{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:PQGC6HYBVMSN4TFQPQJG4QYMXM","short_pith_number":"pith:PQGC6HYB","canonical_record":{"source":{"id":"0911.3214","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-11-17T06:27:14Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"00ee5565300d2f2702226825c3e22733a8c8cb08a06da357e6d28d92ffd87b84","abstract_canon_sha256":"c31e03936510644befd097ef9d9e418ab78e6c02b97e6d0a10339b66e21841ca"},"schema_version":"1.0"},"canonical_sha256":"7c0c2f1f01ab24de4cb07c126e430cbb0398cd41b0493f348e6654c561e0a6a6","source":{"kind":"arxiv","id":"0911.3214","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3214","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3214v2","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3214","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"PQGC6HYBVMSN","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PQGC6HYBVMSN4TFQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PQGC6HYB","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:PQGC6HYBVMSN4TFQPQJG4QYMXM","target":"record","payload":{"canonical_record":{"source":{"id":"0911.3214","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-11-17T06:27:14Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"00ee5565300d2f2702226825c3e22733a8c8cb08a06da357e6d28d92ffd87b84","abstract_canon_sha256":"c31e03936510644befd097ef9d9e418ab78e6c02b97e6d0a10339b66e21841ca"},"schema_version":"1.0"},"canonical_sha256":"7c0c2f1f01ab24de4cb07c126e430cbb0398cd41b0493f348e6654c561e0a6a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:40.243408Z","signature_b64":"3Lc2n+9ScKPcdWlznj4UPeEXPpB8E9UNNvFFoeJ6JdIZYMf4SdnaaJq38ewv/a5rQdy9pMCNq6xvAfJzeykICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c0c2f1f01ab24de4cb07c126e430cbb0398cd41b0493f348e6654c561e0a6a6","last_reissued_at":"2026-05-18T01:37:40.242679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:40.242679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.3214","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":"2026-05-18T01:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i43Xxv0VOOePPAZ9g1DXEfUW1zOQ1V4f05h2fCgM+ByGDPtCrGitC4yl+y5Pj3GH6zyFsC21Vnys1n0KHurkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:17:24.805668Z"},"content_sha256":"65a2fa9712a8f78d65c415a7803194caa92779ecc7bf86e4b77a463550954330","schema_version":"1.0","event_id":"sha256:65a2fa9712a8f78d65c415a7803194caa92779ecc7bf86e4b77a463550954330"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:PQGC6HYBVMSN4TFQPQJG4QYMXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifinite Chu Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.LO","authors_text":"Guo-Qiang Zhang, Manfred Droste","submitted_at":"2009-11-17T06:27:14Z","abstract_excerpt":"This paper studies colimits of sequences of finite Chu spaces and their ramifications. Besides generic Chu spaces, we consider extensional and biextensional variants. In the corresponding categories we first characterize the monics and then the existence (or the lack thereof) of the desired colimits. In each case, we provide a characterization of the finite objects in terms of monomorphisms/injections. Bifinite Chu spaces are then expressed with respect to the monics of generic Chu spaces, and universal, homogeneous Chu spaces are shown to exist in this category. Unanticipated results driving "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3214","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":"2026-05-18T01:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgR/OuDUYKixd8yovVU4PlAJz+DhoMbiv2e8fnkSPRIbaeS34HaKidvT9M9kF5JbaSGQ97UGuX0rwPzrKhmqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:17:24.806324Z"},"content_sha256":"3eb843af1333ffc27701ee7df18ee1281bd0396101c743ec906a5fff9359eac3","schema_version":"1.0","event_id":"sha256:3eb843af1333ffc27701ee7df18ee1281bd0396101c743ec906a5fff9359eac3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQGC6HYBVMSN4TFQPQJG4QYMXM/bundle.json","state_url":"https://pith.science/pith/PQGC6HYBVMSN4TFQPQJG4QYMXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQGC6HYBVMSN4TFQPQJG4QYMXM/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":"2026-05-31T18:17:24Z","links":{"resolver":"https://pith.science/pith/PQGC6HYBVMSN4TFQPQJG4QYMXM","bundle":"https://pith.science/pith/PQGC6HYBVMSN4TFQPQJG4QYMXM/bundle.json","state":"https://pith.science/pith/PQGC6HYBVMSN4TFQPQJG4QYMXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQGC6HYBVMSN4TFQPQJG4QYMXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:PQGC6HYBVMSN4TFQPQJG4QYMXM","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":"c31e03936510644befd097ef9d9e418ab78e6c02b97e6d0a10339b66e21841ca","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-11-17T06:27:14Z","title_canon_sha256":"00ee5565300d2f2702226825c3e22733a8c8cb08a06da357e6d28d92ffd87b84"},"schema_version":"1.0","source":{"id":"0911.3214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.3214","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"0911.3214v2","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.3214","created_at":"2026-05-18T01:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"PQGC6HYBVMSN","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"PQGC6HYBVMSN4TFQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"PQGC6HYB","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:3eb843af1333ffc27701ee7df18ee1281bd0396101c743ec906a5fff9359eac3","target":"graph","created_at":"2026-05-18T01:37:40Z","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":"This paper studies colimits of sequences of finite Chu spaces and their ramifications. Besides generic Chu spaces, we consider extensional and biextensional variants. In the corresponding categories we first characterize the monics and then the existence (or the lack thereof) of the desired colimits. In each case, we provide a characterization of the finite objects in terms of monomorphisms/injections. Bifinite Chu spaces are then expressed with respect to the monics of generic Chu spaces, and universal, homogeneous Chu spaces are shown to exist in this category. Unanticipated results driving ","authors_text":"Guo-Qiang Zhang, Manfred Droste","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-11-17T06:27:14Z","title":"Bifinite Chu Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.3214","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":"sha256:65a2fa9712a8f78d65c415a7803194caa92779ecc7bf86e4b77a463550954330","target":"record","created_at":"2026-05-18T01:37:40Z","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":"c31e03936510644befd097ef9d9e418ab78e6c02b97e6d0a10339b66e21841ca","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2009-11-17T06:27:14Z","title_canon_sha256":"00ee5565300d2f2702226825c3e22733a8c8cb08a06da357e6d28d92ffd87b84"},"schema_version":"1.0","source":{"id":"0911.3214","kind":"arxiv","version":2}},"canonical_sha256":"7c0c2f1f01ab24de4cb07c126e430cbb0398cd41b0493f348e6654c561e0a6a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c0c2f1f01ab24de4cb07c126e430cbb0398cd41b0493f348e6654c561e0a6a6","first_computed_at":"2026-05-18T01:37:40.242679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:40.242679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Lc2n+9ScKPcdWlznj4UPeEXPpB8E9UNNvFFoeJ6JdIZYMf4SdnaaJq38ewv/a5rQdy9pMCNq6xvAfJzeykICA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:40.243408Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.3214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65a2fa9712a8f78d65c415a7803194caa92779ecc7bf86e4b77a463550954330","sha256:3eb843af1333ffc27701ee7df18ee1281bd0396101c743ec906a5fff9359eac3"],"state_sha256":"61ee68eb6a16cf996c0090433f907ffedb2d9fda18a094562d838df07862a70f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/xV+cIlO7+2XZrfzwXqWOofjZPAN+wTeRTK2ppyDaJ1gEN6olnSwN4zHFJRdt4tsPTFZ3b0AzGZ+zYZgHAcdAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:17:24.809756Z","bundle_sha256":"93197dd064a992756b7777e6c9b2821faeceb566081dc4f694365a244452ea4a"}}