schema_version":"1.0","source":{"id":"1906.08196","kind":"arxiv","version":1}},"canonical_sha256":"567a0cfabc12451792eb81eb9ee2689a5d23aa82c170839ffe5092c551c6ffdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"567a0cfabc12451792eb81eb9ee2689a5d23aa82c170839ffe5092c551c6ffdd","first_computed_at":"2026-05-17T23:42:54.338263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:54.338263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rdVfyky+Z+xWLfbjUPCgfNwC0WIS8sB/TyH2in48eQB48nc1HFZqcMo+LAOKu+y+CZgstAdYb1zrYz1xCC1FAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:54.338901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.08196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a24a813ea15cf11116ce31f5ba75adc2a044a3944bfa06fabbe55c2e82bf44c","sha256:2c7d1d3b41bee01081a176e5d316e6dbea60d664633ea18cd36ad3025d631b95"],"state_sha256":"78bb56df043e6e2ad58bc6ffdf9e52dd5ba5f46b3e1fc52307154addde518602"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGu+0QJLr/9KokKtrIiO0iLgQOhQ/f2FyhSE5/qXKlMxc7lLCqKXf6QResDX7nqhwfHzQlJDNOC0m0tfHTbBDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T06:15:35.371024Z","bundle_sha256":"feec9139c3ac030c8bd52ba18a6dc11d8d378e7386c615042b672f57396354f9"}}