{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:63RKBQG3GLPTXTZ3OWQJVZQMEF","short_pith_number":"pith:63RKBQG3","canonical_record":{"source":{"id":"2607.02526","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-11T17:25:15Z","cross_cats_sorted":[],"title_canon_sha256":"e236828578b2485a1b289c65b727da4aa73584ab55c3447a61e4f24af87a1451","abstract_canon_sha256":"f2b587565d0fbf6ab5c03ee4df5105eaa2340361bba14a26d68b807a13e99f7b"},"schema_version":"1.0"},"canonical_sha256":"f6e2a0c0db32df3bcf3b75a09ae60c2148dc09dc7598e0edb9a92bffbb21923b","source":{"kind":"arxiv","id":"2607.02526","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02526","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02526v1","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02526","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"63RKBQG3GLPT","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"pith_short_16","alias_value":"63RKBQG3GLPTXTZ3","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"pith_short_8","alias_value":"63RKBQG3","created_at":"2026-07-07T00:15:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:63RKBQG3GLPTXTZ3OWQJVZQMEF","target":"record","payload":{"canonical_record":{"source":{"id":"2607.02526","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-11T17:25:15Z","cross_cats_sorted":[],"title_canon_sha256":"e236828578b2485a1b289c65b727da4aa73584ab55c3447a61e4f24af87a1451","abstract_canon_sha256":"f2b587565d0fbf6ab5c03ee4df5105eaa2340361bba14a26d68b807a13e99f7b"},"schema_version":"1.0"},"canonical_sha256":"f6e2a0c0db32df3bcf3b75a09ae60c2148dc09dc7598e0edb9a92bffbb21923b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T00:15:59.043041Z","signature_b64":"ovGv5B3SwXf5B5GXSre6O6MSsScYhXFzvYMxbdqGD8Le3+Zc8FZG78Ccf/SR5ET0cbLi8bnOy3ReuwvXFlOnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e2a0c0db32df3bcf3b75a09ae60c2148dc09dc7598e0edb9a92bffbb21923b","last_reissued_at":"2026-07-07T00:15:59.042059Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T00:15:59.042059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.02526","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":"2026-07-07T00:15:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cvnb7PuaQkkuUCZXWzMzuf4RLBL2vaBmOrHJuqNYRozK6j6xamL1eRMmMLl9IWJMB95YBo4gxKEaj/7uYnOfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T12:46:45.611823Z"},"content_sha256":"caacb41eba84a28c0f15146d4e22407fb1e3d0d8687a4212d90754e36f4055ee","schema_version":"1.0","event_id":"sha256:caacb41eba84a28c0f15146d4e22407fb1e3d0d8687a4212d90754e36f4055ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:63RKBQG3GLPTXTZ3OWQJVZQMEF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Reginald Anderson","submitted_at":"2026-05-11T17:25:15Z","abstract_excerpt":"We study descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds. We use the wall-crossing setup developed by the author and Joyce in Joyce's Lie algebra $H_*(\\N^{\\pl},\\Q)$ of the projective-linear pairs stack, and next pass to Gross's polynomial realization $e^{\\kappa}\\Q[s_{jk\\ell}]$.\n  We compute explicit examples of one-dimensional Donaldson--Thomas invariants on Fano 3-folds and, via wall-crossing, Pandharipande--Thomas stable pair invariants and descendent generating series. We compute examples on $\\PP^3$, on a smooth cubic threefold, on $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02526","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.02526/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-07T00:15:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XAzVWeyIXIUjKFtTWSs8BCmZtngQ7n53+97XS7aimgz6dX1RZ9IQ5Zx+dzEvTwKHCPW2Al9btl9b4sKGU63mDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T12:46:45.612351Z"},"content_sha256":"9f3e9e38cf08d1469e1ade8fba1910ba5bf7c27efd493aabd13e82fd744287fe","schema_version":"1.0","event_id":"sha256:9f3e9e38cf08d1469e1ade8fba1910ba5bf7c27efd493aabd13e82fd744287fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63RKBQG3GLPTXTZ3OWQJVZQMEF/bundle.json","state_url":"https://pith.science/pith/63RKBQG3GLPTXTZ3OWQJVZQMEF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63RKBQG3GLPTXTZ3OWQJVZQMEF/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":"2026-08-02T12:46:45Z","links":{"resolver":"https://pith.science/pith/63RKBQG3GLPTXTZ3OWQJVZQMEF","bundle":"https://pith.science/pith/63RKBQG3GLPTXTZ3OWQJVZQMEF/bundle.json","state":"https://pith.science/pith/63RKBQG3GLPTXTZ3OWQJVZQMEF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63RKBQG3GLPTXTZ3OWQJVZQMEF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:63RKBQG3GLPTXTZ3OWQJVZQMEF","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":"f2b587565d0fbf6ab5c03ee4df5105eaa2340361bba14a26d68b807a13e99f7b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-11T17:25:15Z","title_canon_sha256":"e236828578b2485a1b289c65b727da4aa73584ab55c3447a61e4f24af87a1451"},"schema_version":"1.0","source":{"id":"2607.02526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02526","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02526v1","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02526","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"pith_short_12","alias_value":"63RKBQG3GLPT","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"pith_short_16","alias_value":"63RKBQG3GLPTXTZ3","created_at":"2026-07-07T00:15:59Z"},{"alias_kind":"pith_short_8","alias_value":"63RKBQG3","created_at":"2026-07-07T00:15:59Z"}],"graph_snapshots":[{"event_id":"sha256:9f3e9e38cf08d1469e1ade8fba1910ba5bf7c27efd493aabd13e82fd744287fe","target":"graph","created_at":"2026-07-07T00:15:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.02526/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds. We use the wall-crossing setup developed by the author and Joyce in Joyce's Lie algebra $H_*(\\N^{\\pl},\\Q)$ of the projective-linear pairs stack, and next pass to Gross's polynomial realization $e^{\\kappa}\\Q[s_{jk\\ell}]$.\n  We compute explicit examples of one-dimensional Donaldson--Thomas invariants on Fano 3-folds and, via wall-crossing, Pandharipande--Thomas stable pair invariants and descendent generating series. We compute examples on $\\PP^3$, on a smooth cubic threefold, on $\\","authors_text":"Reginald Anderson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-11T17:25:15Z","title":"Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02526","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:caacb41eba84a28c0f15146d4e22407fb1e3d0d8687a4212d90754e36f4055ee","target":"record","created_at":"2026-07-07T00:15:59Z","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":"f2b587565d0fbf6ab5c03ee4df5105eaa2340361bba14a26d68b807a13e99f7b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-11T17:25:15Z","title_canon_sha256":"e236828578b2485a1b289c65b727da4aa73584ab55c3447a61e4f24af87a1451"},"schema_version":"1.0","source":{"id":"2607.02526","kind":"arxiv","version":1}},"canonical_sha256":"f6e2a0c0db32df3bcf3b75a09ae60c2148dc09dc7598e0edb9a92bffbb21923b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e2a0c0db32df3bcf3b75a09ae60c2148dc09dc7598e0edb9a92bffbb21923b","first_computed_at":"2026-07-07T00:15:59.042059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T00:15:59.042059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ovGv5B3SwXf5B5GXSre6O6MSsScYhXFzvYMxbdqGD8Le3+Zc8FZG78Ccf/SR5ET0cbLi8bnOy3ReuwvXFlOnAQ==","signature_status":"signed_v1","signed_at":"2026-07-07T00:15:59.043041Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caacb41eba84a28c0f15146d4e22407fb1e3d0d8687a4212d90754e36f4055ee","sha256:9f3e9e38cf08d1469e1ade8fba1910ba5bf7c27efd493aabd13e82fd744287fe"],"state_sha256":"25acd7d47834509b899539dcf61584712c4bc44d858130e0a8d34fa3fa205e34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1LBkTB3nSb+5GypUec2NX/O7r60Up9reyUtY53rgM9iPiAg/A4n+FxgMDnpvoOYT2hbtj9CV0V7MaTwLinKCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T12:46:45.616886Z","bundle_sha256":"aeac0d24ca6207a18b4b0ddb17319a04988d986c90a0062c6fa8ac705d8e29d1"}}