{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EQP3OCMIA7K4PQJID34MFZWBVH","short_pith_number":"pith:EQP3OCMI","canonical_record":{"source":{"id":"1702.04296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-14T17:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"a457043fb17491e081a72c78554e449d00b1ec315911d038cfddd6e26218c59d","abstract_canon_sha256":"5bde48e7dfc8198e589b2753116b21ac2fbab2202ff76a322575e1b50a01956b"},"schema_version":"1.0"},"canonical_sha256":"241fb7098807d5c7c1281ef8c2e6c1a9c2cb7f30bae7f6e95c3f1501e8ccec32","source":{"kind":"arxiv","id":"1702.04296","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04296","created_at":"2026-05-18T00:50:48Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04296v1","created_at":"2026-05-18T00:50:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04296","created_at":"2026-05-18T00:50:48Z"},{"alias_kind":"pith_short_12","alias_value":"EQP3OCMIA7K4","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EQP3OCMIA7K4PQJI","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EQP3OCMI","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EQP3OCMIA7K4PQJID34MFZWBVH","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-14T17:14:59Z","cross_cats_sorted":[],"title_canon_sha256":"a457043fb17491e081a72c78554e449d00b1ec315911d038cfddd6e26218c59d","abstract_canon_sha256":"5bde48e7dfc8198e589b2753116b21ac2fbab2202ff76a322575e1b50a01956b"},"schema_version":"1.0"},"canonical_sha256":"241fb7098807d5c7c1281ef8c2e6c1a9c2cb7f30bae7f6e95c3f1501e8ccec32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:48.446758Z","signature_b64":"N/5mGxS9wRq1br3df9uVIPkLJXPc6wVTL30zsgDCkpu23MlnWS/GaiTnTQ5CSmzUSoy0rI2H8KvLR2KlBktZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"241fb7098807d5c7c1281ef8c2e6c1a9c2cb7f30bae7f6e95c3f1501e8ccec32","last_reissued_at":"2026-05-18T00:50:48.446003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:48.446003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04296","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":"2026-05-18T00:50:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/LUF7dEdeYbo/meeGcw5Q3vNaIo7ioN82Tg2+n1JFc8hwiRNU8xqcvRSmJOw6a4OUCsEqbDiL0w/uvE0MnIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:16.486676Z"},"content_sha256":"37ac03656ef3c0bfeb507a465f0d00e69c29ca7b41594e0feb6b689b62ca65c9","schema_version":"1.0","event_id":"sha256:37ac03656ef3c0bfeb507a465f0d00e69c29ca7b41594e0feb6b689b62ca65c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EQP3OCMIA7K4PQJID34MFZWBVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Divide and Color models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jeffrey E. Steif, Johan Tykesson","submitted_at":"2017-02-14T17:14:59Z","abstract_excerpt":"In this paper, we initiate the study of \"Generalized Divide and Color Models\". A very special interesting case of this is the \"Divide and Color Model\" (which motivates the name we use) introduced and studied by Olle H\\\"aggstr\\\"om.\n  In this generalized model, one starts with a finite or countable set $V$, a random partition of $V$ and a parameter $p\\in [0,1]$. The corresponding Generalized Divide and Color Model is the $\\{0,1\\}$-valued process indexed by $V$ obtained by independently, for each partition element in the random partition chosen, with probability $p$, assigning all the elements of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04296","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":"2026-05-18T00:50:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1nz9XFjvZjc5d7HoNqmJxJuouCgDeJPptjsdUuJAH9Angvu+debNeEif/4dcekos1O0gRMwFYeuTKE/nvjqwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:16:16.487030Z"},"content_sha256":"1accd4a618fe0aba37964c32a3076fad5dd21767775c55ece08d7ced6e9eb71a","schema_version":"1.0","event_id":"sha256:1accd4a618fe0aba37964c32a3076fad5dd21767775c55ece08d7ced6e9eb71a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQP3OCMIA7K4PQJID34MFZWBVH/bundle.json","state_url":"https://pith.science/pith/EQP3OCMIA7K4PQJID34MFZWBVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQP3OCMIA7K4PQJID34MFZWBVH/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":"2026-05-28T06:16:16Z","links":{"resolver":"https://pith.science/pith/EQP3OCMIA7K4PQJID34MFZWBVH","bundle":"https://pith.science/pith/EQP3OCMIA7K4PQJID34MFZWBVH/bundle.json","state":"https://pith.science/pith/EQP3OCMIA7K4PQJID34MFZWBVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQP3OCMIA7K4PQJID34MFZWBVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EQP3OCMIA7K4PQJID34MFZWBVH","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":"5bde48e7dfc8198e589b2753116b21ac2fbab2202ff76a322575e1b50a01956b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-14T17:14:59Z","title_canon_sha256":"a457043fb17491e081a72c78554e449d00b1ec315911d038cfddd6e26218c59d"},"schema_version":"1.0","source":{"id":"1702.04296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04296","created_at":"2026-05-18T00:50:48Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04296v1","created_at":"2026-05-18T00:50:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04296","created_at":"2026-05-18T00:50:48Z"},{"alias_kind":"pith_short_12","alias_value":"EQP3OCMIA7K4","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EQP3OCMIA7K4PQJI","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EQP3OCMI","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:1accd4a618fe0aba37964c32a3076fad5dd21767775c55ece08d7ced6e9eb71a","target":"graph","created_at":"2026-05-18T00:50:48Z","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":"In this paper, we initiate the study of \"Generalized Divide and Color Models\". A very special interesting case of this is the \"Divide and Color Model\" (which motivates the name we use) introduced and studied by Olle H\\\"aggstr\\\"om.\n  In this generalized model, one starts with a finite or countable set $V$, a random partition of $V$ and a parameter $p\\in [0,1]$. The corresponding Generalized Divide and Color Model is the $\\{0,1\\}$-valued process indexed by $V$ obtained by independently, for each partition element in the random partition chosen, with probability $p$, assigning all the elements of","authors_text":"Jeffrey E. Steif, Johan Tykesson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-14T17:14:59Z","title":"Generalized Divide and Color models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04296","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":"sha256:37ac03656ef3c0bfeb507a465f0d00e69c29ca7b41594e0feb6b689b62ca65c9","target":"record","created_at":"2026-05-18T00:50:48Z","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":"5bde48e7dfc8198e589b2753116b21ac2fbab2202ff76a322575e1b50a01956b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-02-14T17:14:59Z","title_canon_sha256":"a457043fb17491e081a72c78554e449d00b1ec315911d038cfddd6e26218c59d"},"schema_version":"1.0","source":{"id":"1702.04296","kind":"arxiv","version":1}},"canonical_sha256":"241fb7098807d5c7c1281ef8c2e6c1a9c2cb7f30bae7f6e95c3f1501e8ccec32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"241fb7098807d5c7c1281ef8c2e6c1a9c2cb7f30bae7f6e95c3f1501e8ccec32","first_computed_at":"2026-05-18T00:50:48.446003Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:48.446003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/5mGxS9wRq1br3df9uVIPkLJXPc6wVTL30zsgDCkpu23MlnWS/GaiTnTQ5CSmzUSoy0rI2H8KvLR2KlBktZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:48.446758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37ac03656ef3c0bfeb507a465f0d00e69c29ca7b41594e0feb6b689b62ca65c9","sha256:1accd4a618fe0aba37964c32a3076fad5dd21767775c55ece08d7ced6e9eb71a"],"state_sha256":"7fc1484e613722c589ab69def91dc9ec15187722e9dd92df843d05246d38889d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f8YsOqZSHmweePOch84BmW+MVogiVsEyGEV0qv12WyMUE/azNf8lXzq9OjXvBIr6ldHAkMzq2wwWgovmMDhzCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:16:16.489188Z","bundle_sha256":"5e754350edf7d6bb8b719e74f87301b1f97f194831b9b873980539bf76429900"}}