{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4SNJMOBNA7U3236O5Z7WN35HNK","short_pith_number":"pith:4SNJMOBN","canonical_record":{"source":{"id":"1306.5909","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-25T10:28:39Z","cross_cats_sorted":[],"title_canon_sha256":"0025a6ecbd5ee3e9bd2b79a8bc9e654d4e28c24fc0559d699f1ef1aba43c2c0c","abstract_canon_sha256":"10f70f1b7b70f153f3bc68e9e20d465946f110f4ea318120b702bf993cbdc6b7"},"schema_version":"1.0"},"canonical_sha256":"e49a96382d07e9bd6fceee7f66efa76abca8d432272cc685056cd6b9311c069e","source":{"kind":"arxiv","id":"1306.5909","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5909","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5909v4","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5909","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"4SNJMOBNA7U3","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4SNJMOBNA7U3236O","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4SNJMOBN","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4SNJMOBNA7U3236O5Z7WN35HNK","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5909","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-25T10:28:39Z","cross_cats_sorted":[],"title_canon_sha256":"0025a6ecbd5ee3e9bd2b79a8bc9e654d4e28c24fc0559d699f1ef1aba43c2c0c","abstract_canon_sha256":"10f70f1b7b70f153f3bc68e9e20d465946f110f4ea318120b702bf993cbdc6b7"},"schema_version":"1.0"},"canonical_sha256":"e49a96382d07e9bd6fceee7f66efa76abca8d432272cc685056cd6b9311c069e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:44.262110Z","signature_b64":"xB/pSuQUmlWclgPqN3SkRtEDLsvUa8c6c4ajdDDxBdgX5CdNRLKZCBK0VEl53t0R6o2lCJ6mSb0jQUzHmxVHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e49a96382d07e9bd6fceee7f66efa76abca8d432272cc685056cd6b9311c069e","last_reissued_at":"2026-05-18T03:07:44.261414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:44.261414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5909","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52BjxfGFpUzjDsSpW4Us5eoT08uCOTmswx33QKWrYmnc6nLqFoNOf+62+hY1sWFkzBGivUz2yuJkFY6xqFBfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:07:32.442415Z"},"content_sha256":"cb40227ad4355ef5352312d13594ef3b4cf281fa054e0a61974b1ef6c0e86ff4","schema_version":"1.0","event_id":"sha256:cb40227ad4355ef5352312d13594ef3b4cf281fa054e0a61974b1ef6c0e86ff4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4SNJMOBNA7U3236O5Z7WN35HNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unavodiable collections of balls for isotropic L\\'{e}vy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ante Mimica, Zoran Vondra\\v{c}ek","submitted_at":"2013-06-25T10:28:39Z","abstract_excerpt":"A collection $\\{\\bar{B}(x_n,r_n)\\}_{n\\ge 1}$ of pairwise disjoint balls in the Euclidean space $\\R^d$ is said to be avoidable with respect to a transient process $X$ if the process with positive probability escapes to infinity without hitting any ball. In this paper we study sufficient and necessary conditions for avoidability with respect to unimodal isotropic L\\'evy processes satisfying a certain scaling hypothesis. These conditions are expressed in terms of the characteristic exponent of the process, or alternatively, in terms of the corresponding Green function. We also discuss the same pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5909","kind":"arxiv","version":4},"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":"2026-05-18T03:07:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9To7OLYfR9D8PE1j7lYnOqv0Y9E13WE9JwEZwFxocV6a2l0joK9Pibopvimqf5TtrlX2NJYpGS+dzql40uSfCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:07:32.443098Z"},"content_sha256":"72f380d0770aabee6957adb22e7f726a70fe860de389c2c446986b41f0ace5bb","schema_version":"1.0","event_id":"sha256:72f380d0770aabee6957adb22e7f726a70fe860de389c2c446986b41f0ace5bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SNJMOBNA7U3236O5Z7WN35HNK/bundle.json","state_url":"https://pith.science/pith/4SNJMOBNA7U3236O5Z7WN35HNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SNJMOBNA7U3236O5Z7WN35HNK/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":"2026-05-31T21:07:32Z","links":{"resolver":"https://pith.science/pith/4SNJMOBNA7U3236O5Z7WN35HNK","bundle":"https://pith.science/pith/4SNJMOBNA7U3236O5Z7WN35HNK/bundle.json","state":"https://pith.science/pith/4SNJMOBNA7U3236O5Z7WN35HNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SNJMOBNA7U3236O5Z7WN35HNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4SNJMOBNA7U3236O5Z7WN35HNK","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":"10f70f1b7b70f153f3bc68e9e20d465946f110f4ea318120b702bf993cbdc6b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-25T10:28:39Z","title_canon_sha256":"0025a6ecbd5ee3e9bd2b79a8bc9e654d4e28c24fc0559d699f1ef1aba43c2c0c"},"schema_version":"1.0","source":{"id":"1306.5909","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5909","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5909v4","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5909","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"4SNJMOBNA7U3","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4SNJMOBNA7U3236O","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4SNJMOBN","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:72f380d0770aabee6957adb22e7f726a70fe860de389c2c446986b41f0ace5bb","target":"graph","created_at":"2026-05-18T03:07:44Z","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":"A collection $\\{\\bar{B}(x_n,r_n)\\}_{n\\ge 1}$ of pairwise disjoint balls in the Euclidean space $\\R^d$ is said to be avoidable with respect to a transient process $X$ if the process with positive probability escapes to infinity without hitting any ball. In this paper we study sufficient and necessary conditions for avoidability with respect to unimodal isotropic L\\'evy processes satisfying a certain scaling hypothesis. These conditions are expressed in terms of the characteristic exponent of the process, or alternatively, in terms of the corresponding Green function. We also discuss the same pr","authors_text":"Ante Mimica, Zoran Vondra\\v{c}ek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-25T10:28:39Z","title":"Unavodiable collections of balls for isotropic L\\'{e}vy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5909","kind":"arxiv","version":4},"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:cb40227ad4355ef5352312d13594ef3b4cf281fa054e0a61974b1ef6c0e86ff4","target":"record","created_at":"2026-05-18T03:07:44Z","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":"10f70f1b7b70f153f3bc68e9e20d465946f110f4ea318120b702bf993cbdc6b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-25T10:28:39Z","title_canon_sha256":"0025a6ecbd5ee3e9bd2b79a8bc9e654d4e28c24fc0559d699f1ef1aba43c2c0c"},"schema_version":"1.0","source":{"id":"1306.5909","kind":"arxiv","version":4}},"canonical_sha256":"e49a96382d07e9bd6fceee7f66efa76abca8d432272cc685056cd6b9311c069e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e49a96382d07e9bd6fceee7f66efa76abca8d432272cc685056cd6b9311c069e","first_computed_at":"2026-05-18T03:07:44.261414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:44.261414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xB/pSuQUmlWclgPqN3SkRtEDLsvUa8c6c4ajdDDxBdgX5CdNRLKZCBK0VEl53t0R6o2lCJ6mSb0jQUzHmxVHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:44.262110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5909","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb40227ad4355ef5352312d13594ef3b4cf281fa054e0a61974b1ef6c0e86ff4","sha256:72f380d0770aabee6957adb22e7f726a70fe860de389c2c446986b41f0ace5bb"],"state_sha256":"f5f759c2f6ba8c1cee5282fdee9b4464f97d855b9c91979eb9e7fc717b7e8603"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SO9Ky8KthzeE93LQrI6uBwpZuzWT9SCazTgxEVJ1OhhVmAvY1IF0A+rIzcvKF7AOddmTRNjX9bQLBowJYAO3Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:07:32.446726Z","bundle_sha256":"48d499dd498d3ae386ea2bd401520a9422f3195be0242b3cfb2913d456ea468d"}}