{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NDP7BCPDPMKESLMAH7UG7B4DDS","short_pith_number":"pith:NDP7BCPD","canonical_record":{"source":{"id":"1806.01381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-06-04T20:49:41Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"dd786789f45300df1e3843c6cfb27e603aed77de57f234cf32bca9b03e5a4a1d","abstract_canon_sha256":"99bb9e8d7d6c3c5875e0f10626afa1610c39bca8381688852a0b48609e3940a3"},"schema_version":"1.0"},"canonical_sha256":"68dff089e37b14492d803fe86f87831caaa3e024336c95fbd4f1371a9bbcd67a","source":{"kind":"arxiv","id":"1806.01381","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01381","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01381v2","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01381","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"NDP7BCPDPMKE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NDP7BCPDPMKESLMA","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NDP7BCPD","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NDP7BCPDPMKESLMAH7UG7B4DDS","target":"record","payload":{"canonical_record":{"source":{"id":"1806.01381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-06-04T20:49:41Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"dd786789f45300df1e3843c6cfb27e603aed77de57f234cf32bca9b03e5a4a1d","abstract_canon_sha256":"99bb9e8d7d6c3c5875e0f10626afa1610c39bca8381688852a0b48609e3940a3"},"schema_version":"1.0"},"canonical_sha256":"68dff089e37b14492d803fe86f87831caaa3e024336c95fbd4f1371a9bbcd67a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:03.660842Z","signature_b64":"4/cxP76MmmtaGmnfQuCf732qZeSLq1XaWHyzHW1KRovon5i9hhwDDdSqIyG2SSiToPJWDphXYnxuR8ByA1OQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68dff089e37b14492d803fe86f87831caaa3e024336c95fbd4f1371a9bbcd67a","last_reissued_at":"2026-05-18T00:14:03.660075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:03.660075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.01381","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fAipwviyX8UP5KxoRN9TVYmSkSOmi4mqduR4cL2VgCv//KSQoICziY0uW5T76FQ28QZyvOkI1V0rO1Ceu7bVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:08:39.025715Z"},"content_sha256":"31b97bf4a60c6e64bc3b2a8f9328f773fc1fdd78fc14e07dd6f1f1a6623fd31b","schema_version":"1.0","event_id":"sha256:31b97bf4a60c6e64bc3b2a8f9328f773fc1fdd78fc14e07dd6f1f1a6623fd31b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NDP7BCPDPMKESLMAH7UG7B4DDS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wall-crossing for toric mutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.SG","authors_text":"David Nadler","submitted_at":"2018-06-04T20:49:41Z","abstract_excerpt":"This note explains how to deduce the wall-crossing formula for toric mutations established by Pascaleff-Tonkonog from the perverse schober of the corresponding local Landau-Ginzburg model. Along the way, we develop a general framework to extract a wall-crossing formula from a perverse schober on the projective line with a single critical point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01381","kind":"arxiv","version":2},"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":"2026-05-18T00:14:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXRtv1eNEXanEuUhC/BSa+8eobPBwG+mrIMmSzvWMmFihiDXqFDwIqX1runKG8dbJucMgktOWQTGUJoeEhOeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:08:39.026066Z"},"content_sha256":"18468b1201dfe0019573f75fc778192cc0537ba733fd8f0ad17b7bce8c448d45","schema_version":"1.0","event_id":"sha256:18468b1201dfe0019573f75fc778192cc0537ba733fd8f0ad17b7bce8c448d45"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDP7BCPDPMKESLMAH7UG7B4DDS/bundle.json","state_url":"https://pith.science/pith/NDP7BCPDPMKESLMAH7UG7B4DDS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDP7BCPDPMKESLMAH7UG7B4DDS/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":"2026-05-30T19:08:39Z","links":{"resolver":"https://pith.science/pith/NDP7BCPDPMKESLMAH7UG7B4DDS","bundle":"https://pith.science/pith/NDP7BCPDPMKESLMAH7UG7B4DDS/bundle.json","state":"https://pith.science/pith/NDP7BCPDPMKESLMAH7UG7B4DDS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDP7BCPDPMKESLMAH7UG7B4DDS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NDP7BCPDPMKESLMAH7UG7B4DDS","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":"99bb9e8d7d6c3c5875e0f10626afa1610c39bca8381688852a0b48609e3940a3","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-06-04T20:49:41Z","title_canon_sha256":"dd786789f45300df1e3843c6cfb27e603aed77de57f234cf32bca9b03e5a4a1d"},"schema_version":"1.0","source":{"id":"1806.01381","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.01381","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"1806.01381v2","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.01381","created_at":"2026-05-18T00:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"NDP7BCPDPMKE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NDP7BCPDPMKESLMA","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NDP7BCPD","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:18468b1201dfe0019573f75fc778192cc0537ba733fd8f0ad17b7bce8c448d45","target":"graph","created_at":"2026-05-18T00:14:03Z","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":"This note explains how to deduce the wall-crossing formula for toric mutations established by Pascaleff-Tonkonog from the perverse schober of the corresponding local Landau-Ginzburg model. Along the way, we develop a general framework to extract a wall-crossing formula from a perverse schober on the projective line with a single critical point.","authors_text":"David Nadler","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-06-04T20:49:41Z","title":"Wall-crossing for toric mutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.01381","kind":"arxiv","version":2},"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":"sha256:31b97bf4a60c6e64bc3b2a8f9328f773fc1fdd78fc14e07dd6f1f1a6623fd31b","target":"record","created_at":"2026-05-18T00:14:03Z","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":"99bb9e8d7d6c3c5875e0f10626afa1610c39bca8381688852a0b48609e3940a3","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2018-06-04T20:49:41Z","title_canon_sha256":"dd786789f45300df1e3843c6cfb27e603aed77de57f234cf32bca9b03e5a4a1d"},"schema_version":"1.0","source":{"id":"1806.01381","kind":"arxiv","version":2}},"canonical_sha256":"68dff089e37b14492d803fe86f87831caaa3e024336c95fbd4f1371a9bbcd67a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68dff089e37b14492d803fe86f87831caaa3e024336c95fbd4f1371a9bbcd67a","first_computed_at":"2026-05-18T00:14:03.660075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:03.660075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/cxP76MmmtaGmnfQuCf732qZeSLq1XaWHyzHW1KRovon5i9hhwDDdSqIyG2SSiToPJWDphXYnxuR8ByA1OQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:03.660842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.01381","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31b97bf4a60c6e64bc3b2a8f9328f773fc1fdd78fc14e07dd6f1f1a6623fd31b","sha256:18468b1201dfe0019573f75fc778192cc0537ba733fd8f0ad17b7bce8c448d45"],"state_sha256":"6835a919ca61f8ae97e8bba442c2676080219ab4fbd5a4b6209c41809774097c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RcAbRqMc+cKetfDU9/bOMWoyxpaq2npahvD3eNllgPPhScTCrtA5vS4fWULPCWpwcaaRcHKtOOpzxhI+R8+RAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:08:39.028071Z","bundle_sha256":"03750106a87a918480a6b30cf9e496314d539b3cd8cd7f16f4831797aef95df3"}}