{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ET7TWMFCHDZEPXEJUGBRUT4EDS","short_pith_number":"pith:ET7TWMFC","canonical_record":{"source":{"id":"1308.4722","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-21T21:38:08Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"06cc4ce140ab1747855910467097d20fd9795d161cef8f493dd474be50a3a7de","abstract_canon_sha256":"4ab53a8914b7ce72c613d56f562bcf9cfc76961e86d981f066b7a152e7757226"},"schema_version":"1.0"},"canonical_sha256":"24ff3b30a238f247dc89a1831a4f841c82a75c20519f8db365899713b2f9b303","source":{"kind":"arxiv","id":"1308.4722","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4722","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4722v5","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4722","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"ET7TWMFCHDZE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ET7TWMFCHDZEPXEJ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ET7TWMFC","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ET7TWMFCHDZEPXEJUGBRUT4EDS","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4722","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-21T21:38:08Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"06cc4ce140ab1747855910467097d20fd9795d161cef8f493dd474be50a3a7de","abstract_canon_sha256":"4ab53a8914b7ce72c613d56f562bcf9cfc76961e86d981f066b7a152e7757226"},"schema_version":"1.0"},"canonical_sha256":"24ff3b30a238f247dc89a1831a4f841c82a75c20519f8db365899713b2f9b303","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:34.008255Z","signature_b64":"cntxcu1BwoGvNn9YqrtVaYVWcnBYSm1smT9CutYG2LWpJU5R7q4GmcZYdpuqSwSStlQ96p7Hfyb7eG3Oqi61BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24ff3b30a238f247dc89a1831a4f841c82a75c20519f8db365899713b2f9b303","last_reissued_at":"2026-05-18T00:40:34.007323Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:34.007323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4722","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iIPCOYEqR9V+NJb2gh6m1wpd/maGwEmOmweITQpqC2E/LC6fA0jMM2qcX9yaB7kP+nB9bvgn2sCmgQV1nhWoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T23:28:57.989135Z"},"content_sha256":"25f2ca6bb370392b764b8baa25682cbeaf984c744c9561ef98fdab6843b899b0","schema_version":"1.0","event_id":"sha256:25f2ca6bb370392b764b8baa25682cbeaf984c744c9561ef98fdab6843b899b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ET7TWMFCHDZEPXEJUGBRUT4EDS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable pairs on nodal K3 fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Amin Gholampour, Artan Sheshmani, Yukinobu Toda","submitted_at":"2013-08-21T21:38:08Z","abstract_excerpt":"We study Pandharipande-Thomas's stable pair theory on $K3$ fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of Kawai-Yoshioka's formula for the Euler characteristics of moduli spaces of stable pairs on $K3$ surfaces and Noether-Lefschetz numbers of the fibration. Moreover, we investigate the relation of these invariants with the perverse (non-commutative) stable pair invariants of the $K3$ fibration. In the case that the $K3$ fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4722","kind":"arxiv","version":5},"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":"2026-05-18T00:40:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5ZHfbR0XuYgQHYJi96dwT1soQmyLKi9Pe//LDvN0ZyMvu/RFtt+xQD0m9UVzcTqR2GIXoHaHyLaQkvh6b2IBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T23:28:57.989756Z"},"content_sha256":"f025a6ce1cbe16dfaaebbf038779570a39e7a4a1f696dc0bf93c9ebbe732e992","schema_version":"1.0","event_id":"sha256:f025a6ce1cbe16dfaaebbf038779570a39e7a4a1f696dc0bf93c9ebbe732e992"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ET7TWMFCHDZEPXEJUGBRUT4EDS/bundle.json","state_url":"https://pith.science/pith/ET7TWMFCHDZEPXEJUGBRUT4EDS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ET7TWMFCHDZEPXEJUGBRUT4EDS/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":"2026-06-05T23:28:57Z","links":{"resolver":"https://pith.science/pith/ET7TWMFCHDZEPXEJUGBRUT4EDS","bundle":"https://pith.science/pith/ET7TWMFCHDZEPXEJUGBRUT4EDS/bundle.json","state":"https://pith.science/pith/ET7TWMFCHDZEPXEJUGBRUT4EDS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ET7TWMFCHDZEPXEJUGBRUT4EDS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ET7TWMFCHDZEPXEJUGBRUT4EDS","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":"4ab53a8914b7ce72c613d56f562bcf9cfc76961e86d981f066b7a152e7757226","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-21T21:38:08Z","title_canon_sha256":"06cc4ce140ab1747855910467097d20fd9795d161cef8f493dd474be50a3a7de"},"schema_version":"1.0","source":{"id":"1308.4722","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4722","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4722v5","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4722","created_at":"2026-05-18T00:40:34Z"},{"alias_kind":"pith_short_12","alias_value":"ET7TWMFCHDZE","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ET7TWMFCHDZEPXEJ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ET7TWMFC","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:f025a6ce1cbe16dfaaebbf038779570a39e7a4a1f696dc0bf93c9ebbe732e992","target":"graph","created_at":"2026-05-18T00:40:34Z","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 study Pandharipande-Thomas's stable pair theory on $K3$ fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of Kawai-Yoshioka's formula for the Euler characteristics of moduli spaces of stable pairs on $K3$ surfaces and Noether-Lefschetz numbers of the fibration. Moreover, we investigate the relation of these invariants with the perverse (non-commutative) stable pair invariants of the $K3$ fibration. In the case that the $K3$ fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniq","authors_text":"Amin Gholampour, Artan Sheshmani, Yukinobu Toda","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-21T21:38:08Z","title":"Stable pairs on nodal K3 fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4722","kind":"arxiv","version":5},"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":"sha256:25f2ca6bb370392b764b8baa25682cbeaf984c744c9561ef98fdab6843b899b0","target":"record","created_at":"2026-05-18T00:40:34Z","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":"4ab53a8914b7ce72c613d56f562bcf9cfc76961e86d981f066b7a152e7757226","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-21T21:38:08Z","title_canon_sha256":"06cc4ce140ab1747855910467097d20fd9795d161cef8f493dd474be50a3a7de"},"schema_version":"1.0","source":{"id":"1308.4722","kind":"arxiv","version":5}},"canonical_sha256":"24ff3b30a238f247dc89a1831a4f841c82a75c20519f8db365899713b2f9b303","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24ff3b30a238f247dc89a1831a4f841c82a75c20519f8db365899713b2f9b303","first_computed_at":"2026-05-18T00:40:34.007323Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:34.007323Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cntxcu1BwoGvNn9YqrtVaYVWcnBYSm1smT9CutYG2LWpJU5R7q4GmcZYdpuqSwSStlQ96p7Hfyb7eG3Oqi61BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:34.008255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4722","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25f2ca6bb370392b764b8baa25682cbeaf984c744c9561ef98fdab6843b899b0","sha256:f025a6ce1cbe16dfaaebbf038779570a39e7a4a1f696dc0bf93c9ebbe732e992"],"state_sha256":"9a5ab587928196aaa7b17dba4c215bf2bee3b5492d09d98d566033dcdddd87b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NvTOpsXcvWRRPAKTUZARfNhTDo0nO2evjQOht+bWP3XFO2GKBmDo/QUk+6lAdFmUf/Q2S7fzPHJcCCi+U2mDBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T23:28:57.993690Z","bundle_sha256":"5c5585b4f663aceeff76d9e8fbd903a67c49170d0b7bad87e92de063c38cc7a2"}}