{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5ZQBAFBT3PLM7S4QA5KUA3HPBW","short_pith_number":"pith:5ZQBAFBT","canonical_record":{"source":{"id":"1010.4783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-22T19:30:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4334220a7f43d31eae581c1a84222bf5eb87043d505ef7fabce535ac9c5c108d","abstract_canon_sha256":"81642f66c8fd46a9f9bd79f02e1dae2796a09cea5b6277bbea5567828be3e3b9"},"schema_version":"1.0"},"canonical_sha256":"ee60101433dbd6cfcb900755406cef0d9cc516ec2ccc986511299c8c90d9e2f8","source":{"kind":"arxiv","id":"1010.4783","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4783","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4783v1","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4783","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"pith_short_12","alias_value":"5ZQBAFBT3PLM","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5ZQBAFBT3PLM7S4Q","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5ZQBAFBT","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5ZQBAFBT3PLM7S4QA5KUA3HPBW","target":"record","payload":{"canonical_record":{"source":{"id":"1010.4783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-22T19:30:13Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4334220a7f43d31eae581c1a84222bf5eb87043d505ef7fabce535ac9c5c108d","abstract_canon_sha256":"81642f66c8fd46a9f9bd79f02e1dae2796a09cea5b6277bbea5567828be3e3b9"},"schema_version":"1.0"},"canonical_sha256":"ee60101433dbd6cfcb900755406cef0d9cc516ec2ccc986511299c8c90d9e2f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:57.413700Z","signature_b64":"lrtTWfuVQ8lYcYNxvkGpWcrV1QPHEhmbDcwP/VJvCCzDG0NA/cU4RvIBD2+BMhJ6/SF6Uiax4R3svFrKAbI3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee60101433dbd6cfcb900755406cef0d9cc516ec2ccc986511299c8c90d9e2f8","last_reissued_at":"2026-05-18T04:38:57.412987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:57.412987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.4783","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":"2026-05-18T04:38:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrZC5nbH3lNtrCKMYtL1zRkPivQnWb9m2slPSgUWJ415aHo/a9yQqzmjW87/q63J6m3n7XW1g65+ROtwZT4wBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:45:53.246120Z"},"content_sha256":"ac37ba0de6b832f18892ac291274f63dfe96eb9322557eab69cbb569f15fa564","schema_version":"1.0","event_id":"sha256:ac37ba0de6b832f18892ac291274f63dfe96eb9322557eab69cbb569f15fa564"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5ZQBAFBT3PLM7S4QA5KUA3HPBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Oracle Approach for Interaction Neighborhood Estimation in Random Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Daniel Yasumasa Takahashi, Matthieu Lerasle","submitted_at":"2010-10-22T19:30:13Z","abstract_excerpt":"We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4783","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":"2026-05-18T04:38:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93sUeHKLKB7zuJxBYgnLhhc7pGUCnfu7xM1eyJM3d8fHPy20u/6fBbzMAPjI3te76sWDolfpJXfBwUm0qJsLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:45:53.246617Z"},"content_sha256":"143ce6a54dd971c9c2391abcb3269c3543725492f8b468c5d26eacb63429bc86","schema_version":"1.0","event_id":"sha256:143ce6a54dd971c9c2391abcb3269c3543725492f8b468c5d26eacb63429bc86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ZQBAFBT3PLM7S4QA5KUA3HPBW/bundle.json","state_url":"https://pith.science/pith/5ZQBAFBT3PLM7S4QA5KUA3HPBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ZQBAFBT3PLM7S4QA5KUA3HPBW/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":"2026-06-23T15:45:53Z","links":{"resolver":"https://pith.science/pith/5ZQBAFBT3PLM7S4QA5KUA3HPBW","bundle":"https://pith.science/pith/5ZQBAFBT3PLM7S4QA5KUA3HPBW/bundle.json","state":"https://pith.science/pith/5ZQBAFBT3PLM7S4QA5KUA3HPBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ZQBAFBT3PLM7S4QA5KUA3HPBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5ZQBAFBT3PLM7S4QA5KUA3HPBW","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":"81642f66c8fd46a9f9bd79f02e1dae2796a09cea5b6277bbea5567828be3e3b9","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-22T19:30:13Z","title_canon_sha256":"4334220a7f43d31eae581c1a84222bf5eb87043d505ef7fabce535ac9c5c108d"},"schema_version":"1.0","source":{"id":"1010.4783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4783","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4783v1","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4783","created_at":"2026-05-18T04:38:57Z"},{"alias_kind":"pith_short_12","alias_value":"5ZQBAFBT3PLM","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5ZQBAFBT3PLM7S4Q","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5ZQBAFBT","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:143ce6a54dd971c9c2391abcb3269c3543725492f8b468c5d26eacb63429bc86","target":"graph","created_at":"2026-05-18T04:38:57Z","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":"We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that t","authors_text":"Daniel Yasumasa Takahashi, Matthieu Lerasle","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-22T19:30:13Z","title":"An Oracle Approach for Interaction Neighborhood Estimation in Random Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4783","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:ac37ba0de6b832f18892ac291274f63dfe96eb9322557eab69cbb569f15fa564","target":"record","created_at":"2026-05-18T04:38:57Z","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":"81642f66c8fd46a9f9bd79f02e1dae2796a09cea5b6277bbea5567828be3e3b9","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-10-22T19:30:13Z","title_canon_sha256":"4334220a7f43d31eae581c1a84222bf5eb87043d505ef7fabce535ac9c5c108d"},"schema_version":"1.0","source":{"id":"1010.4783","kind":"arxiv","version":1}},"canonical_sha256":"ee60101433dbd6cfcb900755406cef0d9cc516ec2ccc986511299c8c90d9e2f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee60101433dbd6cfcb900755406cef0d9cc516ec2ccc986511299c8c90d9e2f8","first_computed_at":"2026-05-18T04:38:57.412987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:57.412987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lrtTWfuVQ8lYcYNxvkGpWcrV1QPHEhmbDcwP/VJvCCzDG0NA/cU4RvIBD2+BMhJ6/SF6Uiax4R3svFrKAbI3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:57.413700Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac37ba0de6b832f18892ac291274f63dfe96eb9322557eab69cbb569f15fa564","sha256:143ce6a54dd971c9c2391abcb3269c3543725492f8b468c5d26eacb63429bc86"],"state_sha256":"1936fc556ff55b26a6f3d23477c45a0a90cb51ed3681597f3001d3486afd48bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KWiRtqx5P8KuBX/wRnNqhU31S4zZDz7cXgZ5+kTrc00/ktqU1rBTTi9GVGDl8dAV2mbpXIhV6L3tRCnvC+WjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:45:53.248616Z","bundle_sha256":"6f5995f4232bb12311f32d2bb8210e0550f9cdb3361ad86614a16c5e63968df2"}}