{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:DMSJMWQBZU4SGRKKBI23WGOT6N","short_pith_number":"pith:DMSJMWQB","canonical_record":{"source":{"id":"0910.1055","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-06T17:04:23Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"983f1a60f30ce667ecfce4fbb8b686f04eaf45b73c56fa5dd94651432a3eaacb","abstract_canon_sha256":"40cb4cf49377febc76fb9bb9f112ab0b5c40f3c6c355bc433bd6221b7a364fc8"},"schema_version":"1.0"},"canonical_sha256":"1b24965a01cd3923454a0a35bb19d3f3761ec01b273b09b9fa65df99c9fa67a2","source":{"kind":"arxiv","id":"0910.1055","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1055","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1055v3","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1055","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"DMSJMWQBZU4S","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DMSJMWQBZU4SGRKK","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DMSJMWQB","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:DMSJMWQBZU4SGRKKBI23WGOT6N","target":"record","payload":{"canonical_record":{"source":{"id":"0910.1055","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-06T17:04:23Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"983f1a60f30ce667ecfce4fbb8b686f04eaf45b73c56fa5dd94651432a3eaacb","abstract_canon_sha256":"40cb4cf49377febc76fb9bb9f112ab0b5c40f3c6c355bc433bd6221b7a364fc8"},"schema_version":"1.0"},"canonical_sha256":"1b24965a01cd3923454a0a35bb19d3f3761ec01b273b09b9fa65df99c9fa67a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:14.954772Z","signature_b64":"N48LGQqZ6DZTiU5/zTW/UzASUre2IU8xSB1YKAgtyIByWTmylsF92YyndcGEOz5HQlLbhgeNoxvXZYBa4zQlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b24965a01cd3923454a0a35bb19d3f3761ec01b273b09b9fa65df99c9fa67a2","last_reissued_at":"2026-05-18T04:35:14.954226Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:14.954226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.1055","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":"2026-05-18T04:35:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CvAQ1aVzWR+cf9Bj6XmJC2xqmjD7sfvvWZvRM+Gja7ca3KUqtP/3Ue9LpzkSaNIRU19/U94h8u2mg3+B737zDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:57:59.704798Z"},"content_sha256":"dd93c6eb4f81e2df87303cdc80bab3ebdd3022fbd9fdda581207a061becb1ec0","schema_version":"1.0","event_id":"sha256:dd93c6eb4f81e2df87303cdc80bab3ebdd3022fbd9fdda581207a061becb1ec0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:DMSJMWQBZU4SGRKKBI23WGOT6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Green functions and Martin compactification for killed random walks related to SU(3)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"Kilian Raschel","submitted_at":"2009-10-06T17:04:23Z","abstract_excerpt":"We consider the random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior, and which admit a positive harmonic polynomial of degree three. For these processes, we find the asymptotic of the Green functions along all infinite paths of states, and from this we deduce that the Martin compactification is the one-point compactification."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1055","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":"2026-05-18T04:35:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6bW9nvvvieXHsZqRX4/9BG2hMU4fdLJuoPFHVFYu36kfqt8cxOgnFT/K50C8Ll5sMuU1VGRP46DivmKKI6CECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:57:59.705143Z"},"content_sha256":"7799fd8536c885ab077ffd2d02ec8409a6191acc9769052c361875c213f4aab9","schema_version":"1.0","event_id":"sha256:7799fd8536c885ab077ffd2d02ec8409a6191acc9769052c361875c213f4aab9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMSJMWQBZU4SGRKKBI23WGOT6N/bundle.json","state_url":"https://pith.science/pith/DMSJMWQBZU4SGRKKBI23WGOT6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMSJMWQBZU4SGRKKBI23WGOT6N/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":"2026-05-28T00:57:59Z","links":{"resolver":"https://pith.science/pith/DMSJMWQBZU4SGRKKBI23WGOT6N","bundle":"https://pith.science/pith/DMSJMWQBZU4SGRKKBI23WGOT6N/bundle.json","state":"https://pith.science/pith/DMSJMWQBZU4SGRKKBI23WGOT6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMSJMWQBZU4SGRKKBI23WGOT6N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DMSJMWQBZU4SGRKKBI23WGOT6N","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":"40cb4cf49377febc76fb9bb9f112ab0b5c40f3c6c355bc433bd6221b7a364fc8","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-06T17:04:23Z","title_canon_sha256":"983f1a60f30ce667ecfce4fbb8b686f04eaf45b73c56fa5dd94651432a3eaacb"},"schema_version":"1.0","source":{"id":"0910.1055","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1055","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1055v3","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1055","created_at":"2026-05-18T04:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"DMSJMWQBZU4S","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DMSJMWQBZU4SGRKK","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DMSJMWQB","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:7799fd8536c885ab077ffd2d02ec8409a6191acc9769052c361875c213f4aab9","target":"graph","created_at":"2026-05-18T04:35:14Z","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 random walks killed at the boundary of the quarter plane, with homogeneous non-zero jump probabilities to the eight nearest neighbors and drift zero in the interior, and which admit a positive harmonic polynomial of degree three. For these processes, we find the asymptotic of the Green functions along all infinite paths of states, and from this we deduce that the Martin compactification is the one-point compactification.","authors_text":"Kilian Raschel","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-06T17:04:23Z","title":"Green functions and Martin compactification for killed random walks related to SU(3)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1055","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:dd93c6eb4f81e2df87303cdc80bab3ebdd3022fbd9fdda581207a061becb1ec0","target":"record","created_at":"2026-05-18T04:35:14Z","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":"40cb4cf49377febc76fb9bb9f112ab0b5c40f3c6c355bc433bd6221b7a364fc8","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-10-06T17:04:23Z","title_canon_sha256":"983f1a60f30ce667ecfce4fbb8b686f04eaf45b73c56fa5dd94651432a3eaacb"},"schema_version":"1.0","source":{"id":"0910.1055","kind":"arxiv","version":3}},"canonical_sha256":"1b24965a01cd3923454a0a35bb19d3f3761ec01b273b09b9fa65df99c9fa67a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b24965a01cd3923454a0a35bb19d3f3761ec01b273b09b9fa65df99c9fa67a2","first_computed_at":"2026-05-18T04:35:14.954226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:14.954226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N48LGQqZ6DZTiU5/zTW/UzASUre2IU8xSB1YKAgtyIByWTmylsF92YyndcGEOz5HQlLbhgeNoxvXZYBa4zQlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:14.954772Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1055","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd93c6eb4f81e2df87303cdc80bab3ebdd3022fbd9fdda581207a061becb1ec0","sha256:7799fd8536c885ab077ffd2d02ec8409a6191acc9769052c361875c213f4aab9"],"state_sha256":"0c81d9c62907e46c234a4a75ff63a28a88fbf88b9f214ad7be1ed6c1c63145fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"59yOlQiVREtSCm+V55ew3HN8IAuuWSKvdW9R9AjPwA8Piumj6jaIcxpIB2IRHpEgnCoC3C65BBfP47tdfYE1DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:57:59.708299Z","bundle_sha256":"cb2930357d4840b6d2206b69e766b7a2f4e852639befa4a681c5053faebc604e"}}