{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:I2QLUVS6IL2LLY7RQFRBNXUW3W","short_pith_number":"pith:I2QLUVS6","canonical_record":{"source":{"id":"1504.01722","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-07T19:56:53Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"3df2049199b9e3f20d61267a57716cfdae75d58b4a29c6aed64e2fcfb6e53973","abstract_canon_sha256":"4ecc0bd60e3b7858b9fc350e3046fd5635077bddb79720b31b77333f6f381998"},"schema_version":"1.0"},"canonical_sha256":"46a0ba565e42f4b5e3f1816216de96ddb3e5c606da8c1bb4441e8cc75bf402c3","source":{"kind":"arxiv","id":"1504.01722","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01722","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01722v3","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01722","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"pith_short_12","alias_value":"I2QLUVS6IL2L","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I2QLUVS6IL2LLY7R","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I2QLUVS6","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:I2QLUVS6IL2LLY7RQFRBNXUW3W","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01722","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-07T19:56:53Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"3df2049199b9e3f20d61267a57716cfdae75d58b4a29c6aed64e2fcfb6e53973","abstract_canon_sha256":"4ecc0bd60e3b7858b9fc350e3046fd5635077bddb79720b31b77333f6f381998"},"schema_version":"1.0"},"canonical_sha256":"46a0ba565e42f4b5e3f1816216de96ddb3e5c606da8c1bb4441e8cc75bf402c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:21.299986Z","signature_b64":"tmyhmYIw3CWAvzgrsRalJuewVIZncTw9PVmmvUbyPn7QfwNQwe4dPCsa0EAUJAC97yWdFgw7F5EAfjwmPJrHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46a0ba565e42f4b5e3f1816216de96ddb3e5c606da8c1bb4441e8cc75bf402c3","last_reissued_at":"2026-05-18T01:08:21.299342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:21.299342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01722","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":"2026-05-18T01:08:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y6VeapBsxZ3M7dUwgBceq/fcBIBbSe7qV/+JfMTIgetQ78jT/OJiSYabCoqmkHPyi77L0Q251j3ga0abhRskAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T00:08:44.749699Z"},"content_sha256":"641c1cc59686f29f1b12f5f605774cea8c4826b506d1a91c7aa6b143ab44406f","schema_version":"1.0","event_id":"sha256:641c1cc59686f29f1b12f5f605774cea8c4826b506d1a91c7aa6b143ab44406f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:I2QLUVS6IL2LLY7RQFRBNXUW3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Tony Yue Yu","submitted_at":"2015-04-07T19:56:53Z","abstract_excerpt":"We define the counting of holomorphic cylinders in log Calabi-Yau surfaces. Although we start with a complex log Calabi-Yau surface, the counting is achieved by applying methods from non-archimedean geometry. This gives rise to new geometric invariants. Moreover, we prove that the counting satisfies a property of symmetry. Explicit calculations are given for a del Pezzo surface in detail, which verify the conjectured wall-crossing formula for the focus-focus singularity. Our holomorphic cylinders are expected to give a geometric understanding of the combinatorial notion of broken line by Gross"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01722","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":"2026-05-18T01:08:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5oeSIajVjty8oQCuaxCQaLbW+TzTTrkKW9e7VYc+TTHwKSYHVaoPkZ2D6+FedEstixxFHBwJx+ouQm8h+Y63DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T00:08:44.750053Z"},"content_sha256":"fc9d1253f08fff751caad0c855aa9cdc97ab8575ebf290598491057aa0db7577","schema_version":"1.0","event_id":"sha256:fc9d1253f08fff751caad0c855aa9cdc97ab8575ebf290598491057aa0db7577"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2QLUVS6IL2LLY7RQFRBNXUW3W/bundle.json","state_url":"https://pith.science/pith/I2QLUVS6IL2LLY7RQFRBNXUW3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2QLUVS6IL2LLY7RQFRBNXUW3W/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":"2026-07-01T00:08:44Z","links":{"resolver":"https://pith.science/pith/I2QLUVS6IL2LLY7RQFRBNXUW3W","bundle":"https://pith.science/pith/I2QLUVS6IL2LLY7RQFRBNXUW3W/bundle.json","state":"https://pith.science/pith/I2QLUVS6IL2LLY7RQFRBNXUW3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2QLUVS6IL2LLY7RQFRBNXUW3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I2QLUVS6IL2LLY7RQFRBNXUW3W","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":"4ecc0bd60e3b7858b9fc350e3046fd5635077bddb79720b31b77333f6f381998","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-07T19:56:53Z","title_canon_sha256":"3df2049199b9e3f20d61267a57716cfdae75d58b4a29c6aed64e2fcfb6e53973"},"schema_version":"1.0","source":{"id":"1504.01722","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01722","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01722v3","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01722","created_at":"2026-05-18T01:08:21Z"},{"alias_kind":"pith_short_12","alias_value":"I2QLUVS6IL2L","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I2QLUVS6IL2LLY7R","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I2QLUVS6","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:fc9d1253f08fff751caad0c855aa9cdc97ab8575ebf290598491057aa0db7577","target":"graph","created_at":"2026-05-18T01:08:21Z","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 define the counting of holomorphic cylinders in log Calabi-Yau surfaces. Although we start with a complex log Calabi-Yau surface, the counting is achieved by applying methods from non-archimedean geometry. This gives rise to new geometric invariants. Moreover, we prove that the counting satisfies a property of symmetry. Explicit calculations are given for a del Pezzo surface in detail, which verify the conjectured wall-crossing formula for the focus-focus singularity. Our holomorphic cylinders are expected to give a geometric understanding of the combinatorial notion of broken line by Gross","authors_text":"Tony Yue Yu","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-07T19:56:53Z","title":"Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01722","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":"sha256:641c1cc59686f29f1b12f5f605774cea8c4826b506d1a91c7aa6b143ab44406f","target":"record","created_at":"2026-05-18T01:08:21Z","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":"4ecc0bd60e3b7858b9fc350e3046fd5635077bddb79720b31b77333f6f381998","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-07T19:56:53Z","title_canon_sha256":"3df2049199b9e3f20d61267a57716cfdae75d58b4a29c6aed64e2fcfb6e53973"},"schema_version":"1.0","source":{"id":"1504.01722","kind":"arxiv","version":3}},"canonical_sha256":"46a0ba565e42f4b5e3f1816216de96ddb3e5c606da8c1bb4441e8cc75bf402c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46a0ba565e42f4b5e3f1816216de96ddb3e5c606da8c1bb4441e8cc75bf402c3","first_computed_at":"2026-05-18T01:08:21.299342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:21.299342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tmyhmYIw3CWAvzgrsRalJuewVIZncTw9PVmmvUbyPn7QfwNQwe4dPCsa0EAUJAC97yWdFgw7F5EAfjwmPJrHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:21.299986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01722","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:641c1cc59686f29f1b12f5f605774cea8c4826b506d1a91c7aa6b143ab44406f","sha256:fc9d1253f08fff751caad0c855aa9cdc97ab8575ebf290598491057aa0db7577"],"state_sha256":"5c100c6f768f2712230d829da299a186a87332c7ab2acf3bb13420cc4ef602ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vpbkNxii4BneaVONHUGpqCeOYS6YArU6f65NndFM2Htv9gSyKq+o+V3NT4NWLcuwx3sIFX/T2qXLlGSTuB09DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T00:08:44.752203Z","bundle_sha256":"8dbd977c0b93e2f461bac93f65d5f23ed163bbe71d05bcef84b5351279c6b175"}}