{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ODEGP7QLTJHA5Y2G7HRFJWU26M","short_pith_number":"pith:ODEGP7QL","canonical_record":{"source":{"id":"1607.02403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-08T15:10:55Z","cross_cats_sorted":["math.CT","math.GN","math.MG"],"title_canon_sha256":"1ba737ff91b5122129427be337fb6325e9f2aabef66bde961febf64971ffd697","abstract_canon_sha256":"2a95b11814e08fa527874fd3b066ba26bd5b876d78de881d3781d276a3464117"},"schema_version":"1.0"},"canonical_sha256":"70c867fe0b9a4e0ee346f9e254da9af33b2594fbbcc37ce6956989e5eca6942e","source":{"kind":"arxiv","id":"1607.02403","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02403","created_at":"2026-05-18T01:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02403v2","created_at":"2026-05-18T01:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02403","created_at":"2026-05-18T01:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"ODEGP7QLTJHA","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ODEGP7QLTJHA5Y2G","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ODEGP7QL","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ODEGP7QLTJHA5Y2G7HRFJWU26M","target":"record","payload":{"canonical_record":{"source":{"id":"1607.02403","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-08T15:10:55Z","cross_cats_sorted":["math.CT","math.GN","math.MG"],"title_canon_sha256":"1ba737ff91b5122129427be337fb6325e9f2aabef66bde961febf64971ffd697","abstract_canon_sha256":"2a95b11814e08fa527874fd3b066ba26bd5b876d78de881d3781d276a3464117"},"schema_version":"1.0"},"canonical_sha256":"70c867fe0b9a4e0ee346f9e254da9af33b2594fbbcc37ce6956989e5eca6942e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:16.226113Z","signature_b64":"dosctOLJtTrQ7Lqkt90gNSwmeSInP1Z+VCrhL0/BaxNl6TfjYLPaprFzE4aYZHLcJ5P0bsNUnWnHSNuTmt5hDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70c867fe0b9a4e0ee346f9e254da9af33b2594fbbcc37ce6956989e5eca6942e","last_reissued_at":"2026-05-18T01:08:16.225518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:16.225518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.02403","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7CNqkjPrvsEsZvM42ii8qlT86R+mOjRtYJEuxzcwF9NJ32T5j/4wUt+BmS7CO2y7GLgR+oXDO9lF2WDVLMN0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:49:02.635217Z"},"content_sha256":"ce1799cb474b8f0e0d573f7478a02d2d81324056fe8eb9e7d2eb3fc4c5a7f57f","schema_version":"1.0","event_id":"sha256:ce1799cb474b8f0e0d573f7478a02d2d81324056fe8eb9e7d2eb3fc4c5a7f57f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ODEGP7QLTJHA5Y2G7HRFJWU26M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotone-light factorizations in coarse geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.GN","math.MG"],"primary_cat":"math.GT","authors_text":"Jerzy Dydak, Thomas Weighill","submitted_at":"2016-07-08T15:10:55Z","abstract_excerpt":"We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of maps constitute a factorization system on the coarse category. We also show how coarsely monotone maps arise from a reflection in a similar way to classically monotone maps, and prove that coarsely monotone maps are stable under those pullbacks which exist in the coarse category. For the case of maps between proper metric spaces, we exhibit some connections between the coarse and classical notions of monotone and ligh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02403","kind":"arxiv","version":2},"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":"2026-05-18T01:08:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RmQUjbWdXGXne3U/5Svt7pZVSyS2tSlZ6N3VNBXsV/QgL+FlDH1zo0j/IT0fQmDY7k+d6psN13MAluGaPdNeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:49:02.635588Z"},"content_sha256":"1f7081a9df7f9aacccab55f0ceb8d8e7a9958fe344217654cc1807fd235c4410","schema_version":"1.0","event_id":"sha256:1f7081a9df7f9aacccab55f0ceb8d8e7a9958fe344217654cc1807fd235c4410"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ODEGP7QLTJHA5Y2G7HRFJWU26M/bundle.json","state_url":"https://pith.science/pith/ODEGP7QLTJHA5Y2G7HRFJWU26M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ODEGP7QLTJHA5Y2G7HRFJWU26M/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":"2026-06-12T09:49:02Z","links":{"resolver":"https://pith.science/pith/ODEGP7QLTJHA5Y2G7HRFJWU26M","bundle":"https://pith.science/pith/ODEGP7QLTJHA5Y2G7HRFJWU26M/bundle.json","state":"https://pith.science/pith/ODEGP7QLTJHA5Y2G7HRFJWU26M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ODEGP7QLTJHA5Y2G7HRFJWU26M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ODEGP7QLTJHA5Y2G7HRFJWU26M","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":"2a95b11814e08fa527874fd3b066ba26bd5b876d78de881d3781d276a3464117","cross_cats_sorted":["math.CT","math.GN","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-08T15:10:55Z","title_canon_sha256":"1ba737ff91b5122129427be337fb6325e9f2aabef66bde961febf64971ffd697"},"schema_version":"1.0","source":{"id":"1607.02403","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.02403","created_at":"2026-05-18T01:08:16Z"},{"alias_kind":"arxiv_version","alias_value":"1607.02403v2","created_at":"2026-05-18T01:08:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.02403","created_at":"2026-05-18T01:08:16Z"},{"alias_kind":"pith_short_12","alias_value":"ODEGP7QLTJHA","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"ODEGP7QLTJHA5Y2G","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"ODEGP7QL","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:1f7081a9df7f9aacccab55f0ceb8d8e7a9958fe344217654cc1807fd235c4410","target":"graph","created_at":"2026-05-18T01:08:16Z","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"},"paper":{"abstract_excerpt":"We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of maps constitute a factorization system on the coarse category. We also show how coarsely monotone maps arise from a reflection in a similar way to classically monotone maps, and prove that coarsely monotone maps are stable under those pullbacks which exist in the coarse category. For the case of maps between proper metric spaces, we exhibit some connections between the coarse and classical notions of monotone and ligh","authors_text":"Jerzy Dydak, Thomas Weighill","cross_cats":["math.CT","math.GN","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-08T15:10:55Z","title":"Monotone-light factorizations in coarse geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02403","kind":"arxiv","version":2},"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:ce1799cb474b8f0e0d573f7478a02d2d81324056fe8eb9e7d2eb3fc4c5a7f57f","target":"record","created_at":"2026-05-18T01:08:16Z","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":"2a95b11814e08fa527874fd3b066ba26bd5b876d78de881d3781d276a3464117","cross_cats_sorted":["math.CT","math.GN","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-07-08T15:10:55Z","title_canon_sha256":"1ba737ff91b5122129427be337fb6325e9f2aabef66bde961febf64971ffd697"},"schema_version":"1.0","source":{"id":"1607.02403","kind":"arxiv","version":2}},"canonical_sha256":"70c867fe0b9a4e0ee346f9e254da9af33b2594fbbcc37ce6956989e5eca6942e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70c867fe0b9a4e0ee346f9e254da9af33b2594fbbcc37ce6956989e5eca6942e","first_computed_at":"2026-05-18T01:08:16.225518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:16.225518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dosctOLJtTrQ7Lqkt90gNSwmeSInP1Z+VCrhL0/BaxNl6TfjYLPaprFzE4aYZHLcJ5P0bsNUnWnHSNuTmt5hDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:16.226113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.02403","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce1799cb474b8f0e0d573f7478a02d2d81324056fe8eb9e7d2eb3fc4c5a7f57f","sha256:1f7081a9df7f9aacccab55f0ceb8d8e7a9958fe344217654cc1807fd235c4410"],"state_sha256":"3eabb7175cfe8df3c517cecdfd3c02966e0d8016232fb2849d6d1c0a7aa8e453"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sTTYtovIoadB+6hMqhR1Ye7tBbnIplHbDejYXrHLpzOG4uCJnwW4XNWkhYlVHzHWwXHD9u2fDSO9J7+AVjm4Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:49:02.637562Z","bundle_sha256":"3f7fbff71f002ff7d7f7db7da910af03ec6b4c1675bbe005f1c4df870eb90d52"}}