{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RG6G435MWQ5Z6KFVGR7KE7BPSD","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":"eed4c154e60a1ae69062d778ce53079e31af99971e92f9f4a345f7f036606cfd","cross_cats_sorted":["stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.AP","submitted_at":"2022-01-13T14:45:35Z","title_canon_sha256":"d453ac2b85cafdf8a92c93b5f8a2ff502b5b36fd946b78c087ecf61b7b5df7e2"},"schema_version":"1.0","source":{"id":"2201.05009","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.05009","created_at":"2026-07-05T06:49:00Z"},{"alias_kind":"arxiv_version","alias_value":"2201.05009v2","created_at":"2026-07-05T06:49:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.05009","created_at":"2026-07-05T06:49:00Z"},{"alias_kind":"pith_short_12","alias_value":"RG6G435MWQ5Z","created_at":"2026-07-05T06:49:00Z"},{"alias_kind":"pith_short_16","alias_value":"RG6G435MWQ5Z6KFV","created_at":"2026-07-05T06:49:00Z"},{"alias_kind":"pith_short_8","alias_value":"RG6G435M","created_at":"2026-07-05T06:49:00Z"}],"graph_snapshots":[{"event_id":"sha256:45aa834ba1a5cd8cdf68687f9b56fa0206f93d905828379a9eff48d37b741fe4","target":"graph","created_at":"2026-07-05T06:49:00Z","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/2201.05009/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Product cannibalisation in the marketplace refers to the decrease in the sales of one product due to competition from another product. We examine this phenomenon in a wholesale data set provided by an international company. We use a multivariate Hawkes process where each product is represented by a dimension, with cross-inhibition effects that model product cannibalisation. To implement the Hawkes process with inhibition we resolve challenges regarding the integration of the intensity function and introduce a new, stronger conditions for stability as existing conditions are unnecessarily stric","authors_text":"Gordon J. Ross, Isabella Deutsch","cross_cats":["stat.ME"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.AP","submitted_at":"2022-01-13T14:45:35Z","title":"Estimating Product Cannibalisation in Wholesale using Multivariate Hawkes Processes with Inhibition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.05009","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":"sha256:6f1b1fcab514dfaf5794d67ba60181ed02a61c808a9a2b8ebec21e3c71eb6303","target":"record","created_at":"2026-07-05T06:49:00Z","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":"eed4c154e60a1ae69062d778ce53079e31af99971e92f9f4a345f7f036606cfd","cross_cats_sorted":["stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.AP","submitted_at":"2022-01-13T14:45:35Z","title_canon_sha256":"d453ac2b85cafdf8a92c93b5f8a2ff502b5b36fd946b78c087ecf61b7b5df7e2"},"schema_version":"1.0","source":{"id":"2201.05009","kind":"arxiv","version":2}},"canonical_sha256":"89bc6e6facb43b9f28b5347ea27c2f90e236d65bba59198c9e1c2c70213e6bbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89bc6e6facb43b9f28b5347ea27c2f90e236d65bba59198c9e1c2c70213e6bbc","first_computed_at":"2026-07-05T06:49:00.897666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:49:00.897666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+sqkcFdgu28vksxvXe54zDMWWuE7pfreimuBlJxuk4D13pzTx83468EuGxxfMrqTNr4F8DZo0rxSfXhhtda/Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:49:00.898124Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.05009","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f1b1fcab514dfaf5794d67ba60181ed02a61c808a9a2b8ebec21e3c71eb6303","sha256:45aa834ba1a5cd8cdf68687f9b56fa0206f93d905828379a9eff48d37b741fe4"],"state_sha256":"77d35f4addd5570e2f508079e3ec40f52ceb13dc66979b69d06d8f7924e6e042"}