{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:Q3XHJUP3LQ3E6JB2C3BHKESFXZ","short_pith_number":"pith:Q3XHJUP3","canonical_record":{"source":{"id":"2105.14807","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-05-31T09:08:20Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"ad210a855562f196ef7c4436c3a7e9cd2f4e50ce1fa1fe8bbf3f30d307938cc5","abstract_canon_sha256":"cb629a0df3e53c1a747c7f1bc003d1d124139490a36d63d0c7f96d442e0e5e8a"},"schema_version":"1.0"},"canonical_sha256":"86ee74d1fb5c364f243a16c2751245be6507410a0ca3b633644b6ea958454ed7","source":{"kind":"arxiv","id":"2105.14807","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.14807","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"2105.14807v2","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.14807","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"Q3XHJUP3LQ3E","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q3XHJUP3LQ3E6JB2","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q3XHJUP3","created_at":"2026-07-05T11:34:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:Q3XHJUP3LQ3E6JB2C3BHKESFXZ","target":"record","payload":{"canonical_record":{"source":{"id":"2105.14807","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-05-31T09:08:20Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"ad210a855562f196ef7c4436c3a7e9cd2f4e50ce1fa1fe8bbf3f30d307938cc5","abstract_canon_sha256":"cb629a0df3e53c1a747c7f1bc003d1d124139490a36d63d0c7f96d442e0e5e8a"},"schema_version":"1.0"},"canonical_sha256":"86ee74d1fb5c364f243a16c2751245be6507410a0ca3b633644b6ea958454ed7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:39.054518Z","signature_b64":"q3X0u8nlRFJdt76Ed4Awp0wB1kCCSbBf18/ztf0IttYCZm3xzxLZZBSr9oj9z99Z6oz71mewVZi7VgMFaNZNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86ee74d1fb5c364f243a16c2751245be6507410a0ca3b633644b6ea958454ed7","last_reissued_at":"2026-07-05T11:34:39.054017Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:39.054017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.14807","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:34:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mty3Y+ZcN9Wzz8/byj2hCujZrcREjTp6m/A7t6UeVDfQ+JFbrBjc9ZermhNuo3G7I3mBvj5hln6GfsnBE510Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:58:41.802843Z"},"content_sha256":"0d907acff35ce077c04ee5e16f4c7c334ef45a73f0d4ca74ce1e6765b77f7747","schema_version":"1.0","event_id":"sha256:0d907acff35ce077c04ee5e16f4c7c334ef45a73f0d4ca74ce1e6765b77f7747"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:Q3XHJUP3LQ3E6JB2C3BHKESFXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Martin compactifications of affine buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.GR","authors_text":"Bartosz Trojan, Bertrand R\\'emy","submitted_at":"2021-05-31T09:08:20Z","abstract_excerpt":"We carry out an in-depth study of Martin compactifications of affine buildings, from the viewpoint of potential theory and random walks. This work does not use any group action on buildings, although all the results are also stated within the framework of the Bruhat--Tits theory of semisimple groups over non-Archimedean local fields. This choice should allow the use of these building compactifications in intriguing geometric group theory situations, where only lattice actions are available. The resulting compactified spaces use and, at the same time, make it possible to understand geometricall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.14807","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.14807/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:34:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7LOGvdkUaTR6TYVCKSNdvpqEAhqRfNEW4bp+wuZLyH5aK/BmpQd4SUuTVeK3IK5m1to8Verri5zHuZSjY/LBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T02:58:41.803596Z"},"content_sha256":"97b4287e04909a8bf373d71c29c7ca349d362dd2e75a523a0d06f835e96aa006","schema_version":"1.0","event_id":"sha256:97b4287e04909a8bf373d71c29c7ca349d362dd2e75a523a0d06f835e96aa006"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3XHJUP3LQ3E6JB2C3BHKESFXZ/bundle.json","state_url":"https://pith.science/pith/Q3XHJUP3LQ3E6JB2C3BHKESFXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3XHJUP3LQ3E6JB2C3BHKESFXZ/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":"2026-08-18T02:58:41Z","links":{"resolver":"https://pith.science/pith/Q3XHJUP3LQ3E6JB2C3BHKESFXZ","bundle":"https://pith.science/pith/Q3XHJUP3LQ3E6JB2C3BHKESFXZ/bundle.json","state":"https://pith.science/pith/Q3XHJUP3LQ3E6JB2C3BHKESFXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3XHJUP3LQ3E6JB2C3BHKESFXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:Q3XHJUP3LQ3E6JB2C3BHKESFXZ","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":"cb629a0df3e53c1a747c7f1bc003d1d124139490a36d63d0c7f96d442e0e5e8a","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-05-31T09:08:20Z","title_canon_sha256":"ad210a855562f196ef7c4436c3a7e9cd2f4e50ce1fa1fe8bbf3f30d307938cc5"},"schema_version":"1.0","source":{"id":"2105.14807","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.14807","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"arxiv_version","alias_value":"2105.14807v2","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.14807","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"pith_short_12","alias_value":"Q3XHJUP3LQ3E","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q3XHJUP3LQ3E6JB2","created_at":"2026-07-05T11:34:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q3XHJUP3","created_at":"2026-07-05T11:34:39Z"}],"graph_snapshots":[{"event_id":"sha256:97b4287e04909a8bf373d71c29c7ca349d362dd2e75a523a0d06f835e96aa006","target":"graph","created_at":"2026-07-05T11:34:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2105.14807/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We carry out an in-depth study of Martin compactifications of affine buildings, from the viewpoint of potential theory and random walks. This work does not use any group action on buildings, although all the results are also stated within the framework of the Bruhat--Tits theory of semisimple groups over non-Archimedean local fields. This choice should allow the use of these building compactifications in intriguing geometric group theory situations, where only lattice actions are available. The resulting compactified spaces use and, at the same time, make it possible to understand geometricall","authors_text":"Bartosz Trojan, Bertrand R\\'emy","cross_cats":["math.CA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-05-31T09:08:20Z","title":"Martin compactifications of affine buildings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.14807","kind":"arxiv","version":2},"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":"sha256:0d907acff35ce077c04ee5e16f4c7c334ef45a73f0d4ca74ce1e6765b77f7747","target":"record","created_at":"2026-07-05T11:34:39Z","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":"cb629a0df3e53c1a747c7f1bc003d1d124139490a36d63d0c7f96d442e0e5e8a","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2021-05-31T09:08:20Z","title_canon_sha256":"ad210a855562f196ef7c4436c3a7e9cd2f4e50ce1fa1fe8bbf3f30d307938cc5"},"schema_version":"1.0","source":{"id":"2105.14807","kind":"arxiv","version":2}},"canonical_sha256":"86ee74d1fb5c364f243a16c2751245be6507410a0ca3b633644b6ea958454ed7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86ee74d1fb5c364f243a16c2751245be6507410a0ca3b633644b6ea958454ed7","first_computed_at":"2026-07-05T11:34:39.054017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:39.054017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q3X0u8nlRFJdt76Ed4Awp0wB1kCCSbBf18/ztf0IttYCZm3xzxLZZBSr9oj9z99Z6oz71mewVZi7VgMFaNZNAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:39.054518Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.14807","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d907acff35ce077c04ee5e16f4c7c334ef45a73f0d4ca74ce1e6765b77f7747","sha256:97b4287e04909a8bf373d71c29c7ca349d362dd2e75a523a0d06f835e96aa006"],"state_sha256":"fe0cf130c88216c648b3084c91303fa0ca6672daef9afb0d390be0183178ecff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jFWEGyYc+JBQMYf8tVi54+d/C9SlCo/KRvP98meLJBgVZ8br200kHSnyv1TCNxEpNXg6zm7L//u9MtXyKbMYBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T02:58:41.810381Z","bundle_sha256":"b4b655f025ae573d011b93b7eedb9d81e9d6d95c64c6033ee35f7284e0e7d2ee"}}