{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PNROZOAOCY7LHURNPRMGIION7U","short_pith_number":"pith:PNROZOAO","canonical_record":{"source":{"id":"1108.2802","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-13T15:09:09Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"8f50900994c7a8b4a1931d461cb911ea11e8be18a7390165e538f8f32bdd9bd2","abstract_canon_sha256":"b29582bb6088bfada4be359e0e0bcc4eda4ed5266e2c22c8478fc319c0d802bd"},"schema_version":"1.0"},"canonical_sha256":"7b62ecb80e163eb3d22d7c586421cdfd3c6bee60e31500e9558b010b523bbb97","source":{"kind":"arxiv","id":"1108.2802","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2802","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2802v3","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2802","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"PNROZOAOCY7L","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PNROZOAOCY7LHURN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PNROZOAO","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PNROZOAOCY7LHURNPRMGIION7U","target":"record","payload":{"canonical_record":{"source":{"id":"1108.2802","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-13T15:09:09Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"8f50900994c7a8b4a1931d461cb911ea11e8be18a7390165e538f8f32bdd9bd2","abstract_canon_sha256":"b29582bb6088bfada4be359e0e0bcc4eda4ed5266e2c22c8478fc319c0d802bd"},"schema_version":"1.0"},"canonical_sha256":"7b62ecb80e163eb3d22d7c586421cdfd3c6bee60e31500e9558b010b523bbb97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:55.832885Z","signature_b64":"u8EDBhq0bGnZnftp4pNiJzajsV6tytUmBOh1k4sfEcFI660ywZEJ4XZicp4VgrJacY+HJn51dYIfOxG4vQV5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b62ecb80e163eb3d22d7c586421cdfd3c6bee60e31500e9558b010b523bbb97","last_reissued_at":"2026-05-18T01:30:55.832397Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:55.832397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.2802","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bBGPGmUPpJVeGNG38w0v7gNhnw/vEDAq7DNtb7jI4x96z1OMJX3Q7raxKjfnbVIQnIJoSGSqhVKGlsfvOEg1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:13:56.351909Z"},"content_sha256":"f9f16637ad14a861a5990dd72a22c575949a0d4cc48a685db51927224318a1a1","schema_version":"1.0","event_id":"sha256:f9f16637ad14a861a5990dd72a22c575949a0d4cc48a685db51927224318a1a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PNROZOAOCY7LHURNPRMGIION7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting curves via degeneration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Takeo Nishinou","submitted_at":"2011-08-13T15:09:09Z","abstract_excerpt":"We develop a technique to study curves in a variety which has a degeneration into some union of varieties. The class of such varieties is very broad, but the theory becomes particularly useful when the variety has a degeneration into a union of toric varieties. Hypersurfaces are typical examples, and we study lines on K3 surfaces and quintic Calabi-Yau hypersurfaces in detail. In particular, we combinatorially prove the existence of 2875 lines in a generic quintic Calabi-Yau 3-fold. Also, we give a geometric construction of walls in the Gross-Siebert construction of Calabi-Yau varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2802","kind":"arxiv","version":3},"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":"2026-05-18T01:30:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4o40tE0Xe7gPg00EWEqd2RChpdAUmKPbFD0hwqyThS01qikf7hzcRHh2558W3ccbh3FWFEGSStzO5jnZAwlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:13:56.352255Z"},"content_sha256":"a7a715c4d1f1b6b3a1e41e40760570d0e6c4ab07d789cde7b2f93e8ae4ea1dae","schema_version":"1.0","event_id":"sha256:a7a715c4d1f1b6b3a1e41e40760570d0e6c4ab07d789cde7b2f93e8ae4ea1dae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PNROZOAOCY7LHURNPRMGIION7U/bundle.json","state_url":"https://pith.science/pith/PNROZOAOCY7LHURNPRMGIION7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PNROZOAOCY7LHURNPRMGIION7U/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":"2026-06-09T13:13:56Z","links":{"resolver":"https://pith.science/pith/PNROZOAOCY7LHURNPRMGIION7U","bundle":"https://pith.science/pith/PNROZOAOCY7LHURNPRMGIION7U/bundle.json","state":"https://pith.science/pith/PNROZOAOCY7LHURNPRMGIION7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PNROZOAOCY7LHURNPRMGIION7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PNROZOAOCY7LHURNPRMGIION7U","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":"b29582bb6088bfada4be359e0e0bcc4eda4ed5266e2c22c8478fc319c0d802bd","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-13T15:09:09Z","title_canon_sha256":"8f50900994c7a8b4a1931d461cb911ea11e8be18a7390165e538f8f32bdd9bd2"},"schema_version":"1.0","source":{"id":"1108.2802","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.2802","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"arxiv_version","alias_value":"1108.2802v3","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2802","created_at":"2026-05-18T01:30:55Z"},{"alias_kind":"pith_short_12","alias_value":"PNROZOAOCY7L","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PNROZOAOCY7LHURN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PNROZOAO","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:a7a715c4d1f1b6b3a1e41e40760570d0e6c4ab07d789cde7b2f93e8ae4ea1dae","target":"graph","created_at":"2026-05-18T01:30:55Z","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 develop a technique to study curves in a variety which has a degeneration into some union of varieties. The class of such varieties is very broad, but the theory becomes particularly useful when the variety has a degeneration into a union of toric varieties. Hypersurfaces are typical examples, and we study lines on K3 surfaces and quintic Calabi-Yau hypersurfaces in detail. In particular, we combinatorially prove the existence of 2875 lines in a generic quintic Calabi-Yau 3-fold. Also, we give a geometric construction of walls in the Gross-Siebert construction of Calabi-Yau varieties.","authors_text":"Takeo Nishinou","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-13T15:09:09Z","title":"Counting curves via degeneration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2802","kind":"arxiv","version":3},"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:f9f16637ad14a861a5990dd72a22c575949a0d4cc48a685db51927224318a1a1","target":"record","created_at":"2026-05-18T01:30:55Z","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":"b29582bb6088bfada4be359e0e0bcc4eda4ed5266e2c22c8478fc319c0d802bd","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-08-13T15:09:09Z","title_canon_sha256":"8f50900994c7a8b4a1931d461cb911ea11e8be18a7390165e538f8f32bdd9bd2"},"schema_version":"1.0","source":{"id":"1108.2802","kind":"arxiv","version":3}},"canonical_sha256":"7b62ecb80e163eb3d22d7c586421cdfd3c6bee60e31500e9558b010b523bbb97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b62ecb80e163eb3d22d7c586421cdfd3c6bee60e31500e9558b010b523bbb97","first_computed_at":"2026-05-18T01:30:55.832397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:55.832397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u8EDBhq0bGnZnftp4pNiJzajsV6tytUmBOh1k4sfEcFI660ywZEJ4XZicp4VgrJacY+HJn51dYIfOxG4vQV5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:55.832885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.2802","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9f16637ad14a861a5990dd72a22c575949a0d4cc48a685db51927224318a1a1","sha256:a7a715c4d1f1b6b3a1e41e40760570d0e6c4ab07d789cde7b2f93e8ae4ea1dae"],"state_sha256":"1dfa8d5e5236f30fc844621f553dcfdd74738d22dfc205c056b8ba045d41cc17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kjnNRHBgZeIQj/1FoUBpsSWB34WHF6jenaMaw3MAi3Ns3VYzOU9rn1YkYiD/6fvOowxpY3c527uoBsOXoZNsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:13:56.354217Z","bundle_sha256":"1f6df2c05a86f8debb01ad0a9205b1cb918071d568c6a5edd52669634906d0e4"}}