{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DTG3P4CCBXD2SQJ2X7MRPJJTC4","short_pith_number":"pith:DTG3P4CC","canonical_record":{"source":{"id":"1707.05704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T15:49:52Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"dcc5ac52e9b1c11cdb31fe5c19523b3755419d44926a113498f28c8fb69eb93e","abstract_canon_sha256":"acd34860e12f4c41c74da717cca227e3d283bd3ef4ed293e5b906dedcea4f375"},"schema_version":"1.0"},"canonical_sha256":"1ccdb7f0420dc7a9413abfd917a5331716efd3e98123f63ec75356b177ffda89","source":{"kind":"arxiv","id":"1707.05704","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05704","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05704v1","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05704","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"DTG3P4CCBXD2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTG3P4CCBXD2SQJ2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTG3P4CC","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DTG3P4CCBXD2SQJ2X7MRPJJTC4","target":"record","payload":{"canonical_record":{"source":{"id":"1707.05704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T15:49:52Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"dcc5ac52e9b1c11cdb31fe5c19523b3755419d44926a113498f28c8fb69eb93e","abstract_canon_sha256":"acd34860e12f4c41c74da717cca227e3d283bd3ef4ed293e5b906dedcea4f375"},"schema_version":"1.0"},"canonical_sha256":"1ccdb7f0420dc7a9413abfd917a5331716efd3e98123f63ec75356b177ffda89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:01.682487Z","signature_b64":"LvNmfXJqTA9OTNYQxulHFuLzHmiZpG4js/lyi0JGTYKeZKNiE6rtaumyWmbZ2R7IR6lKJItXq8cs1+DsmqW6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ccdb7f0420dc7a9413abfd917a5331716efd3e98123f63ec75356b177ffda89","last_reissued_at":"2026-05-18T00:40:01.681930Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:01.681930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.05704","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":"2026-05-18T00:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Cnw0MHGYu84MIaP1XWYfofq0xCrXcABhzMWPBZIFSbtSk8hqCWyzVqRQ09GyOT6SJxhWEh6Ld5W+yV3YwlNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:52:19.431794Z"},"content_sha256":"42b33b5a7b780a6cab9a712c2eefc7a9e3fc96f515b87546f8b39a4879827bb9","schema_version":"1.0","event_id":"sha256:42b33b5a7b780a6cab9a712c2eefc7a9e3fc96f515b87546f8b39a4879827bb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DTG3P4CCBXD2SQJ2X7MRPJJTC4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toric Cycles in the Complement of a Complex Curve in $(\\mathbb{C}^{\\times})^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Alexey Lushin, Dmitry Pochekutov","submitted_at":"2017-07-18T15:49:52Z","abstract_excerpt":"The amoeba of a complex curve in the 2-dimensional complex torus is its image under the projection onto the real subspace in the logarithmic scale. The complement to an amoeba is a disjoint union of connected components that are open and convex. A toric cycle is a 2-cycle in the complement to a curve associated with a component of the complement to an amoeba. We prove homological independence of toric cycles in the complement to a complex algebraic curve with amoeba of maximal area."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05704","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":"2026-05-18T00:40:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1UsKD1/wFYICvXDEW5E6PXdQGe9ag/pjgxPpVRiLNZqWGvCWXXfiRIdvBJCHueILWo9VSm+eevuifYiUKCXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:52:19.432421Z"},"content_sha256":"cf9f55d84b47bfc8c0b488d99f7397b5bbbd29752ba0b88c39ecb939ea2aa735","schema_version":"1.0","event_id":"sha256:cf9f55d84b47bfc8c0b488d99f7397b5bbbd29752ba0b88c39ecb939ea2aa735"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTG3P4CCBXD2SQJ2X7MRPJJTC4/bundle.json","state_url":"https://pith.science/pith/DTG3P4CCBXD2SQJ2X7MRPJJTC4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTG3P4CCBXD2SQJ2X7MRPJJTC4/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":"2026-06-08T17:52:19Z","links":{"resolver":"https://pith.science/pith/DTG3P4CCBXD2SQJ2X7MRPJJTC4","bundle":"https://pith.science/pith/DTG3P4CCBXD2SQJ2X7MRPJJTC4/bundle.json","state":"https://pith.science/pith/DTG3P4CCBXD2SQJ2X7MRPJJTC4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTG3P4CCBXD2SQJ2X7MRPJJTC4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DTG3P4CCBXD2SQJ2X7MRPJJTC4","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":"acd34860e12f4c41c74da717cca227e3d283bd3ef4ed293e5b906dedcea4f375","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T15:49:52Z","title_canon_sha256":"dcc5ac52e9b1c11cdb31fe5c19523b3755419d44926a113498f28c8fb69eb93e"},"schema_version":"1.0","source":{"id":"1707.05704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05704","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05704v1","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05704","created_at":"2026-05-18T00:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"DTG3P4CCBXD2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTG3P4CCBXD2SQJ2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTG3P4CC","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:cf9f55d84b47bfc8c0b488d99f7397b5bbbd29752ba0b88c39ecb939ea2aa735","target":"graph","created_at":"2026-05-18T00:40:01Z","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 amoeba of a complex curve in the 2-dimensional complex torus is its image under the projection onto the real subspace in the logarithmic scale. The complement to an amoeba is a disjoint union of connected components that are open and convex. A toric cycle is a 2-cycle in the complement to a curve associated with a component of the complement to an amoeba. We prove homological independence of toric cycles in the complement to a complex algebraic curve with amoeba of maximal area.","authors_text":"Alexey Lushin, Dmitry Pochekutov","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T15:49:52Z","title":"Toric Cycles in the Complement of a Complex Curve in $(\\mathbb{C}^{\\times})^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05704","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":"sha256:42b33b5a7b780a6cab9a712c2eefc7a9e3fc96f515b87546f8b39a4879827bb9","target":"record","created_at":"2026-05-18T00:40:01Z","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":"acd34860e12f4c41c74da717cca227e3d283bd3ef4ed293e5b906dedcea4f375","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-18T15:49:52Z","title_canon_sha256":"dcc5ac52e9b1c11cdb31fe5c19523b3755419d44926a113498f28c8fb69eb93e"},"schema_version":"1.0","source":{"id":"1707.05704","kind":"arxiv","version":1}},"canonical_sha256":"1ccdb7f0420dc7a9413abfd917a5331716efd3e98123f63ec75356b177ffda89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ccdb7f0420dc7a9413abfd917a5331716efd3e98123f63ec75356b177ffda89","first_computed_at":"2026-05-18T00:40:01.681930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:01.681930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LvNmfXJqTA9OTNYQxulHFuLzHmiZpG4js/lyi0JGTYKeZKNiE6rtaumyWmbZ2R7IR6lKJItXq8cs1+DsmqW6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:01.682487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42b33b5a7b780a6cab9a712c2eefc7a9e3fc96f515b87546f8b39a4879827bb9","sha256:cf9f55d84b47bfc8c0b488d99f7397b5bbbd29752ba0b88c39ecb939ea2aa735"],"state_sha256":"2ef4fffe9c2bcbad2603dd5ba994d4c6571094a4e128705428b623af180f1563"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6zT/+9R1judQtT0KUUPUfiEu5+N8dR0m+bA6txp533zwDPNYR5bCITdzq/waIhaB8q/WZ2WY6L/M/zHrADeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:52:19.436528Z","bundle_sha256":"aaedd4947f167239edd379892fdb544dde2dea7319c95ce900277d94ca5532e7"}}