{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:WBNUGO4OQ6QF5OPU4Q3EQ3FKUN","short_pith_number":"pith:WBNUGO4O","canonical_record":{"source":{"id":"1906.10030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.GN","submitted_at":"2019-06-24T15:42:33Z","cross_cats_sorted":["q-fin.EC"],"title_canon_sha256":"f7caec428101089b4041749b2919b86d81517b3182332b377b79c60fecb57a72","abstract_canon_sha256":"734b5ba757b350bf8e35b2ac98628c2fb524f543c01026c56187bdea9811008c"},"schema_version":"1.0"},"canonical_sha256":"b05b433b8e87a05eb9f4e436486caaa37ded5e4d45f283d56148ffe50bb44983","source":{"kind":"arxiv","id":"1906.10030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10030","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10030v1","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10030","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"WBNUGO4OQ6QF","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WBNUGO4OQ6QF5OPU","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WBNUGO4O","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:WBNUGO4OQ6QF5OPU4Q3EQ3FKUN","target":"record","payload":{"canonical_record":{"source":{"id":"1906.10030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.GN","submitted_at":"2019-06-24T15:42:33Z","cross_cats_sorted":["q-fin.EC"],"title_canon_sha256":"f7caec428101089b4041749b2919b86d81517b3182332b377b79c60fecb57a72","abstract_canon_sha256":"734b5ba757b350bf8e35b2ac98628c2fb524f543c01026c56187bdea9811008c"},"schema_version":"1.0"},"canonical_sha256":"b05b433b8e87a05eb9f4e436486caaa37ded5e4d45f283d56148ffe50bb44983","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:35.679438Z","signature_b64":"6YOwWW3V13J+HAzG/nqc41upUniJyk7iIyWtvT2oo5xMY0YmNI9cMSTWF/tCLvPj+Z2YRTW5qRmwZ5eD9warCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b05b433b8e87a05eb9f4e436486caaa37ded5e4d45f283d56148ffe50bb44983","last_reissued_at":"2026-05-17T23:42:35.678686Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:35.678686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.10030","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":"2026-05-17T23:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ol5RuR70MIfgv9wRnSBlRMmwo1bviJgnZFt4QKza/c0K8MufdfkAEnBtB5/8N/UuVqeYdzNChRRgyRsx33qBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T14:45:10.176988Z"},"content_sha256":"e767dfee153d5dc84b66285037414a124f6b4dfdcf9bab73478bbefd8e313907","schema_version":"1.0","event_id":"sha256:e767dfee153d5dc84b66285037414a124f6b4dfdcf9bab73478bbefd8e313907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:WBNUGO4OQ6QF5OPU4Q3EQ3FKUN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Solution to Market Definition: An Approach Based on Multi-dimensional Substitutability Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.EC"],"primary_cat":"econ.GN","authors_text":"Yan Yang","submitted_at":"2019-06-24T15:42:33Z","abstract_excerpt":"Market definition is an important component in the premerger investigation, but the models used in the market definition have not developed much in the past three decades since the Critical Loss Analysis (CLA) was proposed in 1989. The CLA helps the Hypothetical Monopolist Test to determine whether the hypothetical monopolist is going to profit from the small but significant and non-transitory increase in price (SSNIP). However, the CLA has long been criticized by academic scholars for its tendency to conclude a narrow market. Although the CLA was adopted by the 2010 Horizontal Merger Guidelin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10030","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":""},"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":"2026-05-17T23:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+IkTuc2BTQZBlblyiJJSgojlUbkxkU9N8O+hGzbHfA5z4OrG2HAAGtOrkmuNDcoghmiEEtIsVBOyw+8DwlGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T14:45:10.177350Z"},"content_sha256":"23938a37ea3add3006a813b1ed63af762a9b9cb10a7582a60af6c21bb14656fa","schema_version":"1.0","event_id":"sha256:23938a37ea3add3006a813b1ed63af762a9b9cb10a7582a60af6c21bb14656fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WBNUGO4OQ6QF5OPU4Q3EQ3FKUN/bundle.json","state_url":"https://pith.science/pith/WBNUGO4OQ6QF5OPU4Q3EQ3FKUN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WBNUGO4OQ6QF5OPU4Q3EQ3FKUN/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":"2026-07-01T14:45:10Z","links":{"resolver":"https://pith.science/pith/WBNUGO4OQ6QF5OPU4Q3EQ3FKUN","bundle":"https://pith.science/pith/WBNUGO4OQ6QF5OPU4Q3EQ3FKUN/bundle.json","state":"https://pith.science/pith/WBNUGO4OQ6QF5OPU4Q3EQ3FKUN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WBNUGO4OQ6QF5OPU4Q3EQ3FKUN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WBNUGO4OQ6QF5OPU4Q3EQ3FKUN","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":"734b5ba757b350bf8e35b2ac98628c2fb524f543c01026c56187bdea9811008c","cross_cats_sorted":["q-fin.EC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.GN","submitted_at":"2019-06-24T15:42:33Z","title_canon_sha256":"f7caec428101089b4041749b2919b86d81517b3182332b377b79c60fecb57a72"},"schema_version":"1.0","source":{"id":"1906.10030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10030","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10030v1","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10030","created_at":"2026-05-17T23:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"WBNUGO4OQ6QF","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WBNUGO4OQ6QF5OPU","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WBNUGO4O","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:23938a37ea3add3006a813b1ed63af762a9b9cb10a7582a60af6c21bb14656fa","target":"graph","created_at":"2026-05-17T23:42:35Z","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":"Market definition is an important component in the premerger investigation, but the models used in the market definition have not developed much in the past three decades since the Critical Loss Analysis (CLA) was proposed in 1989. The CLA helps the Hypothetical Monopolist Test to determine whether the hypothetical monopolist is going to profit from the small but significant and non-transitory increase in price (SSNIP). However, the CLA has long been criticized by academic scholars for its tendency to conclude a narrow market. Although the CLA was adopted by the 2010 Horizontal Merger Guidelin","authors_text":"Yan Yang","cross_cats":["q-fin.EC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.GN","submitted_at":"2019-06-24T15:42:33Z","title":"A New Solution to Market Definition: An Approach Based on Multi-dimensional Substitutability Statistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10030","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:e767dfee153d5dc84b66285037414a124f6b4dfdcf9bab73478bbefd8e313907","target":"record","created_at":"2026-05-17T23:42:35Z","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":"734b5ba757b350bf8e35b2ac98628c2fb524f543c01026c56187bdea9811008c","cross_cats_sorted":["q-fin.EC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.GN","submitted_at":"2019-06-24T15:42:33Z","title_canon_sha256":"f7caec428101089b4041749b2919b86d81517b3182332b377b79c60fecb57a72"},"schema_version":"1.0","source":{"id":"1906.10030","kind":"arxiv","version":1}},"canonical_sha256":"b05b433b8e87a05eb9f4e436486caaa37ded5e4d45f283d56148ffe50bb44983","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b05b433b8e87a05eb9f4e436486caaa37ded5e4d45f283d56148ffe50bb44983","first_computed_at":"2026-05-17T23:42:35.678686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:35.678686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6YOwWW3V13J+HAzG/nqc41upUniJyk7iIyWtvT2oo5xMY0YmNI9cMSTWF/tCLvPj+Z2YRTW5qRmwZ5eD9warCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:35.679438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.10030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e767dfee153d5dc84b66285037414a124f6b4dfdcf9bab73478bbefd8e313907","sha256:23938a37ea3add3006a813b1ed63af762a9b9cb10a7582a60af6c21bb14656fa"],"state_sha256":"0c872dfd37f9f550c228917b74848d9f0baa4943faa508958c6132abcd73e3e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6T+Qs7tYwDKPyVCCrKSOz30z9ZLFyXIYQc6mY0Kqw3pqwg9tKJlI7U7sdQMw75KNIqm2uZpmRZK+fY0JkWG7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T14:45:10.179325Z","bundle_sha256":"8cb162e9a9226e2472bbeaa4d7391cf7854accb9a9a2363cd0da62dc4bb1706f"}}