{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MDUBHYDP3LIHCGCENQKMUMS7JG","short_pith_number":"pith:MDUBHYDP","canonical_record":{"source":{"id":"1309.0056","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-31T02:49:30Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"f1ce2a205be29cb1d50646d7d3136aa6a8a3a6b607aa7c4ec979b0f1900789be","abstract_canon_sha256":"5246761c8dbad1f22aed52a05f13549d58ff0547c9318a723affef307b19d6ee"},"schema_version":"1.0"},"canonical_sha256":"60e813e06fdad07118446c14ca325f4992f0cbd5af665e078a49c25a844db835","source":{"kind":"arxiv","id":"1309.0056","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0056","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0056v4","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0056","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"MDUBHYDP3LIH","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MDUBHYDP3LIHCGCE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MDUBHYDP","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MDUBHYDP3LIHCGCENQKMUMS7JG","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0056","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-31T02:49:30Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"f1ce2a205be29cb1d50646d7d3136aa6a8a3a6b607aa7c4ec979b0f1900789be","abstract_canon_sha256":"5246761c8dbad1f22aed52a05f13549d58ff0547c9318a723affef307b19d6ee"},"schema_version":"1.0"},"canonical_sha256":"60e813e06fdad07118446c14ca325f4992f0cbd5af665e078a49c25a844db835","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:56.274013Z","signature_b64":"Dof48yQIO0cRJfJzNJOvQFBZGCbNcvF5AxPFCH99yRPnIrwj5PJgL5uMfASi4zT9td6AvJ6Boyu3FvubVUElBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60e813e06fdad07118446c14ca325f4992f0cbd5af665e078a49c25a844db835","last_reissued_at":"2026-05-18T01:20:56.273438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:56.273438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0056","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"54Gf7NSLTir2vWpxOgdPYyi5q3WfvG0YlihkeTxDstSbFRY4ahdmIwFI3cxlOurlRtoKYx8LRVTO9id8uLFJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:11:45.798935Z"},"content_sha256":"b0d44731fa480b2188b4dc523087bc48ef54e190301b5293892a3b20b8d0de17","schema_version":"1.0","event_id":"sha256:b0d44731fa480b2188b4dc523087bc48ef54e190301b5293892a3b20b8d0de17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MDUBHYDP3LIHCGCENQKMUMS7JG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Amin Gholampour, Artan Sheshmani","submitted_at":"2013-08-31T02:49:30Z","abstract_excerpt":"Let X be the total space of the canonical bundle of P^2. We study the generalized Donaldson-Thomas invariants, defined in the work of Joyce-Song, of the moduli spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern class equal to k times the class of the zero section of X. When k=1, 2 or 3, and semistability implies stability, we express the invariants in terms of known modular forms. We prove a combinatorial formula for the invariants when k=2 in the presence of the strictly semistable sheaves, and verify the BPS integrality conjecture of Joyce-Song in some cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0056","kind":"arxiv","version":4},"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":"2026-05-18T01:20:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"402Z1lz2XMQKYUAEbeWu7VflBcEwAX16SDhJib58OzNhrHHLrGCgw3316LBfD1onmqdttKGsbF3YHJXRu/r6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:11:45.799690Z"},"content_sha256":"3b63b40091d4da3bcbf7e2dfc5df88215dd25a9879f6e3c04ec21ee8970b49ba","schema_version":"1.0","event_id":"sha256:3b63b40091d4da3bcbf7e2dfc5df88215dd25a9879f6e3c04ec21ee8970b49ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDUBHYDP3LIHCGCENQKMUMS7JG/bundle.json","state_url":"https://pith.science/pith/MDUBHYDP3LIHCGCENQKMUMS7JG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDUBHYDP3LIHCGCENQKMUMS7JG/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":"2026-06-06T08:11:45Z","links":{"resolver":"https://pith.science/pith/MDUBHYDP3LIHCGCENQKMUMS7JG","bundle":"https://pith.science/pith/MDUBHYDP3LIHCGCENQKMUMS7JG/bundle.json","state":"https://pith.science/pith/MDUBHYDP3LIHCGCENQKMUMS7JG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDUBHYDP3LIHCGCENQKMUMS7JG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MDUBHYDP3LIHCGCENQKMUMS7JG","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":"5246761c8dbad1f22aed52a05f13549d58ff0547c9318a723affef307b19d6ee","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-31T02:49:30Z","title_canon_sha256":"f1ce2a205be29cb1d50646d7d3136aa6a8a3a6b607aa7c4ec979b0f1900789be"},"schema_version":"1.0","source":{"id":"1309.0056","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0056","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0056v4","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0056","created_at":"2026-05-18T01:20:56Z"},{"alias_kind":"pith_short_12","alias_value":"MDUBHYDP3LIH","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MDUBHYDP3LIHCGCE","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MDUBHYDP","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:3b63b40091d4da3bcbf7e2dfc5df88215dd25a9879f6e3c04ec21ee8970b49ba","target":"graph","created_at":"2026-05-18T01:20:56Z","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":"Let X be the total space of the canonical bundle of P^2. We study the generalized Donaldson-Thomas invariants, defined in the work of Joyce-Song, of the moduli spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern class equal to k times the class of the zero section of X. When k=1, 2 or 3, and semistability implies stability, we express the invariants in terms of known modular forms. We prove a combinatorial formula for the invariants when k=2 in the presence of the strictly semistable sheaves, and verify the BPS integrality conjecture of Joyce-Song in some cases.","authors_text":"Amin Gholampour, Artan Sheshmani","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-31T02:49:30Z","title":"Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0056","kind":"arxiv","version":4},"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:b0d44731fa480b2188b4dc523087bc48ef54e190301b5293892a3b20b8d0de17","target":"record","created_at":"2026-05-18T01:20:56Z","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":"5246761c8dbad1f22aed52a05f13549d58ff0547c9318a723affef307b19d6ee","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-31T02:49:30Z","title_canon_sha256":"f1ce2a205be29cb1d50646d7d3136aa6a8a3a6b607aa7c4ec979b0f1900789be"},"schema_version":"1.0","source":{"id":"1309.0056","kind":"arxiv","version":4}},"canonical_sha256":"60e813e06fdad07118446c14ca325f4992f0cbd5af665e078a49c25a844db835","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60e813e06fdad07118446c14ca325f4992f0cbd5af665e078a49c25a844db835","first_computed_at":"2026-05-18T01:20:56.273438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:56.273438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dof48yQIO0cRJfJzNJOvQFBZGCbNcvF5AxPFCH99yRPnIrwj5PJgL5uMfASi4zT9td6AvJ6Boyu3FvubVUElBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:56.274013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0056","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0d44731fa480b2188b4dc523087bc48ef54e190301b5293892a3b20b8d0de17","sha256:3b63b40091d4da3bcbf7e2dfc5df88215dd25a9879f6e3c04ec21ee8970b49ba"],"state_sha256":"88eca0e41b346b74ae2e078d82e118ec6df55baeadb2ac4fec611e8e44121af7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nc4wh5ufwR1rO5FrOibf+vHNtlDGbhP0jSekCjUL+L7njADY5AildZLFB6vt6LMwaWA0Ogpf/JIlO4/FhkjeCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:11:45.803734Z","bundle_sha256":"5b394ad1b3d9c618a15567b6ead7ca15b2bb271ae9fe76f04f9e1f01b81b6b69"}}