{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NBTEW5X4EYSNJJ7Z6QKWKLIZHD","short_pith_number":"pith:NBTEW5X4","canonical_record":{"source":{"id":"1810.08720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-10-20T00:39:43Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"e44c162384542abf196507e9b8713cf60430d4cdad679bea906f5faf694f0457","abstract_canon_sha256":"94b75612354ff0876c9f8a4be3291b094696a995c197a27ad3333abacea7d427"},"schema_version":"1.0"},"canonical_sha256":"68664b76fc2624d4a7f9f415652d1938c3d3ad31fd1051114b9e9608119f3d4e","source":{"kind":"arxiv","id":"1810.08720","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08720","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08720v1","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08720","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"pith_short_12","alias_value":"NBTEW5X4EYSN","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NBTEW5X4EYSNJJ7Z","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NBTEW5X4","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NBTEW5X4EYSNJJ7Z6QKWKLIZHD","target":"record","payload":{"canonical_record":{"source":{"id":"1810.08720","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-10-20T00:39:43Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"e44c162384542abf196507e9b8713cf60430d4cdad679bea906f5faf694f0457","abstract_canon_sha256":"94b75612354ff0876c9f8a4be3291b094696a995c197a27ad3333abacea7d427"},"schema_version":"1.0"},"canonical_sha256":"68664b76fc2624d4a7f9f415652d1938c3d3ad31fd1051114b9e9608119f3d4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:43.713630Z","signature_b64":"mJ0LsvgTipj/jrDmLlrPQulYtQdElHVv6lCMq2pRHm0k0ocSe4iZ+9GirxYZK2OT2A+r0iCvbqZjO/VxOTALDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68664b76fc2624d4a7f9f415652d1938c3d3ad31fd1051114b9e9608119f3d4e","last_reissued_at":"2026-05-18T00:02:43.713191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:43.713191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.08720","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":"2026-05-18T00:02:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZjUFVaDYGhevYOHjg4JlBJJkJkWriQUQC58G3HZnK2YBONQO//6FSa8+ieNZt+TEMA7mpe5PwyUm2xVSzQmHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:43:38.057287Z"},"content_sha256":"95bfc35ae6777eb7cc8a86eb320fb155b7f58519bf8b43278f2f2d5a3c779590","schema_version":"1.0","event_id":"sha256:95bfc35ae6777eb7cc8a86eb320fb155b7f58519bf8b43278f2f2d5a3c779590"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NBTEW5X4EYSNJJ7Z6QKWKLIZHD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coarse compactifications and controlled products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.MG","authors_text":"Shin-ichi Oguni, Takamitsu Yamauchi, Tomohiro Fukaya","submitted_at":"2018-10-20T00:39:43Z","abstract_excerpt":"We introduce the notion of controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space complements the space as a coarse compactification. It is also shown that there is a bijective correspondence between the set of all coarse equivalence classes of controlled products and the set of all equivalence classes of coarse compactifications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08720","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":"2026-05-18T00:02:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gW9qfNtGZgL7WwgGsGxki4Su9ioOLQdCsYgfMkXszfJ4TqAQnrBBXeEXUEemX1rzobWIs+Q0R6KVpUqDenGECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:43:38.057656Z"},"content_sha256":"e83e3ec9b47690ce08e22e5ee04cc088b4efa5fb06352d95d51e934fd47f5838","schema_version":"1.0","event_id":"sha256:e83e3ec9b47690ce08e22e5ee04cc088b4efa5fb06352d95d51e934fd47f5838"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NBTEW5X4EYSNJJ7Z6QKWKLIZHD/bundle.json","state_url":"https://pith.science/pith/NBTEW5X4EYSNJJ7Z6QKWKLIZHD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NBTEW5X4EYSNJJ7Z6QKWKLIZHD/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":"2026-06-02T01:43:38Z","links":{"resolver":"https://pith.science/pith/NBTEW5X4EYSNJJ7Z6QKWKLIZHD","bundle":"https://pith.science/pith/NBTEW5X4EYSNJJ7Z6QKWKLIZHD/bundle.json","state":"https://pith.science/pith/NBTEW5X4EYSNJJ7Z6QKWKLIZHD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NBTEW5X4EYSNJJ7Z6QKWKLIZHD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NBTEW5X4EYSNJJ7Z6QKWKLIZHD","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":"94b75612354ff0876c9f8a4be3291b094696a995c197a27ad3333abacea7d427","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-10-20T00:39:43Z","title_canon_sha256":"e44c162384542abf196507e9b8713cf60430d4cdad679bea906f5faf694f0457"},"schema_version":"1.0","source":{"id":"1810.08720","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08720","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08720v1","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08720","created_at":"2026-05-18T00:02:43Z"},{"alias_kind":"pith_short_12","alias_value":"NBTEW5X4EYSN","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NBTEW5X4EYSNJJ7Z","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NBTEW5X4","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:e83e3ec9b47690ce08e22e5ee04cc088b4efa5fb06352d95d51e934fd47f5838","target":"graph","created_at":"2026-05-18T00:02:43Z","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 controlled products on metric spaces as a generalization of Gromov products, and construct boundaries by using controlled products, which we call the Gromov boundaries. It is shown that the Gromov boundary with respect to a controlled product on a proper metric space complements the space as a coarse compactification. It is also shown that there is a bijective correspondence between the set of all coarse equivalence classes of controlled products and the set of all equivalence classes of coarse compactifications.","authors_text":"Shin-ichi Oguni, Takamitsu Yamauchi, Tomohiro Fukaya","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-10-20T00:39:43Z","title":"Coarse compactifications and controlled products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08720","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":"sha256:95bfc35ae6777eb7cc8a86eb320fb155b7f58519bf8b43278f2f2d5a3c779590","target":"record","created_at":"2026-05-18T00:02:43Z","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":"94b75612354ff0876c9f8a4be3291b094696a995c197a27ad3333abacea7d427","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-10-20T00:39:43Z","title_canon_sha256":"e44c162384542abf196507e9b8713cf60430d4cdad679bea906f5faf694f0457"},"schema_version":"1.0","source":{"id":"1810.08720","kind":"arxiv","version":1}},"canonical_sha256":"68664b76fc2624d4a7f9f415652d1938c3d3ad31fd1051114b9e9608119f3d4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68664b76fc2624d4a7f9f415652d1938c3d3ad31fd1051114b9e9608119f3d4e","first_computed_at":"2026-05-18T00:02:43.713191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:43.713191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mJ0LsvgTipj/jrDmLlrPQulYtQdElHVv6lCMq2pRHm0k0ocSe4iZ+9GirxYZK2OT2A+r0iCvbqZjO/VxOTALDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:43.713630Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08720","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95bfc35ae6777eb7cc8a86eb320fb155b7f58519bf8b43278f2f2d5a3c779590","sha256:e83e3ec9b47690ce08e22e5ee04cc088b4efa5fb06352d95d51e934fd47f5838"],"state_sha256":"6fd8a7c9928524cf24f798051cc72b0eeecbc48398f69145065b27d4cee3b58b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cRW8A+UXhzMcX6B4K8LkVyw11oOkZ5BdGtmlBvdeXWE7sqvOj4Mq6M6zgSj4hT+NmJzEYJUW2/MInh52Riy7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:43:38.061012Z","bundle_sha256":"98eb748fe6d807be008499407b82a3eda83f86738c1532803839d6a6ab357a62"}}