{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WK5U6DL33NX5JNIS55A7Q3OTJY","short_pith_number":"pith:WK5U6DL3","canonical_record":{"source":{"id":"2606.23811","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T18:00:59Z","cross_cats_sorted":[],"title_canon_sha256":"1d96caaf8c789492fd58cdc2c3b73c8da9f6939b57d93b6dbdf513e8178b33d0","abstract_canon_sha256":"420bcdb106f31a4a14554e7e17bbb4cfa478f59a4cf252f5664002dd706f1b8f"},"schema_version":"1.0"},"canonical_sha256":"b2bb4f0d7bdb6fd4b512ef41f86dd34e01313060cc11d4ca99ec52674e123c2b","source":{"kind":"arxiv","id":"2606.23811","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23811","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23811v1","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23811","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"WK5U6DL33NX5","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_16","alias_value":"WK5U6DL33NX5JNIS","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_8","alias_value":"WK5U6DL3","created_at":"2026-06-24T00:14:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WK5U6DL33NX5JNIS55A7Q3OTJY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23811","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T18:00:59Z","cross_cats_sorted":[],"title_canon_sha256":"1d96caaf8c789492fd58cdc2c3b73c8da9f6939b57d93b6dbdf513e8178b33d0","abstract_canon_sha256":"420bcdb106f31a4a14554e7e17bbb4cfa478f59a4cf252f5664002dd706f1b8f"},"schema_version":"1.0"},"canonical_sha256":"b2bb4f0d7bdb6fd4b512ef41f86dd34e01313060cc11d4ca99ec52674e123c2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T00:14:27.572480Z","signature_b64":"fvGqYBETnLuFDaAKgQGmxNXnHwqbXYhigG1WBbCZLPildqAitiJhanJN4MFbRXrer9I9KDqQiLvu8zzhH1nkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2bb4f0d7bdb6fd4b512ef41f86dd34e01313060cc11d4ca99ec52674e123c2b","last_reissued_at":"2026-06-24T00:14:27.572126Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T00:14:27.572126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23811","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":"2026-06-24T00:14:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LuyrT0pNHbsBSjerUiwswPf67TnjwQ386DRAvUSv2rpMMSXI+00sqAfpJ8a5XoosG1p8kw0LBB538RbB+CmsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:47:46.501459Z"},"content_sha256":"8a6181c242c63a3e868f6bdeb69c0d529bf986e70becd1bb4a32053635f48632","schema_version":"1.0","event_id":"sha256:8a6181c242c63a3e868f6bdeb69c0d529bf986e70becd1bb4a32053635f48632"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WK5U6DL33NX5JNIS55A7Q3OTJY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizing property (NL) in {C}oxeter groups","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Rachel Niebler, Roberta Shapiro, Sahana Balasubramanya","submitted_at":"2026-06-22T18:00:59Z","abstract_excerpt":"A group has Property (NL) -- which stands for ``no loxodromics\" -- if no element of the group acts loxodromically on any hyperbolic space. In this brief note, we provide a complete characterization of which Coxeter groups have Property (NL)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23811","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/2606.23811/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":"2026-06-24T00:14:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iSa9Mp+Hb511O3lArcP+5vbkWhX0Rw1lYlBHZk30WHe0PBvXy9ZyDTxKqq9/C+QbBr7sJruislic4AkzI1GwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:47:46.501819Z"},"content_sha256":"2064e29d66778880dbaa6be4e1bc316dc94a29ae535c941e67e505488f02f04d","schema_version":"1.0","event_id":"sha256:2064e29d66778880dbaa6be4e1bc316dc94a29ae535c941e67e505488f02f04d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WK5U6DL33NX5JNIS55A7Q3OTJY/bundle.json","state_url":"https://pith.science/pith/WK5U6DL33NX5JNIS55A7Q3OTJY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WK5U6DL33NX5JNIS55A7Q3OTJY/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":"2026-06-27T07:47:46Z","links":{"resolver":"https://pith.science/pith/WK5U6DL33NX5JNIS55A7Q3OTJY","bundle":"https://pith.science/pith/WK5U6DL33NX5JNIS55A7Q3OTJY/bundle.json","state":"https://pith.science/pith/WK5U6DL33NX5JNIS55A7Q3OTJY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WK5U6DL33NX5JNIS55A7Q3OTJY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WK5U6DL33NX5JNIS55A7Q3OTJY","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":"420bcdb106f31a4a14554e7e17bbb4cfa478f59a4cf252f5664002dd706f1b8f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T18:00:59Z","title_canon_sha256":"1d96caaf8c789492fd58cdc2c3b73c8da9f6939b57d93b6dbdf513e8178b33d0"},"schema_version":"1.0","source":{"id":"2606.23811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23811","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23811v1","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23811","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_12","alias_value":"WK5U6DL33NX5","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_16","alias_value":"WK5U6DL33NX5JNIS","created_at":"2026-06-24T00:14:27Z"},{"alias_kind":"pith_short_8","alias_value":"WK5U6DL3","created_at":"2026-06-24T00:14:27Z"}],"graph_snapshots":[{"event_id":"sha256:2064e29d66778880dbaa6be4e1bc316dc94a29ae535c941e67e505488f02f04d","target":"graph","created_at":"2026-06-24T00:14:27Z","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/2606.23811/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A group has Property (NL) -- which stands for ``no loxodromics\" -- if no element of the group acts loxodromically on any hyperbolic space. In this brief note, we provide a complete characterization of which Coxeter groups have Property (NL).","authors_text":"Rachel Niebler, Roberta Shapiro, Sahana Balasubramanya","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T18:00:59Z","title":"Characterizing property (NL) in {C}oxeter groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23811","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":"sha256:8a6181c242c63a3e868f6bdeb69c0d529bf986e70becd1bb4a32053635f48632","target":"record","created_at":"2026-06-24T00:14:27Z","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":"420bcdb106f31a4a14554e7e17bbb4cfa478f59a4cf252f5664002dd706f1b8f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.GR","submitted_at":"2026-06-22T18:00:59Z","title_canon_sha256":"1d96caaf8c789492fd58cdc2c3b73c8da9f6939b57d93b6dbdf513e8178b33d0"},"schema_version":"1.0","source":{"id":"2606.23811","kind":"arxiv","version":1}},"canonical_sha256":"b2bb4f0d7bdb6fd4b512ef41f86dd34e01313060cc11d4ca99ec52674e123c2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2bb4f0d7bdb6fd4b512ef41f86dd34e01313060cc11d4ca99ec52674e123c2b","first_computed_at":"2026-06-24T00:14:27.572126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T00:14:27.572126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fvGqYBETnLuFDaAKgQGmxNXnHwqbXYhigG1WBbCZLPildqAitiJhanJN4MFbRXrer9I9KDqQiLvu8zzhH1nkBw==","signature_status":"signed_v1","signed_at":"2026-06-24T00:14:27.572480Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a6181c242c63a3e868f6bdeb69c0d529bf986e70becd1bb4a32053635f48632","sha256:2064e29d66778880dbaa6be4e1bc316dc94a29ae535c941e67e505488f02f04d"],"state_sha256":"8279ffe82e973a225e84f6fb71c1b5b77081354b91bcd9b00686d016e173c936"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kgsiURq8tAwMMCG7qEDxnzQKDcxmzJDL7PLONFyFNA0cbUnqLxzhm274hmKk6lyn4R0sO+fA4KcFDk1NqP1WBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T07:47:46.503807Z","bundle_sha256":"534e7aa1efd9f0d5673e8627e26908700c9c10198859ff8d9a665274973f58f6"}}