{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:DRREWCIQ2M72L6LSWVCELXSUKX","short_pith_number":"pith:DRREWCIQ","canonical_record":{"source":{"id":"0809.1620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-09-09T17:53:00Z","cross_cats_sorted":[],"title_canon_sha256":"5583442ef711922f83877b05f4f3a7c2a79e9896041b2fe6fba1f064a41fabe7","abstract_canon_sha256":"d3651e45b11a681fceeab62f2506dd9d9c9919d919900e21f7d4117fe41926d2"},"schema_version":"1.0"},"canonical_sha256":"1c624b0910d33fa5f972b54445de5455f6025e07f14fc4d0481cf7969b9e09ec","source":{"kind":"arxiv","id":"0809.1620","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.1620","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"0809.1620v1","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1620","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"DRREWCIQ2M72","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DRREWCIQ2M72L6LS","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DRREWCIQ","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:DRREWCIQ2M72L6LSWVCELXSUKX","target":"record","payload":{"canonical_record":{"source":{"id":"0809.1620","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-09-09T17:53:00Z","cross_cats_sorted":[],"title_canon_sha256":"5583442ef711922f83877b05f4f3a7c2a79e9896041b2fe6fba1f064a41fabe7","abstract_canon_sha256":"d3651e45b11a681fceeab62f2506dd9d9c9919d919900e21f7d4117fe41926d2"},"schema_version":"1.0"},"canonical_sha256":"1c624b0910d33fa5f972b54445de5455f6025e07f14fc4d0481cf7969b9e09ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:32.492860Z","signature_b64":"GyJO4OW14agz3uNNrGPsEtWoesM9zGur+VQce8JCgok/YHBy9noL75zGfF7/v9fSp/W4xOwbuGYpSgIi7Eb1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c624b0910d33fa5f972b54445de5455f6025e07f14fc4d0481cf7969b9e09ec","last_reissued_at":"2026-05-18T04:16:32.492471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:32.492471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.1620","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":"2026-05-18T04:16:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+MDSf0yxSPoJpAIpyX0Mx+K+lUTxrJQFGzDSac295X4wYEFLMTf99Ht/+gGCo2yUwFnFfhi6kwbcpGk0xPWAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:54:31.270040Z"},"content_sha256":"c7b058894c1313612ec369ee7adf9671eba2cb390cf6b47f716201c6d069f42c","schema_version":"1.0","event_id":"sha256:c7b058894c1313612ec369ee7adf9671eba2cb390cf6b47f716201c6d069f42c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:DRREWCIQ2M72L6LSWVCELXSUKX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Torus actions on small blow ups of CP^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Liat Kessler","submitted_at":"2008-09-09T17:53:00Z","abstract_excerpt":"A manifold obtained by k simultaneous symplectic blow-ups of CP^2 of equal sizes epsilon (where the size of CP^1 in CP^2 is one) admits an effective two-dimensional torus action if k <= 3. We show that it does not admit such an action if k >=4 and epsilon <= 1/(3k 2^{2k}). For the proof, we correspond between the geometry of a symplectic toric four-manifold and the combinatorics of its moment map image. We also use techniques from the theory of J-holomorphic curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1620","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":"2026-05-18T04:16:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXNUjX1u5EScxLVrX+w5P3SV/oH4pjbseAaMWEWsp9sCnTSEd2IKk0cr8I5bPBAHmxKbH660jGGBbFEbqeysDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T18:54:31.270392Z"},"content_sha256":"8034c5933a2ed8d6c96f22e51377d0cdb20ee8124e17749ec27572dd14b4edf4","schema_version":"1.0","event_id":"sha256:8034c5933a2ed8d6c96f22e51377d0cdb20ee8124e17749ec27572dd14b4edf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DRREWCIQ2M72L6LSWVCELXSUKX/bundle.json","state_url":"https://pith.science/pith/DRREWCIQ2M72L6LSWVCELXSUKX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DRREWCIQ2M72L6LSWVCELXSUKX/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":"2026-06-20T18:54:31Z","links":{"resolver":"https://pith.science/pith/DRREWCIQ2M72L6LSWVCELXSUKX","bundle":"https://pith.science/pith/DRREWCIQ2M72L6LSWVCELXSUKX/bundle.json","state":"https://pith.science/pith/DRREWCIQ2M72L6LSWVCELXSUKX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DRREWCIQ2M72L6LSWVCELXSUKX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:DRREWCIQ2M72L6LSWVCELXSUKX","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":"d3651e45b11a681fceeab62f2506dd9d9c9919d919900e21f7d4117fe41926d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-09-09T17:53:00Z","title_canon_sha256":"5583442ef711922f83877b05f4f3a7c2a79e9896041b2fe6fba1f064a41fabe7"},"schema_version":"1.0","source":{"id":"0809.1620","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.1620","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"arxiv_version","alias_value":"0809.1620v1","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1620","created_at":"2026-05-18T04:16:32Z"},{"alias_kind":"pith_short_12","alias_value":"DRREWCIQ2M72","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DRREWCIQ2M72L6LS","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DRREWCIQ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:8034c5933a2ed8d6c96f22e51377d0cdb20ee8124e17749ec27572dd14b4edf4","target":"graph","created_at":"2026-05-18T04:16:32Z","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":"A manifold obtained by k simultaneous symplectic blow-ups of CP^2 of equal sizes epsilon (where the size of CP^1 in CP^2 is one) admits an effective two-dimensional torus action if k <= 3. We show that it does not admit such an action if k >=4 and epsilon <= 1/(3k 2^{2k}). For the proof, we correspond between the geometry of a symplectic toric four-manifold and the combinatorics of its moment map image. We also use techniques from the theory of J-holomorphic curves.","authors_text":"Liat Kessler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-09-09T17:53:00Z","title":"Torus actions on small blow ups of CP^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1620","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:c7b058894c1313612ec369ee7adf9671eba2cb390cf6b47f716201c6d069f42c","target":"record","created_at":"2026-05-18T04:16:32Z","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":"d3651e45b11a681fceeab62f2506dd9d9c9919d919900e21f7d4117fe41926d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2008-09-09T17:53:00Z","title_canon_sha256":"5583442ef711922f83877b05f4f3a7c2a79e9896041b2fe6fba1f064a41fabe7"},"schema_version":"1.0","source":{"id":"0809.1620","kind":"arxiv","version":1}},"canonical_sha256":"1c624b0910d33fa5f972b54445de5455f6025e07f14fc4d0481cf7969b9e09ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c624b0910d33fa5f972b54445de5455f6025e07f14fc4d0481cf7969b9e09ec","first_computed_at":"2026-05-18T04:16:32.492471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:32.492471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GyJO4OW14agz3uNNrGPsEtWoesM9zGur+VQce8JCgok/YHBy9noL75zGfF7/v9fSp/W4xOwbuGYpSgIi7Eb1DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:32.492860Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.1620","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7b058894c1313612ec369ee7adf9671eba2cb390cf6b47f716201c6d069f42c","sha256:8034c5933a2ed8d6c96f22e51377d0cdb20ee8124e17749ec27572dd14b4edf4"],"state_sha256":"5f9ff1334afeb98fb9ed4d33ec9065b8cbec9bf57c040d8da3e94a307147a419"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8r/VrYbsg94u+qkoLJd0kE7Mtnj/i8Di2w4CQLzOo9yHNvbXeRn78054gwR561L0vc4qoo8FunTmHuJSksJaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T18:54:31.272310Z","bundle_sha256":"478d61b0dd1105d44c511cd9fff1b7785d91451f94cea9cedef0f0f9d1a76593"}}