{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4B4V2JK4TEYKP5GAMB6UT4DOZJ","short_pith_number":"pith:4B4V2JK4","canonical_record":{"source":{"id":"1001.1741","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-11T21:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"c471f0bfb07aea1bf5c90edf4ce54a9110fa101d103337e9ab3f310c964e31ec","abstract_canon_sha256":"c6a0988bcd838137eef0dbdb96b467e402496c65d61ffb19d9305d3a001b4e08"},"schema_version":"1.0"},"canonical_sha256":"e0795d255c9930a7f4c0607d49f06eca52e163f698d22919e7519d1445ccc10b","source":{"kind":"arxiv","id":"1001.1741","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1741","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1741v3","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1741","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"4B4V2JK4TEYK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4B4V2JK4TEYKP5GA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4B4V2JK4","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4B4V2JK4TEYKP5GAMB6UT4DOZJ","target":"record","payload":{"canonical_record":{"source":{"id":"1001.1741","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-11T21:09:30Z","cross_cats_sorted":[],"title_canon_sha256":"c471f0bfb07aea1bf5c90edf4ce54a9110fa101d103337e9ab3f310c964e31ec","abstract_canon_sha256":"c6a0988bcd838137eef0dbdb96b467e402496c65d61ffb19d9305d3a001b4e08"},"schema_version":"1.0"},"canonical_sha256":"e0795d255c9930a7f4c0607d49f06eca52e163f698d22919e7519d1445ccc10b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:28.803124Z","signature_b64":"svNfpAFvs2vhudgb3+AsMmAJTKNi1YpVwCwXLNCZQ5QhDXk3WU4XxZmHVUGqMl+7/wBbwR2tduyND4a54+N3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0795d255c9930a7f4c0607d49f06eca52e163f698d22919e7519d1445ccc10b","last_reissued_at":"2026-05-18T03:43:28.802341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:28.802341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.1741","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IeUV6rKKhdctw8wvepEh4mRH18usoeomQO0/IqDD5a+ZDLVn2N02c0I7nBfd0FEdcpfDGkE0CVvmA6cHCdbVDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:57:15.795102Z"},"content_sha256":"61129b16734d7c21afd492e09b8c7807dd910a01f46f3682cef74643438af3f8","schema_version":"1.0","event_id":"sha256:61129b16734d7c21afd492e09b8c7807dd910a01f46f3682cef74643438af3f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4B4V2JK4TEYKP5GAMB6UT4DOZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a general many-dimensional excited random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alejandro F. Ram\\'irez, Marina Vachkovskaia, Mikhail Menshikov, Serguei Popov","submitted_at":"2010-01-11T21:09:30Z","abstract_excerpt":"In this paper we study a substantial generalization of the model of excited random walk introduced in [Electron. Commun. Probab. 8 (2003) 86-92] by Benjamini and Wilson. We consider a discrete-time stochastic process $(X_n,n=0,1,2,...)$ taking values on ${\\mathbb{Z}}^d$, $d\\geq2$, described as follows: when the particle visits a site for the first time, it has a uniformly-positive drift in a given direction $\\ell$; when the particle is at a site which was already visited before, it has zero drift. Assuming uniform ellipticity and that the jumps of the process are uniformly bounded, we prove th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1741","kind":"arxiv","version":3},"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":"2026-05-18T03:43:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gpOlE0pAln4xB4J+eU3O+BhddbDeRkl6DuJM7djifiP3DPvBkBUAHJMYY+0sq9eQ4UIfGeajSB+fc9Ij0rFVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:57:15.795716Z"},"content_sha256":"de6cc003799f16b74d3d851170237fa86c901907ac69cb723a065b2e60a040a9","schema_version":"1.0","event_id":"sha256:de6cc003799f16b74d3d851170237fa86c901907ac69cb723a065b2e60a040a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4B4V2JK4TEYKP5GAMB6UT4DOZJ/bundle.json","state_url":"https://pith.science/pith/4B4V2JK4TEYKP5GAMB6UT4DOZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4B4V2JK4TEYKP5GAMB6UT4DOZJ/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":"2026-05-27T18:57:15Z","links":{"resolver":"https://pith.science/pith/4B4V2JK4TEYKP5GAMB6UT4DOZJ","bundle":"https://pith.science/pith/4B4V2JK4TEYKP5GAMB6UT4DOZJ/bundle.json","state":"https://pith.science/pith/4B4V2JK4TEYKP5GAMB6UT4DOZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4B4V2JK4TEYKP5GAMB6UT4DOZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4B4V2JK4TEYKP5GAMB6UT4DOZJ","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":"c6a0988bcd838137eef0dbdb96b467e402496c65d61ffb19d9305d3a001b4e08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-11T21:09:30Z","title_canon_sha256":"c471f0bfb07aea1bf5c90edf4ce54a9110fa101d103337e9ab3f310c964e31ec"},"schema_version":"1.0","source":{"id":"1001.1741","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1741","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1741v3","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1741","created_at":"2026-05-18T03:43:28Z"},{"alias_kind":"pith_short_12","alias_value":"4B4V2JK4TEYK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4B4V2JK4TEYKP5GA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4B4V2JK4","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:de6cc003799f16b74d3d851170237fa86c901907ac69cb723a065b2e60a040a9","target":"graph","created_at":"2026-05-18T03:43:28Z","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 study a substantial generalization of the model of excited random walk introduced in [Electron. Commun. Probab. 8 (2003) 86-92] by Benjamini and Wilson. We consider a discrete-time stochastic process $(X_n,n=0,1,2,...)$ taking values on ${\\mathbb{Z}}^d$, $d\\geq2$, described as follows: when the particle visits a site for the first time, it has a uniformly-positive drift in a given direction $\\ell$; when the particle is at a site which was already visited before, it has zero drift. Assuming uniform ellipticity and that the jumps of the process are uniformly bounded, we prove th","authors_text":"Alejandro F. Ram\\'irez, Marina Vachkovskaia, Mikhail Menshikov, Serguei Popov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-11T21:09:30Z","title":"On a general many-dimensional excited random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1741","kind":"arxiv","version":3},"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":"sha256:61129b16734d7c21afd492e09b8c7807dd910a01f46f3682cef74643438af3f8","target":"record","created_at":"2026-05-18T03:43:28Z","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":"c6a0988bcd838137eef0dbdb96b467e402496c65d61ffb19d9305d3a001b4e08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-11T21:09:30Z","title_canon_sha256":"c471f0bfb07aea1bf5c90edf4ce54a9110fa101d103337e9ab3f310c964e31ec"},"schema_version":"1.0","source":{"id":"1001.1741","kind":"arxiv","version":3}},"canonical_sha256":"e0795d255c9930a7f4c0607d49f06eca52e163f698d22919e7519d1445ccc10b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0795d255c9930a7f4c0607d49f06eca52e163f698d22919e7519d1445ccc10b","first_computed_at":"2026-05-18T03:43:28.802341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:28.802341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"svNfpAFvs2vhudgb3+AsMmAJTKNi1YpVwCwXLNCZQ5QhDXk3WU4XxZmHVUGqMl+7/wBbwR2tduyND4a54+N3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:28.803124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1741","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61129b16734d7c21afd492e09b8c7807dd910a01f46f3682cef74643438af3f8","sha256:de6cc003799f16b74d3d851170237fa86c901907ac69cb723a065b2e60a040a9"],"state_sha256":"b0ccc07cefdda31b11c341c39b8b50d99fbd1c6917d5b79d98470dae09190844"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJzSRF+m59vL6715d6rCITReMo75j2eTTpU8u6zUxp9mK4MP2BUXpClBHR6ezMMw3a30k3qIXwru+5G932xnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:57:15.799121Z","bundle_sha256":"fe4bd37eb0d632bf255ec8578e2fe7619d007531d63219c169dc107ddca2e791"}}