{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:S4DPJHTJU3UI66MKCIXB2IC7FJ","short_pith_number":"pith:S4DPJHTJ","canonical_record":{"source":{"id":"2607.14668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-16T07:35:21Z","cross_cats_sorted":["math.GR","math.MG"],"title_canon_sha256":"069de3d8fe1dd8d18f84a4b4aeafd60731547d12fa2e2532731f452cc25a261f","abstract_canon_sha256":"c0153cb51d270b8d7635e4938f8cfe349a5b3222dd389454244c34892c6a38a7"},"schema_version":"1.0"},"canonical_sha256":"9706f49e69a6e88f798a122e1d205f2a650cb7d87d4b06fac11e1e3a9300869f","source":{"kind":"arxiv","id":"2607.14668","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14668","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14668v1","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14668","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"pith_short_12","alias_value":"S4DPJHTJU3UI","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"pith_short_16","alias_value":"S4DPJHTJU3UI66MK","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"pith_short_8","alias_value":"S4DPJHTJ","created_at":"2026-07-17T01:21:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:S4DPJHTJU3UI66MKCIXB2IC7FJ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.14668","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-16T07:35:21Z","cross_cats_sorted":["math.GR","math.MG"],"title_canon_sha256":"069de3d8fe1dd8d18f84a4b4aeafd60731547d12fa2e2532731f452cc25a261f","abstract_canon_sha256":"c0153cb51d270b8d7635e4938f8cfe349a5b3222dd389454244c34892c6a38a7"},"schema_version":"1.0"},"canonical_sha256":"9706f49e69a6e88f798a122e1d205f2a650cb7d87d4b06fac11e1e3a9300869f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:24.084169Z","signature_b64":"VWwYX1r45ExrHN7KG2t+SfznnAyfM0eKQyRDTsDyQUpClYy4HhmIysEYl5LsiJvWqJbKQ2mEMsHZSo+QHZMlDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9706f49e69a6e88f798a122e1d205f2a650cb7d87d4b06fac11e1e3a9300869f","last_reissued_at":"2026-07-17T01:21:24.083334Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:24.083334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.14668","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":"2026-07-17T01:21:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GinsmlabZqwXJ0B7AK2x+SyZZQq4BndN1mcgTr4+UMfxcDTjQDBJxB3TxJZ6dpi9/nUvGLNvnE9xbpfM85JFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:22:32.806310Z"},"content_sha256":"bd8e7f1de36e5efc55189012df9ee81deebf94864b044b3ad585e71b83721422","schema_version":"1.0","event_id":"sha256:bd8e7f1de36e5efc55189012df9ee81deebf94864b044b3ad585e71b83721422"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:S4DPJHTJU3UI66MKCIXB2IC7FJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability for boundary actions of cocompact lattices in Euclidean buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MG"],"primary_cat":"math.DS","authors_text":"Thang Nguyen, Theodore Weisman","submitted_at":"2026-07-16T07:35:21Z","abstract_excerpt":"When $X$ is a locally compact Euclidean building, the isometry group\n  of $X$ acts by homeomorphisms on the space of $k$-simplices in the\n  visual boundary of $X$. We consider perturbations of these actions\n  for discrete groups of isometries acting with compact quotient on\n  $X$, showing that all small enough perturbations are semi-conjugate\n  to the original action. This proves in particular that, when $Q$ is\n  any parabolic subgroup in a semisimple $p$-adic Lie group $G$, the\n  induced action of a cocompact lattice in $G$ has a topologically\n  stable action on $G/Q$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14668","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14668/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":"2026-07-17T01:21:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mcIEsz0w9DRAhHxl3SOn9L03d9Y2mxc9Ee4/urX8F5MAIXiCHZqoNebE5f7wDTQqDHOLBIvQUlwYA9+Z47c9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:22:32.806836Z"},"content_sha256":"2f51738dd02c4cff42eb78f471db4572c5f959daf91623197e22a16a0aaa5605","schema_version":"1.0","event_id":"sha256:2f51738dd02c4cff42eb78f471db4572c5f959daf91623197e22a16a0aaa5605"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S4DPJHTJU3UI66MKCIXB2IC7FJ/bundle.json","state_url":"https://pith.science/pith/S4DPJHTJU3UI66MKCIXB2IC7FJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S4DPJHTJU3UI66MKCIXB2IC7FJ/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":"2026-08-13T10:22:32Z","links":{"resolver":"https://pith.science/pith/S4DPJHTJU3UI66MKCIXB2IC7FJ","bundle":"https://pith.science/pith/S4DPJHTJU3UI66MKCIXB2IC7FJ/bundle.json","state":"https://pith.science/pith/S4DPJHTJU3UI66MKCIXB2IC7FJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S4DPJHTJU3UI66MKCIXB2IC7FJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:S4DPJHTJU3UI66MKCIXB2IC7FJ","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":"c0153cb51d270b8d7635e4938f8cfe349a5b3222dd389454244c34892c6a38a7","cross_cats_sorted":["math.GR","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-16T07:35:21Z","title_canon_sha256":"069de3d8fe1dd8d18f84a4b4aeafd60731547d12fa2e2532731f452cc25a261f"},"schema_version":"1.0","source":{"id":"2607.14668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.14668","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"arxiv_version","alias_value":"2607.14668v1","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14668","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"pith_short_12","alias_value":"S4DPJHTJU3UI","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"pith_short_16","alias_value":"S4DPJHTJU3UI66MK","created_at":"2026-07-17T01:21:24Z"},{"alias_kind":"pith_short_8","alias_value":"S4DPJHTJ","created_at":"2026-07-17T01:21:24Z"}],"graph_snapshots":[{"event_id":"sha256:2f51738dd02c4cff42eb78f471db4572c5f959daf91623197e22a16a0aaa5605","target":"graph","created_at":"2026-07-17T01:21:24Z","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/2607.14668/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When $X$ is a locally compact Euclidean building, the isometry group\n  of $X$ acts by homeomorphisms on the space of $k$-simplices in the\n  visual boundary of $X$. We consider perturbations of these actions\n  for discrete groups of isometries acting with compact quotient on\n  $X$, showing that all small enough perturbations are semi-conjugate\n  to the original action. This proves in particular that, when $Q$ is\n  any parabolic subgroup in a semisimple $p$-adic Lie group $G$, the\n  induced action of a cocompact lattice in $G$ has a topologically\n  stable action on $G/Q$.","authors_text":"Thang Nguyen, Theodore Weisman","cross_cats":["math.GR","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-16T07:35:21Z","title":"Stability for boundary actions of cocompact lattices in Euclidean buildings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14668","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:bd8e7f1de36e5efc55189012df9ee81deebf94864b044b3ad585e71b83721422","target":"record","created_at":"2026-07-17T01:21:24Z","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":"c0153cb51d270b8d7635e4938f8cfe349a5b3222dd389454244c34892c6a38a7","cross_cats_sorted":["math.GR","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-07-16T07:35:21Z","title_canon_sha256":"069de3d8fe1dd8d18f84a4b4aeafd60731547d12fa2e2532731f452cc25a261f"},"schema_version":"1.0","source":{"id":"2607.14668","kind":"arxiv","version":1}},"canonical_sha256":"9706f49e69a6e88f798a122e1d205f2a650cb7d87d4b06fac11e1e3a9300869f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9706f49e69a6e88f798a122e1d205f2a650cb7d87d4b06fac11e1e3a9300869f","first_computed_at":"2026-07-17T01:21:24.083334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-17T01:21:24.083334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VWwYX1r45ExrHN7KG2t+SfznnAyfM0eKQyRDTsDyQUpClYy4HhmIysEYl5LsiJvWqJbKQ2mEMsHZSo+QHZMlDA==","signature_status":"signed_v1","signed_at":"2026-07-17T01:21:24.084169Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.14668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd8e7f1de36e5efc55189012df9ee81deebf94864b044b3ad585e71b83721422","sha256:2f51738dd02c4cff42eb78f471db4572c5f959daf91623197e22a16a0aaa5605"],"state_sha256":"58c9179d8f4bf06e6ef220be76b06e3d6ed06fcff0239a97d162953c6c603e8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XzZGAw5of8NyZpHKNAptw0zhuzSfctX0bzvPDZxQv57OtXc1Hr4wD6cD/t5LY3BbZPPRuAHhevwpsFfDrlEgBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T10:22:32.810714Z","bundle_sha256":"d47734527d0a408657a6f4a040e19b746e6f303fad6e2a14bec67b5101217a59"}}