{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XUY4YTY6VNOGYO7MPYJOIPSIRF","short_pith_number":"pith:XUY4YTY6","canonical_record":{"source":{"id":"1203.3459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-15T19:55:03Z","cross_cats_sorted":[],"title_canon_sha256":"586b2093ab1ebda00fc80dd232612aab7ac1f197d21807489dcad57445acf3d6","abstract_canon_sha256":"489c18fd2e3c1596b6b505289b3a9ba7af46880ab798cffc50c89bc47dab6d52"},"schema_version":"1.0"},"canonical_sha256":"bd31cc4f1eab5c6c3bec7e12e43e488956b0ffd6d9f7576a0963d7e59ceb6f46","source":{"kind":"arxiv","id":"1203.3459","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3459","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3459v1","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3459","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"XUY4YTY6VNOG","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XUY4YTY6VNOGYO7M","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XUY4YTY6","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XUY4YTY6VNOGYO7MPYJOIPSIRF","target":"record","payload":{"canonical_record":{"source":{"id":"1203.3459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-15T19:55:03Z","cross_cats_sorted":[],"title_canon_sha256":"586b2093ab1ebda00fc80dd232612aab7ac1f197d21807489dcad57445acf3d6","abstract_canon_sha256":"489c18fd2e3c1596b6b505289b3a9ba7af46880ab798cffc50c89bc47dab6d52"},"schema_version":"1.0"},"canonical_sha256":"bd31cc4f1eab5c6c3bec7e12e43e488956b0ffd6d9f7576a0963d7e59ceb6f46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:01.612090Z","signature_b64":"gOUtZTRWCeAVAzxpfKe57GEq2HL8YR3qghPCrdAnJfLZDJwbg0ASJjJ+TVP85t/vUPHInJPEq4ZFRLSaKoZECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd31cc4f1eab5c6c3bec7e12e43e488956b0ffd6d9f7576a0963d7e59ceb6f46","last_reissued_at":"2026-05-18T04:00:01.611406Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:01.611406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.3459","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":"2026-05-18T04:00:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gGL7/uF9nBGIfbzT24EAtwhett8mXLd8qxisUoJJPeGAu6eyvzhjdreBVdyOJGen0+i+MiBfQAnnOY5aljpMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:27:40.639474Z"},"content_sha256":"6b34c1b491de5ff15da1e4ef431c5551e8db3d5a6152c4dee69e030bd5fb3387","schema_version":"1.0","event_id":"sha256:6b34c1b491de5ff15da1e4ef431c5551e8db3d5a6152c4dee69e030bd5fb3387"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XUY4YTY6VNOGYO7MPYJOIPSIRF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-interacting random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Perla Sousi, Serguei Popov, Yuval Peres","submitted_at":"2012-03-15T19:55:03Z","abstract_excerpt":"Let $\\mu_1,... \\mu_k$ be $d$-dimensional probability measures in $\\R^d$ with mean 0. At each step we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3459","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":"2026-05-18T04:00:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YtDKRwpn7FDOuaTL67HDaomp5Q+jBJVCCLT1sKx6iuqkbn5A/cYZxXrIkzg8Jav3CcbuaAGsFKVOaVo8mhvnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:27:40.640152Z"},"content_sha256":"fea7e9208a9abc4101cc3d4afe83fc85da23a2855cb57ed0a31f687e4847dff1","schema_version":"1.0","event_id":"sha256:fea7e9208a9abc4101cc3d4afe83fc85da23a2855cb57ed0a31f687e4847dff1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUY4YTY6VNOGYO7MPYJOIPSIRF/bundle.json","state_url":"https://pith.science/pith/XUY4YTY6VNOGYO7MPYJOIPSIRF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUY4YTY6VNOGYO7MPYJOIPSIRF/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":"2026-05-29T15:27:40Z","links":{"resolver":"https://pith.science/pith/XUY4YTY6VNOGYO7MPYJOIPSIRF","bundle":"https://pith.science/pith/XUY4YTY6VNOGYO7MPYJOIPSIRF/bundle.json","state":"https://pith.science/pith/XUY4YTY6VNOGYO7MPYJOIPSIRF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUY4YTY6VNOGYO7MPYJOIPSIRF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XUY4YTY6VNOGYO7MPYJOIPSIRF","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":"489c18fd2e3c1596b6b505289b3a9ba7af46880ab798cffc50c89bc47dab6d52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-15T19:55:03Z","title_canon_sha256":"586b2093ab1ebda00fc80dd232612aab7ac1f197d21807489dcad57445acf3d6"},"schema_version":"1.0","source":{"id":"1203.3459","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.3459","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1203.3459v1","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.3459","created_at":"2026-05-18T04:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"XUY4YTY6VNOG","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XUY4YTY6VNOGYO7M","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XUY4YTY6","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:fea7e9208a9abc4101cc3d4afe83fc85da23a2855cb57ed0a31f687e4847dff1","target":"graph","created_at":"2026-05-18T04:00:01Z","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":"Let $\\mu_1,... \\mu_k$ be $d$-dimensional probability measures in $\\R^d$ with mean 0. At each step we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.","authors_text":"Perla Sousi, Serguei Popov, Yuval Peres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-15T19:55:03Z","title":"Self-interacting random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.3459","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":"sha256:6b34c1b491de5ff15da1e4ef431c5551e8db3d5a6152c4dee69e030bd5fb3387","target":"record","created_at":"2026-05-18T04:00:01Z","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":"489c18fd2e3c1596b6b505289b3a9ba7af46880ab798cffc50c89bc47dab6d52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-15T19:55:03Z","title_canon_sha256":"586b2093ab1ebda00fc80dd232612aab7ac1f197d21807489dcad57445acf3d6"},"schema_version":"1.0","source":{"id":"1203.3459","kind":"arxiv","version":1}},"canonical_sha256":"bd31cc4f1eab5c6c3bec7e12e43e488956b0ffd6d9f7576a0963d7e59ceb6f46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd31cc4f1eab5c6c3bec7e12e43e488956b0ffd6d9f7576a0963d7e59ceb6f46","first_computed_at":"2026-05-18T04:00:01.611406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:01.611406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gOUtZTRWCeAVAzxpfKe57GEq2HL8YR3qghPCrdAnJfLZDJwbg0ASJjJ+TVP85t/vUPHInJPEq4ZFRLSaKoZECA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:01.612090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.3459","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b34c1b491de5ff15da1e4ef431c5551e8db3d5a6152c4dee69e030bd5fb3387","sha256:fea7e9208a9abc4101cc3d4afe83fc85da23a2855cb57ed0a31f687e4847dff1"],"state_sha256":"e340b303bb24a63b281ea742b47b8ea32f636a81c32b37e6e2f8a56fde25367f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbEWcwllf9NwnNVC1BggSqbF6AuKTRJpX9P7XMdjJj2jRT5nFcyvJKSBdCVcuYF49/9uy2LBLNd1YWT6glMTCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:27:40.644118Z","bundle_sha256":"fd7fff952854b8bd5c892ba0497f5d76ff9bfd76659fc2e3cb69a90d8b544f41"}}