{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NIDJOJ4J2ESDZSJYMJP2CLVDOH","short_pith_number":"pith:NIDJOJ4J","canonical_record":{"source":{"id":"1708.08431","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-28T17:30:53Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"b863237e6b0cb1f1965512e9079a988f10be26173641d41bbff208d6c3479887","abstract_canon_sha256":"939c4aad65062dd543c4aaad5602329e15da5130fce3b899a86a3340512a0e76"},"schema_version":"1.0"},"canonical_sha256":"6a06972789d1243cc938625fa12ea371f36955289faa0c2f52644e237e2f905c","source":{"kind":"arxiv","id":"1708.08431","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08431","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08431v3","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08431","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"NIDJOJ4J2ESD","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NIDJOJ4J2ESDZSJY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NIDJOJ4J","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NIDJOJ4J2ESDZSJYMJP2CLVDOH","target":"record","payload":{"canonical_record":{"source":{"id":"1708.08431","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-28T17:30:53Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"b863237e6b0cb1f1965512e9079a988f10be26173641d41bbff208d6c3479887","abstract_canon_sha256":"939c4aad65062dd543c4aaad5602329e15da5130fce3b899a86a3340512a0e76"},"schema_version":"1.0"},"canonical_sha256":"6a06972789d1243cc938625fa12ea371f36955289faa0c2f52644e237e2f905c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:19.520286Z","signature_b64":"az4Jky90EQLUwnTTDz1VFqzH21drPUBwfdtjQYmaXXiP9G/+OewucQQ1mFG5Wbo4Mbu9GombHB2xkxjPWqH0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a06972789d1243cc938625fa12ea371f36955289faa0c2f52644e237e2f905c","last_reissued_at":"2026-05-18T00:02:19.519903Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:19.519903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.08431","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":"2026-05-18T00:02:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PKT1H6VzkepHlQR98FhzBAqnJiy0UcjSTrHcTvXM3SLQRlyfEizByWaGWhyO0lv75pg8wYWoWeTOZi3KeWWpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:32:40.972530Z"},"content_sha256":"670834a76dfd2d92b60f4b06627e59c1ed6e2847b053ea2117cddd8ab9863f0c","schema_version":"1.0","event_id":"sha256:670834a76dfd2d92b60f4b06627e59c1ed6e2847b053ea2117cddd8ab9863f0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NIDJOJ4J2ESDZSJYMJP2CLVDOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On geodesic ray bundles in buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Timoth\\'ee Marquis","submitted_at":"2017-08-28T17:30:53Z","abstract_excerpt":"Let $X$ be a building, identified with its Davis realisation. In this paper, we provide for each $x\\in X$ and each $\\eta$ in the visual boundary $\\partial X$ of $X$ a description of the geodesic ray bundle $Geo(x,\\eta)$, namely, of the reunion of all combinatorial geodesic rays (corresponding to infinite minimal galleries in the chamber graph of $X$) starting from $x$ and pointing towards $\\eta$. When $X$ is locally finite and hyperbolic, we show that the symmetric difference between $Geo(x,\\eta)$ and $Geo(y,\\eta)$ is always finite, for $x,y\\in X$ and $\\eta\\in\\partial X$. This gives a positive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08431","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":"2026-05-18T00:02:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJR0/vK796V1ElKTeeype3gjGed2/p6X9iSLriJs2gpD68yj9ng95W46gNfJAVvvz6EJyMvisTxBRiOYh8sBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:32:40.973273Z"},"content_sha256":"dca9e0ac71b4f953c1767e766a1186bd8d34c07f9defffa21497a13b5d235c26","schema_version":"1.0","event_id":"sha256:dca9e0ac71b4f953c1767e766a1186bd8d34c07f9defffa21497a13b5d235c26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NIDJOJ4J2ESDZSJYMJP2CLVDOH/bundle.json","state_url":"https://pith.science/pith/NIDJOJ4J2ESDZSJYMJP2CLVDOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NIDJOJ4J2ESDZSJYMJP2CLVDOH/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":"2026-05-31T14:32:40Z","links":{"resolver":"https://pith.science/pith/NIDJOJ4J2ESDZSJYMJP2CLVDOH","bundle":"https://pith.science/pith/NIDJOJ4J2ESDZSJYMJP2CLVDOH/bundle.json","state":"https://pith.science/pith/NIDJOJ4J2ESDZSJYMJP2CLVDOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NIDJOJ4J2ESDZSJYMJP2CLVDOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NIDJOJ4J2ESDZSJYMJP2CLVDOH","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":"939c4aad65062dd543c4aaad5602329e15da5130fce3b899a86a3340512a0e76","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-28T17:30:53Z","title_canon_sha256":"b863237e6b0cb1f1965512e9079a988f10be26173641d41bbff208d6c3479887"},"schema_version":"1.0","source":{"id":"1708.08431","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08431","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08431v3","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08431","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"NIDJOJ4J2ESD","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NIDJOJ4J2ESDZSJY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NIDJOJ4J","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:dca9e0ac71b4f953c1767e766a1186bd8d34c07f9defffa21497a13b5d235c26","target":"graph","created_at":"2026-05-18T00:02:19Z","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":"Let $X$ be a building, identified with its Davis realisation. In this paper, we provide for each $x\\in X$ and each $\\eta$ in the visual boundary $\\partial X$ of $X$ a description of the geodesic ray bundle $Geo(x,\\eta)$, namely, of the reunion of all combinatorial geodesic rays (corresponding to infinite minimal galleries in the chamber graph of $X$) starting from $x$ and pointing towards $\\eta$. When $X$ is locally finite and hyperbolic, we show that the symmetric difference between $Geo(x,\\eta)$ and $Geo(y,\\eta)$ is always finite, for $x,y\\in X$ and $\\eta\\in\\partial X$. This gives a positive","authors_text":"Timoth\\'ee Marquis","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-28T17:30:53Z","title":"On geodesic ray bundles in buildings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08431","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":"sha256:670834a76dfd2d92b60f4b06627e59c1ed6e2847b053ea2117cddd8ab9863f0c","target":"record","created_at":"2026-05-18T00:02:19Z","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":"939c4aad65062dd543c4aaad5602329e15da5130fce3b899a86a3340512a0e76","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-08-28T17:30:53Z","title_canon_sha256":"b863237e6b0cb1f1965512e9079a988f10be26173641d41bbff208d6c3479887"},"schema_version":"1.0","source":{"id":"1708.08431","kind":"arxiv","version":3}},"canonical_sha256":"6a06972789d1243cc938625fa12ea371f36955289faa0c2f52644e237e2f905c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a06972789d1243cc938625fa12ea371f36955289faa0c2f52644e237e2f905c","first_computed_at":"2026-05-18T00:02:19.519903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:19.519903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"az4Jky90EQLUwnTTDz1VFqzH21drPUBwfdtjQYmaXXiP9G/+OewucQQ1mFG5Wbo4Mbu9GombHB2xkxjPWqH0Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:19.520286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08431","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:670834a76dfd2d92b60f4b06627e59c1ed6e2847b053ea2117cddd8ab9863f0c","sha256:dca9e0ac71b4f953c1767e766a1186bd8d34c07f9defffa21497a13b5d235c26"],"state_sha256":"ac440aa5eb2321aeb390a276980adef7bc91555cd815020133e506ae29480020"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oJCLiLigs5aFju+TfejjwtcHE+zTcXfafaCMTOY+QcuoOHzkFkYcQTVw9133pjJ0NqqU9sHLl3kB2ILc3Y1wAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:32:40.976927Z","bundle_sha256":"442a05121400d50cc530708e8aa4aa8044a6376ef3b7b308cbbd3d7a73a4136b"}}