{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7HAXA2I32ZCTLWX4B7XHXKBKEX","short_pith_number":"pith:7HAXA2I3","canonical_record":{"source":{"id":"2410.22464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-10-29T18:59:55Z","cross_cats_sorted":[],"title_canon_sha256":"8da4c714630479c6f7c34673ad5d072c5e6ec7bb5c5ea889870ada6b71d4d92d","abstract_canon_sha256":"6950c23b04c481f8654c342e861f198ba849768c6c57224288c31572a5a4d137"},"schema_version":"1.0"},"canonical_sha256":"f9c170691bd64535dafc0fee7ba82a25d086070e63e2c7fca3c883d7e626e985","source":{"kind":"arxiv","id":"2410.22464","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.22464","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"2410.22464v1","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.22464","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"7HAXA2I32ZCT","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7HAXA2I32ZCTLWX4","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7HAXA2I3","created_at":"2026-07-05T09:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7HAXA2I32ZCTLWX4B7XHXKBKEX","target":"record","payload":{"canonical_record":{"source":{"id":"2410.22464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-10-29T18:59:55Z","cross_cats_sorted":[],"title_canon_sha256":"8da4c714630479c6f7c34673ad5d072c5e6ec7bb5c5ea889870ada6b71d4d92d","abstract_canon_sha256":"6950c23b04c481f8654c342e861f198ba849768c6c57224288c31572a5a4d137"},"schema_version":"1.0"},"canonical_sha256":"f9c170691bd64535dafc0fee7ba82a25d086070e63e2c7fca3c883d7e626e985","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:28:16.998211Z","signature_b64":"KKVomx321ycbTekpD5+McyGTZj4pIlzFx+mxTJacl2sXP8imknHI5W6OqnxJ0S8P0brHGkmJAqPSyg1Qvpj/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9c170691bd64535dafc0fee7ba82a25d086070e63e2c7fca3c883d7e626e985","last_reissued_at":"2026-07-05T09:28:16.997750Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:28:16.997750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.22464","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":"2026-07-05T09:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oqeYi1Y4cM3tVD/D53j66VZIXmkUQWpuixqM1/iu6dV3phCrgjMADIm8tiBshDEbiS7uLzDdTHfxUfEO1brvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:23:42.268921Z"},"content_sha256":"8a9a7481a044de351f8bf597d803ff59be356834e0bfa4b6770f1f53ac667825","schema_version":"1.0","event_id":"sha256:8a9a7481a044de351f8bf597d803ff59be356834e0bfa4b6770f1f53ac667825"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7HAXA2I32ZCTLWX4B7XHXKBKEX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dyer groups: Centres, hyperbolicity, and acylindrical hyperbolicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mireille Soergel, Nicolas Vaskou","submitted_at":"2024-10-29T18:59:55Z","abstract_excerpt":"In this article we describe the centres of all Dyer groups. We also give a complete classification of when a Dyer group $D(\\Gamma)$ is hyperbolic or acylindricality hyperbolic, with conditions that can easily be read on the Dyer graph $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.22464","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/2410.22464/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":"2026-07-05T09:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tD9/PdmYqqE+DJOyCoJPKS8GoBqhmCKryAIbelsktF624JjmdjpFnxicGs5NmPGvVrZtUxyYMuQ3r6KVa06GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T14:23:42.272277Z"},"content_sha256":"7766820bfbe300283b6ba13f7b82f9cf4618e9592eeeb8b39ea3825d3fef9479","schema_version":"1.0","event_id":"sha256:7766820bfbe300283b6ba13f7b82f9cf4618e9592eeeb8b39ea3825d3fef9479"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7HAXA2I32ZCTLWX4B7XHXKBKEX/bundle.json","state_url":"https://pith.science/pith/7HAXA2I32ZCTLWX4B7XHXKBKEX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7HAXA2I32ZCTLWX4B7XHXKBKEX/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":"2026-08-18T14:23:42Z","links":{"resolver":"https://pith.science/pith/7HAXA2I32ZCTLWX4B7XHXKBKEX","bundle":"https://pith.science/pith/7HAXA2I32ZCTLWX4B7XHXKBKEX/bundle.json","state":"https://pith.science/pith/7HAXA2I32ZCTLWX4B7XHXKBKEX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7HAXA2I32ZCTLWX4B7XHXKBKEX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7HAXA2I32ZCTLWX4B7XHXKBKEX","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":"6950c23b04c481f8654c342e861f198ba849768c6c57224288c31572a5a4d137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-10-29T18:59:55Z","title_canon_sha256":"8da4c714630479c6f7c34673ad5d072c5e6ec7bb5c5ea889870ada6b71d4d92d"},"schema_version":"1.0","source":{"id":"2410.22464","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.22464","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"2410.22464v1","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.22464","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"7HAXA2I32ZCT","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7HAXA2I32ZCTLWX4","created_at":"2026-07-05T09:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7HAXA2I3","created_at":"2026-07-05T09:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:7766820bfbe300283b6ba13f7b82f9cf4618e9592eeeb8b39ea3825d3fef9479","target":"graph","created_at":"2026-07-05T09:28:16Z","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/2410.22464/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we describe the centres of all Dyer groups. We also give a complete classification of when a Dyer group $D(\\Gamma)$ is hyperbolic or acylindricality hyperbolic, with conditions that can easily be read on the Dyer graph $\\Gamma$.","authors_text":"Mireille Soergel, Nicolas Vaskou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-10-29T18:59:55Z","title":"Dyer groups: Centres, hyperbolicity, and acylindrical hyperbolicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.22464","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":"sha256:8a9a7481a044de351f8bf597d803ff59be356834e0bfa4b6770f1f53ac667825","target":"record","created_at":"2026-07-05T09:28:16Z","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":"6950c23b04c481f8654c342e861f198ba849768c6c57224288c31572a5a4d137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-10-29T18:59:55Z","title_canon_sha256":"8da4c714630479c6f7c34673ad5d072c5e6ec7bb5c5ea889870ada6b71d4d92d"},"schema_version":"1.0","source":{"id":"2410.22464","kind":"arxiv","version":1}},"canonical_sha256":"f9c170691bd64535dafc0fee7ba82a25d086070e63e2c7fca3c883d7e626e985","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9c170691bd64535dafc0fee7ba82a25d086070e63e2c7fca3c883d7e626e985","first_computed_at":"2026-07-05T09:28:16.997750Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:28:16.997750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KKVomx321ycbTekpD5+McyGTZj4pIlzFx+mxTJacl2sXP8imknHI5W6OqnxJ0S8P0brHGkmJAqPSyg1Qvpj/CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:28:16.998211Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.22464","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a9a7481a044de351f8bf597d803ff59be356834e0bfa4b6770f1f53ac667825","sha256:7766820bfbe300283b6ba13f7b82f9cf4618e9592eeeb8b39ea3825d3fef9479"],"state_sha256":"7e4a16a167688c3f2daa28ef15f279a7b5b4f2a0737b119b30e311c04877ca78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ELYD5tfo8hVVbkGTr82f9HGSWet6G/ojXb/vgzVMWDC3eYLFtxjJueNeP0ujpjkGn2S+LYNxOtSA16OFbu1pDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T14:23:42.292545Z","bundle_sha256":"63c9bf23d18e9431e9a015361ae8edf028b1e870cb765a78b902b9b837754856"}}