{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:RYJAIFVQEQCNHKNFXSR6FX2CTV","short_pith_number":"pith:RYJAIFVQ","canonical_record":{"source":{"id":"1009.0741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T19:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"bb0e3adeea0432e2852f7b13fa6fc851b258183da80cc95c4efcc4ce1e10949f","abstract_canon_sha256":"f7bbe9ddac3c186543e45cf0ab3b092daa641dd897864b08e0e4f797bae007cf"},"schema_version":"1.0"},"canonical_sha256":"8e120416b02404d3a9a5bca3e2df429d7b8ee5b556417c5d81994ade8155c37c","source":{"kind":"arxiv","id":"1009.0741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0741","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0741v1","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0741","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"RYJAIFVQEQCN","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RYJAIFVQEQCNHKNF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RYJAIFVQ","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:RYJAIFVQEQCNHKNFXSR6FX2CTV","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T19:08:56Z","cross_cats_sorted":[],"title_canon_sha256":"bb0e3adeea0432e2852f7b13fa6fc851b258183da80cc95c4efcc4ce1e10949f","abstract_canon_sha256":"f7bbe9ddac3c186543e45cf0ab3b092daa641dd897864b08e0e4f797bae007cf"},"schema_version":"1.0"},"canonical_sha256":"8e120416b02404d3a9a5bca3e2df429d7b8ee5b556417c5d81994ade8155c37c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:25.465985Z","signature_b64":"zoGYmgHiy7svu2p9wRvn9Bmg17NKV2Y7zrogSrP985ntYdvnAvf0309I4pMYBtsqflDabAWPU9ocw7guHPFnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e120416b02404d3a9a5bca3e2df429d7b8ee5b556417c5d81994ade8155c37c","last_reissued_at":"2026-05-18T04:41:25.465493Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:25.465493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0741","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":"2026-05-18T04:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G+JbFx3cRy4wCPWzzfp2SkEPOdzTuEStKfbxGU+tz0utNEWNXcXM5nSThLydvpD6PzXl11eVFN9A4OCGAm1dCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:49:17.558467Z"},"content_sha256":"b5e458a8d29b08770bbe6a5cbc3a89c114d545e693c6df4bafdb9a87b262c604","schema_version":"1.0","event_id":"sha256:b5e458a8d29b08770bbe6a5cbc3a89c114d545e693c6df4bafdb9a87b262c604"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:RYJAIFVQEQCNHKNFXSR6FX2CTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A balanced excited random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Schapira (LM-Orsay), computer Science), Gady Kozma (Faculty of Mathematics, Itai Benjamini (Faculty of Mathematics","submitted_at":"2010-09-03T19:08:56Z","abstract_excerpt":"The following random process on $\\Z^4$ is studied. At first visit to a site, the two first coordinates perform a (2-dimensional) simple random walk step. At further visits, it is the last two coordinates which perform a simple random walk step. We prove that this process is almost surely transient. The lower dimensional versions are discussed and various generalizations and related questions are proposed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0741","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":"2026-05-18T04:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eIew0LhLktOBM62gqp9hJvkk3uBJyPUDCRxMCkL0ZZwNtvGm6XCGiIMVKVq4XsPDmB0aKLg3Fg+2v1y9O2AhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:49:17.558823Z"},"content_sha256":"98fea255e8fdd942b1c8f82134bd56107a3ee02e9775a6e01788a1c087377c1d","schema_version":"1.0","event_id":"sha256:98fea255e8fdd942b1c8f82134bd56107a3ee02e9775a6e01788a1c087377c1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RYJAIFVQEQCNHKNFXSR6FX2CTV/bundle.json","state_url":"https://pith.science/pith/RYJAIFVQEQCNHKNFXSR6FX2CTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RYJAIFVQEQCNHKNFXSR6FX2CTV/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":"2026-06-02T06:49:17Z","links":{"resolver":"https://pith.science/pith/RYJAIFVQEQCNHKNFXSR6FX2CTV","bundle":"https://pith.science/pith/RYJAIFVQEQCNHKNFXSR6FX2CTV/bundle.json","state":"https://pith.science/pith/RYJAIFVQEQCNHKNFXSR6FX2CTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RYJAIFVQEQCNHKNFXSR6FX2CTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RYJAIFVQEQCNHKNFXSR6FX2CTV","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":"f7bbe9ddac3c186543e45cf0ab3b092daa641dd897864b08e0e4f797bae007cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T19:08:56Z","title_canon_sha256":"bb0e3adeea0432e2852f7b13fa6fc851b258183da80cc95c4efcc4ce1e10949f"},"schema_version":"1.0","source":{"id":"1009.0741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0741","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0741v1","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0741","created_at":"2026-05-18T04:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"RYJAIFVQEQCN","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RYJAIFVQEQCNHKNF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RYJAIFVQ","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:98fea255e8fdd942b1c8f82134bd56107a3ee02e9775a6e01788a1c087377c1d","target":"graph","created_at":"2026-05-18T04:41:25Z","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":"The following random process on $\\Z^4$ is studied. At first visit to a site, the two first coordinates perform a (2-dimensional) simple random walk step. At further visits, it is the last two coordinates which perform a simple random walk step. We prove that this process is almost surely transient. The lower dimensional versions are discussed and various generalizations and related questions are proposed.","authors_text":"Bruno Schapira (LM-Orsay), computer Science), Gady Kozma (Faculty of Mathematics, Itai Benjamini (Faculty of Mathematics","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T19:08:56Z","title":"A balanced excited random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0741","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:b5e458a8d29b08770bbe6a5cbc3a89c114d545e693c6df4bafdb9a87b262c604","target":"record","created_at":"2026-05-18T04:41:25Z","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":"f7bbe9ddac3c186543e45cf0ab3b092daa641dd897864b08e0e4f797bae007cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T19:08:56Z","title_canon_sha256":"bb0e3adeea0432e2852f7b13fa6fc851b258183da80cc95c4efcc4ce1e10949f"},"schema_version":"1.0","source":{"id":"1009.0741","kind":"arxiv","version":1}},"canonical_sha256":"8e120416b02404d3a9a5bca3e2df429d7b8ee5b556417c5d81994ade8155c37c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e120416b02404d3a9a5bca3e2df429d7b8ee5b556417c5d81994ade8155c37c","first_computed_at":"2026-05-18T04:41:25.465493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:25.465493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zoGYmgHiy7svu2p9wRvn9Bmg17NKV2Y7zrogSrP985ntYdvnAvf0309I4pMYBtsqflDabAWPU9ocw7guHPFnAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:25.465985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5e458a8d29b08770bbe6a5cbc3a89c114d545e693c6df4bafdb9a87b262c604","sha256:98fea255e8fdd942b1c8f82134bd56107a3ee02e9775a6e01788a1c087377c1d"],"state_sha256":"0e255d3e8c63468314b0670fb34b1fc938295dd4b4846614693f06943eebb8da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ACHhuDQpxox/au+cfn3k2gvBnhYe5tt5yQ6FFTyVkDtfwJCVU5bJmswvcvW4RF2JI5b8apHdwGaeX2chh4qCAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:49:17.561132Z","bundle_sha256":"a3a171e9d4b7933b7c0a623157d900e983e64844e3de7d36b0ceba7088186638"}}