{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5FS752N7YAYMU5CXBREX6RO3WK","short_pith_number":"pith:5FS752N7","canonical_record":{"source":{"id":"1404.6634","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-04-26T11:00:42Z","cross_cats_sorted":[],"title_canon_sha256":"c3adc3e6f93360f0d30a6b0b733b1f386fd650f875d7dda1491ff28af1b0e93c","abstract_canon_sha256":"3e1763128075eae322fa817b59d7129538d3c949c65d22a4382b28787fd73257"},"schema_version":"1.0"},"canonical_sha256":"e965fee9bfc030ca74570c497f45dbb2972c1302d103e0586aa762f0d2dd185a","source":{"kind":"arxiv","id":"1404.6634","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6634","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6634v4","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6634","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"pith_short_12","alias_value":"5FS752N7YAYM","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5FS752N7YAYMU5CX","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5FS752N7","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5FS752N7YAYMU5CXBREX6RO3WK","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6634","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-04-26T11:00:42Z","cross_cats_sorted":[],"title_canon_sha256":"c3adc3e6f93360f0d30a6b0b733b1f386fd650f875d7dda1491ff28af1b0e93c","abstract_canon_sha256":"3e1763128075eae322fa817b59d7129538d3c949c65d22a4382b28787fd73257"},"schema_version":"1.0"},"canonical_sha256":"e965fee9bfc030ca74570c497f45dbb2972c1302d103e0586aa762f0d2dd185a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:02.341822Z","signature_b64":"3wVcKmCGolZoHzzEbgQG7IiyE5xAAu2oMC5blZQ1brcmhurngK6K1G7Zl/k1rY1MS7PnDoTL8+DcXdybginjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e965fee9bfc030ca74570c497f45dbb2972c1302d103e0586aa762f0d2dd185a","last_reissued_at":"2026-05-18T01:37:02.341380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:02.341380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6634","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRNbGOHjNsxSlftmL00NfWmQl4pYt0KHQgdK6tdN+cjr4W/ImQbMb4hR/Mb8rqUwbujtrjcPLB2Iy5NhBcnJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:58:20.030747Z"},"content_sha256":"b3517d3687a69fbc946ea9009a55d1ef520b13bfb92a707462719a28cccda98c","schema_version":"1.0","event_id":"sha256:b3517d3687a69fbc946ea9009a55d1ef520b13bfb92a707462719a28cccda98c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5FS752N7YAYMU5CXBREX6RO3WK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On definably proper maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Luca Prelli, Marcello Mamino, M\\'ario Edmundo","submitted_at":"2014-04-26T11:00:42Z","abstract_excerpt":"In this paper we work in o-minimal structures with definable Skolem functions and show that a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is proper morphism in the category of definable spaces. We give several other characterizations of definably proper including one involving the existence of limits of definable types. We also prove the basic properties of definably proper maps and the invariance of definably proper in elementary extensions and o-minimal expansions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6634","kind":"arxiv","version":4},"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":"2026-05-18T01:37:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"khNMce53iAZ0gLay4BS0O1jxcZIpwKqdiK1fBg63EY8OwwHK/whsDo5GRhkHccoV35bUa9ZpDD6O5fpl73z4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:58:20.031500Z"},"content_sha256":"0999d0205e91512cdc5a32cd9cbd730197cfb34ec1aa44edd56175e79cf38b0c","schema_version":"1.0","event_id":"sha256:0999d0205e91512cdc5a32cd9cbd730197cfb34ec1aa44edd56175e79cf38b0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FS752N7YAYMU5CXBREX6RO3WK/bundle.json","state_url":"https://pith.science/pith/5FS752N7YAYMU5CXBREX6RO3WK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FS752N7YAYMU5CXBREX6RO3WK/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":"2026-06-10T00:58:20Z","links":{"resolver":"https://pith.science/pith/5FS752N7YAYMU5CXBREX6RO3WK","bundle":"https://pith.science/pith/5FS752N7YAYMU5CXBREX6RO3WK/bundle.json","state":"https://pith.science/pith/5FS752N7YAYMU5CXBREX6RO3WK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FS752N7YAYMU5CXBREX6RO3WK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5FS752N7YAYMU5CXBREX6RO3WK","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":"3e1763128075eae322fa817b59d7129538d3c949c65d22a4382b28787fd73257","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-04-26T11:00:42Z","title_canon_sha256":"c3adc3e6f93360f0d30a6b0b733b1f386fd650f875d7dda1491ff28af1b0e93c"},"schema_version":"1.0","source":{"id":"1404.6634","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6634","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6634v4","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6634","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"pith_short_12","alias_value":"5FS752N7YAYM","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5FS752N7YAYMU5CX","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5FS752N7","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:0999d0205e91512cdc5a32cd9cbd730197cfb34ec1aa44edd56175e79cf38b0c","target":"graph","created_at":"2026-05-18T01:37:02Z","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":"In this paper we work in o-minimal structures with definable Skolem functions and show that a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is proper morphism in the category of definable spaces. We give several other characterizations of definably proper including one involving the existence of limits of definable types. We also prove the basic properties of definably proper maps and the invariance of definably proper in elementary extensions and o-minimal expansions.","authors_text":"Luca Prelli, Marcello Mamino, M\\'ario Edmundo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-04-26T11:00:42Z","title":"On definably proper maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6634","kind":"arxiv","version":4},"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:b3517d3687a69fbc946ea9009a55d1ef520b13bfb92a707462719a28cccda98c","target":"record","created_at":"2026-05-18T01:37:02Z","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":"3e1763128075eae322fa817b59d7129538d3c949c65d22a4382b28787fd73257","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-04-26T11:00:42Z","title_canon_sha256":"c3adc3e6f93360f0d30a6b0b733b1f386fd650f875d7dda1491ff28af1b0e93c"},"schema_version":"1.0","source":{"id":"1404.6634","kind":"arxiv","version":4}},"canonical_sha256":"e965fee9bfc030ca74570c497f45dbb2972c1302d103e0586aa762f0d2dd185a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e965fee9bfc030ca74570c497f45dbb2972c1302d103e0586aa762f0d2dd185a","first_computed_at":"2026-05-18T01:37:02.341380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:02.341380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3wVcKmCGolZoHzzEbgQG7IiyE5xAAu2oMC5blZQ1brcmhurngK6K1G7Zl/k1rY1MS7PnDoTL8+DcXdybginjCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:02.341822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6634","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3517d3687a69fbc946ea9009a55d1ef520b13bfb92a707462719a28cccda98c","sha256:0999d0205e91512cdc5a32cd9cbd730197cfb34ec1aa44edd56175e79cf38b0c"],"state_sha256":"686030d300bdcb5445bacedf2e62689a402fa9f98436dd6c332077c4fca37d7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mjBMAukDU2GhMlS7WmnF9JKVvF6efGq8aozHZSrklf3V1eYH4DCgdixcEAA8o3Aj0tmawXCZBw+6/bxNQaiqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:58:20.035713Z","bundle_sha256":"210cf7099803503cfe702f91a509331072ce63fcf048bc40e8c5c983a2154549"}}