{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:24GWKACMU623N2UET7VCTCF76F","short_pith_number":"pith:24GWKACM","canonical_record":{"source":{"id":"2608.09535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T12:35:36Z","cross_cats_sorted":[],"title_canon_sha256":"103b0c037f4bb11bc104752479f2192062fadf8c9abd4875d7e12c35caf3e66e","abstract_canon_sha256":"fd0756020febec2b8f356b2d3eeacdd91582bb8751c960649cc24cf2b0627dd3"},"schema_version":"1.0"},"canonical_sha256":"d70d65004ca7b5b6ea849fea2988bff141573bbe776c806f9b9ade45c0e090d0","source":{"kind":"arxiv","id":"2608.09535","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.09535","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"2608.09535v1","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09535","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"24GWKACMU623","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"pith_short_16","alias_value":"24GWKACMU623N2UE","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"pith_short_8","alias_value":"24GWKACM","created_at":"2026-08-11T02:24:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:24GWKACMU623N2UET7VCTCF76F","target":"record","payload":{"canonical_record":{"source":{"id":"2608.09535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T12:35:36Z","cross_cats_sorted":[],"title_canon_sha256":"103b0c037f4bb11bc104752479f2192062fadf8c9abd4875d7e12c35caf3e66e","abstract_canon_sha256":"fd0756020febec2b8f356b2d3eeacdd91582bb8751c960649cc24cf2b0627dd3"},"schema_version":"1.0"},"canonical_sha256":"d70d65004ca7b5b6ea849fea2988bff141573bbe776c806f9b9ade45c0e090d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T02:24:26.109107Z","signature_b64":"3iMD204Xb4SG6u3xuNwZR68l0EnU894O/9TPmnb56EI7O/AN7dBbIuCWq57/XpvJHw1JAUoVRqmChWFLnsupBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d70d65004ca7b5b6ea849fea2988bff141573bbe776c806f9b9ade45c0e090d0","last_reissued_at":"2026-08-11T02:24:26.107611Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T02:24:26.107611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.09535","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":"2026-08-11T02:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j4nptfJlzsS8en1n0SpyJ5+gJDAI1mFUM9steqVS9xZ0I2DnbOz1lh23AxHgXrvWq9SQHuhdTQmEBRbl5ltfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:54:12.796846Z"},"content_sha256":"787fbcd6f98c1330ea7c712191506da9da5254d5734f204992831c76ba9fca60","schema_version":"1.0","event_id":"sha256:787fbcd6f98c1330ea7c712191506da9da5254d5734f204992831c76ba9fca60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:24GWKACMU623N2UET7VCTCF76F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From algebraic orthogonality to RAAG embedding obstructions in hierarchically hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jihoon Park, Sangrok Oh","submitted_at":"2026-08-10T12:35:36Z","abstract_excerpt":"We introduce the \\emph{expanded core graph}, which records minimal unbounded domains and their axial directions, for two classes of hierarchically hyperbolic group structures modeled on compact special groups and mapping class groups. Our main structural result shows that every embedding of a right-angled Artin group, after replacing its standard generators by positive powers, factors through an intermediate RAAG generated by suitably supported axial elements; for the class modeled on compact special groups, this intermediate RAAG is quasi-isometrically embedded. We show that its extension gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09535","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/2608.09535/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":"2026-08-11T02:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G/FRXQDDZMIr3aEWrtwhm7HSG2GLO+KANWgtpiVP8oOlKTQvBdXKZZa8EahDpFXETt6b1feFHnWBDjPJ0l/XBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:54:12.797739Z"},"content_sha256":"f724354126898aff4d011d90baedd6af7dbfd77a93f9a55c12d4cd763e07b80b","schema_version":"1.0","event_id":"sha256:f724354126898aff4d011d90baedd6af7dbfd77a93f9a55c12d4cd763e07b80b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24GWKACMU623N2UET7VCTCF76F/bundle.json","state_url":"https://pith.science/pith/24GWKACMU623N2UET7VCTCF76F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24GWKACMU623N2UET7VCTCF76F/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":"2026-08-20T10:54:12Z","links":{"resolver":"https://pith.science/pith/24GWKACMU623N2UET7VCTCF76F","bundle":"https://pith.science/pith/24GWKACMU623N2UET7VCTCF76F/bundle.json","state":"https://pith.science/pith/24GWKACMU623N2UET7VCTCF76F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24GWKACMU623N2UET7VCTCF76F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:24GWKACMU623N2UET7VCTCF76F","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":"fd0756020febec2b8f356b2d3eeacdd91582bb8751c960649cc24cf2b0627dd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T12:35:36Z","title_canon_sha256":"103b0c037f4bb11bc104752479f2192062fadf8c9abd4875d7e12c35caf3e66e"},"schema_version":"1.0","source":{"id":"2608.09535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.09535","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"2608.09535v1","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09535","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"24GWKACMU623","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"pith_short_16","alias_value":"24GWKACMU623N2UE","created_at":"2026-08-11T02:24:26Z"},{"alias_kind":"pith_short_8","alias_value":"24GWKACM","created_at":"2026-08-11T02:24:26Z"}],"graph_snapshots":[{"event_id":"sha256:f724354126898aff4d011d90baedd6af7dbfd77a93f9a55c12d4cd763e07b80b","target":"graph","created_at":"2026-08-11T02:24:26Z","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/2608.09535/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the \\emph{expanded core graph}, which records minimal unbounded domains and their axial directions, for two classes of hierarchically hyperbolic group structures modeled on compact special groups and mapping class groups. Our main structural result shows that every embedding of a right-angled Artin group, after replacing its standard generators by positive powers, factors through an intermediate RAAG generated by suitably supported axial elements; for the class modeled on compact special groups, this intermediate RAAG is quasi-isometrically embedded. We show that its extension gra","authors_text":"Jihoon Park, Sangrok Oh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T12:35:36Z","title":"From algebraic orthogonality to RAAG embedding obstructions in hierarchically hyperbolic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09535","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":"sha256:787fbcd6f98c1330ea7c712191506da9da5254d5734f204992831c76ba9fca60","target":"record","created_at":"2026-08-11T02:24:26Z","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":"fd0756020febec2b8f356b2d3eeacdd91582bb8751c960649cc24cf2b0627dd3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-08-10T12:35:36Z","title_canon_sha256":"103b0c037f4bb11bc104752479f2192062fadf8c9abd4875d7e12c35caf3e66e"},"schema_version":"1.0","source":{"id":"2608.09535","kind":"arxiv","version":1}},"canonical_sha256":"d70d65004ca7b5b6ea849fea2988bff141573bbe776c806f9b9ade45c0e090d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d70d65004ca7b5b6ea849fea2988bff141573bbe776c806f9b9ade45c0e090d0","first_computed_at":"2026-08-11T02:24:26.107611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T02:24:26.107611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3iMD204Xb4SG6u3xuNwZR68l0EnU894O/9TPmnb56EI7O/AN7dBbIuCWq57/XpvJHw1JAUoVRqmChWFLnsupBw==","signature_status":"signed_v1","signed_at":"2026-08-11T02:24:26.109107Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.09535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:787fbcd6f98c1330ea7c712191506da9da5254d5734f204992831c76ba9fca60","sha256:f724354126898aff4d011d90baedd6af7dbfd77a93f9a55c12d4cd763e07b80b"],"state_sha256":"520f49010432047a3a1836b95e40b35d5b1cc441c76b59d2e1edf84bd4f5fcf1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODfSex92pAXBU8vE/jb2Vbk64fvHlK5j3jcCr9oH2Sok8aNC9lWk33efaDZQNPO9Y5sLrNfqPUP7g5nakNrzBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T10:54:12.803694Z","bundle_sha256":"a5a8d9cf23abc5a0602124c058ada8c472bfb79939e6a2d7c8b11ca5345cfd60"}}