{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:E47YWK5LAO2DIDOAKFCEMH3XCK","short_pith_number":"pith:E47YWK5L","canonical_record":{"source":{"id":"1506.03594","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-11T09:18:38Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"777053e47bd2c1ef51d4db6f62bb89d14fdfe84d94ad6610f556db517adf4f6e","abstract_canon_sha256":"40e867d1f6867181a25c4288a066a47359bc71f8316c2c0f89a6f1b100533481"},"schema_version":"1.0"},"canonical_sha256":"273f8b2bab03b4340dc05144461f771283d8ae2236e17427120fef6aeadaddd4","source":{"kind":"arxiv","id":"1506.03594","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03594","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03594v2","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03594","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"pith_short_12","alias_value":"E47YWK5LAO2D","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E47YWK5LAO2DIDOA","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E47YWK5L","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:E47YWK5LAO2DIDOAKFCEMH3XCK","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03594","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-11T09:18:38Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"777053e47bd2c1ef51d4db6f62bb89d14fdfe84d94ad6610f556db517adf4f6e","abstract_canon_sha256":"40e867d1f6867181a25c4288a066a47359bc71f8316c2c0f89a6f1b100533481"},"schema_version":"1.0"},"canonical_sha256":"273f8b2bab03b4340dc05144461f771283d8ae2236e17427120fef6aeadaddd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:20.842543Z","signature_b64":"eEii4FShvSbZOhcR3eZx0yuL0LQvQTAKuqb5lWeKUQrQP5WxPFGgpP3BIYJkUPjKT+FXWQyKZtZ8jl0Yg7PPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"273f8b2bab03b4340dc05144461f771283d8ae2236e17427120fef6aeadaddd4","last_reissued_at":"2026-05-18T01:29:20.841769Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:20.841769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03594","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":"2026-05-18T01:29:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K+YF4CJRHZw+CHzujPvJn3iBQfIKREV6dPzM85iLRI3QAjJr0APba5lJM5Ai8PuCJxh4gyMXPagkk5NzFmZmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:16:16.468820Z"},"content_sha256":"d9d9fd8b215abbd7938604baf53999d516495ef10e397d7d1f09456093f2416f","schema_version":"1.0","event_id":"sha256:d9d9fd8b215abbd7938604baf53999d516495ef10e397d7d1f09456093f2416f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:E47YWK5LAO2DIDOAKFCEMH3XCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strongly transitive actions on Euclidean buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.MG","authors_text":"Jeroen Schillewaert, Linus Kramer","submitted_at":"2015-06-11T09:18:38Z","abstract_excerpt":"We prove a decomposition result for a group $G$ acting strongly transitively on the Tits boundary of a Euclidean building. As an application we provide a local to global result for discrete Euclidean buildings, which generalizes results in the locally compact case by Caprace--Ciobotaru and Burger--Mozes. Let $X$ be a Euclidean building without cone factors. If a group $G$ of automorphisms of $X$ acts strongly transitively on the spherical building at infinity $\\partial X$, then the $G$-stabilizer of every affine apartment in $X$ contains all reflections along thick walls. In particular $G$ act"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03594","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":""},"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":"2026-05-18T01:29:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n8CjrwXAwnlxGQvHNr/v5UWPIEOKW1o218QcBNUQztpbCEocUHQa6x1P3VU6Drd98LKDcjgAC5kNQ3zHfESABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:16:16.469528Z"},"content_sha256":"4cea901dfce720bf6ff0ac5021782a486ec24e2d23265dc7f5d8a31d4fb82b19","schema_version":"1.0","event_id":"sha256:4cea901dfce720bf6ff0ac5021782a486ec24e2d23265dc7f5d8a31d4fb82b19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E47YWK5LAO2DIDOAKFCEMH3XCK/bundle.json","state_url":"https://pith.science/pith/E47YWK5LAO2DIDOAKFCEMH3XCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E47YWK5LAO2DIDOAKFCEMH3XCK/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":"2026-05-22T13:16:16Z","links":{"resolver":"https://pith.science/pith/E47YWK5LAO2DIDOAKFCEMH3XCK","bundle":"https://pith.science/pith/E47YWK5LAO2DIDOAKFCEMH3XCK/bundle.json","state":"https://pith.science/pith/E47YWK5LAO2DIDOAKFCEMH3XCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E47YWK5LAO2DIDOAKFCEMH3XCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E47YWK5LAO2DIDOAKFCEMH3XCK","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":"40e867d1f6867181a25c4288a066a47359bc71f8316c2c0f89a6f1b100533481","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-11T09:18:38Z","title_canon_sha256":"777053e47bd2c1ef51d4db6f62bb89d14fdfe84d94ad6610f556db517adf4f6e"},"schema_version":"1.0","source":{"id":"1506.03594","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03594","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03594v2","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03594","created_at":"2026-05-18T01:29:20Z"},{"alias_kind":"pith_short_12","alias_value":"E47YWK5LAO2D","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E47YWK5LAO2DIDOA","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E47YWK5L","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:4cea901dfce720bf6ff0ac5021782a486ec24e2d23265dc7f5d8a31d4fb82b19","target":"graph","created_at":"2026-05-18T01:29:20Z","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 prove a decomposition result for a group $G$ acting strongly transitively on the Tits boundary of a Euclidean building. As an application we provide a local to global result for discrete Euclidean buildings, which generalizes results in the locally compact case by Caprace--Ciobotaru and Burger--Mozes. Let $X$ be a Euclidean building without cone factors. If a group $G$ of automorphisms of $X$ acts strongly transitively on the spherical building at infinity $\\partial X$, then the $G$-stabilizer of every affine apartment in $X$ contains all reflections along thick walls. In particular $G$ act","authors_text":"Jeroen Schillewaert, Linus Kramer","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-11T09:18:38Z","title":"Strongly transitive actions on Euclidean buildings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03594","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:d9d9fd8b215abbd7938604baf53999d516495ef10e397d7d1f09456093f2416f","target":"record","created_at":"2026-05-18T01:29:20Z","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":"40e867d1f6867181a25c4288a066a47359bc71f8316c2c0f89a6f1b100533481","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-06-11T09:18:38Z","title_canon_sha256":"777053e47bd2c1ef51d4db6f62bb89d14fdfe84d94ad6610f556db517adf4f6e"},"schema_version":"1.0","source":{"id":"1506.03594","kind":"arxiv","version":2}},"canonical_sha256":"273f8b2bab03b4340dc05144461f771283d8ae2236e17427120fef6aeadaddd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"273f8b2bab03b4340dc05144461f771283d8ae2236e17427120fef6aeadaddd4","first_computed_at":"2026-05-18T01:29:20.841769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:20.841769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eEii4FShvSbZOhcR3eZx0yuL0LQvQTAKuqb5lWeKUQrQP5WxPFGgpP3BIYJkUPjKT+FXWQyKZtZ8jl0Yg7PPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:20.842543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03594","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9d9fd8b215abbd7938604baf53999d516495ef10e397d7d1f09456093f2416f","sha256:4cea901dfce720bf6ff0ac5021782a486ec24e2d23265dc7f5d8a31d4fb82b19"],"state_sha256":"0e2b16c0168dd4d627d403cf82527412362e3f32e91fff6fe6940271cb25cd9a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxSgKmM6vAumoKYmV8zkPBv6UOpGlXvTTUZ9DdW5kIVnBcIqG3UBjS8lsnT3bk8PEj+Z77V1SPBPcMmanzroDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T13:16:16.472954Z","bundle_sha256":"c41311f5743281dcc4e83e271f3620f69e9905724efad616e3c2bbc91f2df288"}}