{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:S7G6PGJU5VOAJMTCIDTRTW64YJ","short_pith_number":"pith:S7G6PGJU","canonical_record":{"source":{"id":"1504.05734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-22T11:22:38Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"cb899a4355d96618918cac0540f75fe0bb33fc9fc1a661623bed6eb1482fc677","abstract_canon_sha256":"75eec80d4fc6995a4aeaec31167783cfa9199ea7e70b38126d677cb7278bfc59"},"schema_version":"1.0"},"canonical_sha256":"97cde79934ed5c04b26240e719dbdcc250a1a17829581714e7d31f19ba3cd24c","source":{"kind":"arxiv","id":"1504.05734","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05734","created_at":"2026-05-18T01:00:19Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05734v1","created_at":"2026-05-18T01:00:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05734","created_at":"2026-05-18T01:00:19Z"},{"alias_kind":"pith_short_12","alias_value":"S7G6PGJU5VOA","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S7G6PGJU5VOAJMTC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S7G6PGJU","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:S7G6PGJU5VOAJMTCIDTRTW64YJ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-22T11:22:38Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"cb899a4355d96618918cac0540f75fe0bb33fc9fc1a661623bed6eb1482fc677","abstract_canon_sha256":"75eec80d4fc6995a4aeaec31167783cfa9199ea7e70b38126d677cb7278bfc59"},"schema_version":"1.0"},"canonical_sha256":"97cde79934ed5c04b26240e719dbdcc250a1a17829581714e7d31f19ba3cd24c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:19.855927Z","signature_b64":"JtINXHh5UF1aqmkQDN/PLxDcd+u8+ZqMBz1rhOFfuWUiaRuFHkW/NJ9anxpSHwas2BicT2NHEDRsRVAnGgfBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97cde79934ed5c04b26240e719dbdcc250a1a17829581714e7d31f19ba3cd24c","last_reissued_at":"2026-05-18T01:00:19.855248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:19.855248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05734","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":"2026-05-18T01:00:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rGhQfH2xjdy5z3vxSLbeYF56IvB8rzVJwknLSgkUhLc3WTL3Oq/RbOeBV6F0ACqQNu6FFtBK2/1rp1ZlDhPVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T06:48:53.207799Z"},"content_sha256":"a59f5a5b2258eb70892932464c3bf41d790f52f498910b44597d4a8c97f26810","schema_version":"1.0","event_id":"sha256:a59f5a5b2258eb70892932464c3bf41d790f52f498910b44597d4a8c97f26810"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:S7G6PGJU5VOAJMTCIDTRTW64YJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The boundary quotient for algebraic dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Nathan Brownlowe, Nicolai Stammeier","submitted_at":"2015-04-22T11:22:38Z","abstract_excerpt":"We introduce the notion of accurate foundation sets and the accurate refinement property for right LCM semigroups. For right LCM semigroups with this property, we derive a more explicit presentation of the boundary quotient. In the context of algebraic dynamical systems, we also analyse finiteness properties of foundation sets which lead us to a very concrete presentation. Based on Starling's recent work, we provide sharp conditions on certain algebraic dynamical systems for pure infiniteness and simplicity of their boundary quotient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05734","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":""},"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":"2026-05-18T01:00:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phlmtcsYuCvo6CPqCOsfPNHIH92c249I71PI1Tjdo5MmjE3HlnIf8Rmm/ymQL8vFTTach+jVvi0frNRjD47iAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T06:48:53.208404Z"},"content_sha256":"c5eb4879fdd9346c3be62b4b97e110bdd0524ea14f9fb71e76b19081ef30ce35","schema_version":"1.0","event_id":"sha256:c5eb4879fdd9346c3be62b4b97e110bdd0524ea14f9fb71e76b19081ef30ce35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7G6PGJU5VOAJMTCIDTRTW64YJ/bundle.json","state_url":"https://pith.science/pith/S7G6PGJU5VOAJMTCIDTRTW64YJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7G6PGJU5VOAJMTCIDTRTW64YJ/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":"2026-07-01T06:48:53Z","links":{"resolver":"https://pith.science/pith/S7G6PGJU5VOAJMTCIDTRTW64YJ","bundle":"https://pith.science/pith/S7G6PGJU5VOAJMTCIDTRTW64YJ/bundle.json","state":"https://pith.science/pith/S7G6PGJU5VOAJMTCIDTRTW64YJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7G6PGJU5VOAJMTCIDTRTW64YJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S7G6PGJU5VOAJMTCIDTRTW64YJ","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":"75eec80d4fc6995a4aeaec31167783cfa9199ea7e70b38126d677cb7278bfc59","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-22T11:22:38Z","title_canon_sha256":"cb899a4355d96618918cac0540f75fe0bb33fc9fc1a661623bed6eb1482fc677"},"schema_version":"1.0","source":{"id":"1504.05734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05734","created_at":"2026-05-18T01:00:19Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05734v1","created_at":"2026-05-18T01:00:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05734","created_at":"2026-05-18T01:00:19Z"},{"alias_kind":"pith_short_12","alias_value":"S7G6PGJU5VOA","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S7G6PGJU5VOAJMTC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S7G6PGJU","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:c5eb4879fdd9346c3be62b4b97e110bdd0524ea14f9fb71e76b19081ef30ce35","target":"graph","created_at":"2026-05-18T01:00:19Z","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":"We introduce the notion of accurate foundation sets and the accurate refinement property for right LCM semigroups. For right LCM semigroups with this property, we derive a more explicit presentation of the boundary quotient. In the context of algebraic dynamical systems, we also analyse finiteness properties of foundation sets which lead us to a very concrete presentation. Based on Starling's recent work, we provide sharp conditions on certain algebraic dynamical systems for pure infiniteness and simplicity of their boundary quotient.","authors_text":"Nathan Brownlowe, Nicolai Stammeier","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-22T11:22:38Z","title":"The boundary quotient for algebraic dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05734","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:a59f5a5b2258eb70892932464c3bf41d790f52f498910b44597d4a8c97f26810","target":"record","created_at":"2026-05-18T01:00:19Z","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":"75eec80d4fc6995a4aeaec31167783cfa9199ea7e70b38126d677cb7278bfc59","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-22T11:22:38Z","title_canon_sha256":"cb899a4355d96618918cac0540f75fe0bb33fc9fc1a661623bed6eb1482fc677"},"schema_version":"1.0","source":{"id":"1504.05734","kind":"arxiv","version":1}},"canonical_sha256":"97cde79934ed5c04b26240e719dbdcc250a1a17829581714e7d31f19ba3cd24c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97cde79934ed5c04b26240e719dbdcc250a1a17829581714e7d31f19ba3cd24c","first_computed_at":"2026-05-18T01:00:19.855248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:19.855248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JtINXHh5UF1aqmkQDN/PLxDcd+u8+ZqMBz1rhOFfuWUiaRuFHkW/NJ9anxpSHwas2BicT2NHEDRsRVAnGgfBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:19.855927Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a59f5a5b2258eb70892932464c3bf41d790f52f498910b44597d4a8c97f26810","sha256:c5eb4879fdd9346c3be62b4b97e110bdd0524ea14f9fb71e76b19081ef30ce35"],"state_sha256":"5d80c3c0752be461122480ea1c04f34e6810840f481c7964ee1a9a3b96458b42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOWvlFZChumIkpys3wcYtX5RubcUzpFRfW7YiEVJe/mtbrh+2+uqAUhk77wF2LoqxZSW8JG1CTB2KQBv4YSlBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T06:48:53.211738Z","bundle_sha256":"bdd6f7bee382d6cbcee6cf376fd9b7b74be40c41f239b63f0946d78b02a9664d"}}