{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TNOOPPKEKES6ONAETJQC6TPSMP","short_pith_number":"pith:TNOOPPKE","canonical_record":{"source":{"id":"1305.4607","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-05-20T18:46:56Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"7c6ee883cd0de19bdc23787c899497595dbfb72b52ca06b26a96a2d8272e40b3","abstract_canon_sha256":"7ff76b32d6ef63a4b894cc5a2cebde44fb74762a417ac21d149fc2b83b186db0"},"schema_version":"1.0"},"canonical_sha256":"9b5ce7bd445125e734049a602f4df263f6fc51ba1a86a3e879b3a6c31a7275d6","source":{"kind":"arxiv","id":"1305.4607","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4607","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4607v1","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4607","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"pith_short_12","alias_value":"TNOOPPKEKES6","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TNOOPPKEKES6ONAE","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TNOOPPKE","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TNOOPPKEKES6ONAETJQC6TPSMP","target":"record","payload":{"canonical_record":{"source":{"id":"1305.4607","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-05-20T18:46:56Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"7c6ee883cd0de19bdc23787c899497595dbfb72b52ca06b26a96a2d8272e40b3","abstract_canon_sha256":"7ff76b32d6ef63a4b894cc5a2cebde44fb74762a417ac21d149fc2b83b186db0"},"schema_version":"1.0"},"canonical_sha256":"9b5ce7bd445125e734049a602f4df263f6fc51ba1a86a3e879b3a6c31a7275d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:16.581527Z","signature_b64":"abzQANQPYdKvNq6csMcpXYn5m1BBJePqVNAz4WwESR3aYZZfCUMb2NCXWN/0gz3Sh3gqZgjF2ncZaR64+OBqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b5ce7bd445125e734049a602f4df263f6fc51ba1a86a3e879b3a6c31a7275d6","last_reissued_at":"2026-05-18T03:25:16.580800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:16.580800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.4607","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":"2026-05-18T03:25:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"298wBANwG0o+NTCpA8OOmMD44yHfvm4EDrnil7UX94UOs2V/zxuU/gEx7TwAvkg01xZUhpEqcnQBpXuX7Dy1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:31:40.840104Z"},"content_sha256":"f8138ce6a0a62271280d42392b33d73f0350f10580015444abc650daff640e1c","schema_version":"1.0","event_id":"sha256:f8138ce6a0a62271280d42392b33d73f0350f10580015444abc650daff640e1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TNOOPPKEKES6ONAETJQC6TPSMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functorial Factorizations in Pro Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Ilan Barnea, Tomer M. Schlank","submitted_at":"2013-05-20T18:46:56Z","abstract_excerpt":"In this paper we prove a few propositions concerning factorizations of morphisms in pro categories, the most important of which solves an open problem of Isaksen concerning the existence of certain types of functorial factorizations. On our way we explain and correct an error in one of the standard references on pro categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4607","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":"2026-05-18T03:25:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+reZZK2sESPvOGdYAGox/7a9id7VGVqz74oyqr3/+EkcjmTcfar6+6BoydHcpbzhojRFVbd8bktutUkmk19UBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:31:40.840478Z"},"content_sha256":"13c5ccb832bd410075df412c56877373bcd2fc6d444474663610732ad91e145e","schema_version":"1.0","event_id":"sha256:13c5ccb832bd410075df412c56877373bcd2fc6d444474663610732ad91e145e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNOOPPKEKES6ONAETJQC6TPSMP/bundle.json","state_url":"https://pith.science/pith/TNOOPPKEKES6ONAETJQC6TPSMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNOOPPKEKES6ONAETJQC6TPSMP/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":"2026-07-03T13:31:40Z","links":{"resolver":"https://pith.science/pith/TNOOPPKEKES6ONAETJQC6TPSMP","bundle":"https://pith.science/pith/TNOOPPKEKES6ONAETJQC6TPSMP/bundle.json","state":"https://pith.science/pith/TNOOPPKEKES6ONAETJQC6TPSMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNOOPPKEKES6ONAETJQC6TPSMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TNOOPPKEKES6ONAETJQC6TPSMP","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":"7ff76b32d6ef63a4b894cc5a2cebde44fb74762a417ac21d149fc2b83b186db0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-05-20T18:46:56Z","title_canon_sha256":"7c6ee883cd0de19bdc23787c899497595dbfb72b52ca06b26a96a2d8272e40b3"},"schema_version":"1.0","source":{"id":"1305.4607","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.4607","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"arxiv_version","alias_value":"1305.4607v1","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4607","created_at":"2026-05-18T03:25:16Z"},{"alias_kind":"pith_short_12","alias_value":"TNOOPPKEKES6","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TNOOPPKEKES6ONAE","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TNOOPPKE","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:13c5ccb832bd410075df412c56877373bcd2fc6d444474663610732ad91e145e","target":"graph","created_at":"2026-05-18T03:25:16Z","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":"In this paper we prove a few propositions concerning factorizations of morphisms in pro categories, the most important of which solves an open problem of Isaksen concerning the existence of certain types of functorial factorizations. On our way we explain and correct an error in one of the standard references on pro categories.","authors_text":"Ilan Barnea, Tomer M. Schlank","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-05-20T18:46:56Z","title":"Functorial Factorizations in Pro Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4607","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:f8138ce6a0a62271280d42392b33d73f0350f10580015444abc650daff640e1c","target":"record","created_at":"2026-05-18T03:25:16Z","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":"7ff76b32d6ef63a4b894cc5a2cebde44fb74762a417ac21d149fc2b83b186db0","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-05-20T18:46:56Z","title_canon_sha256":"7c6ee883cd0de19bdc23787c899497595dbfb72b52ca06b26a96a2d8272e40b3"},"schema_version":"1.0","source":{"id":"1305.4607","kind":"arxiv","version":1}},"canonical_sha256":"9b5ce7bd445125e734049a602f4df263f6fc51ba1a86a3e879b3a6c31a7275d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b5ce7bd445125e734049a602f4df263f6fc51ba1a86a3e879b3a6c31a7275d6","first_computed_at":"2026-05-18T03:25:16.580800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:16.580800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"abzQANQPYdKvNq6csMcpXYn5m1BBJePqVNAz4WwESR3aYZZfCUMb2NCXWN/0gz3Sh3gqZgjF2ncZaR64+OBqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:16.581527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.4607","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8138ce6a0a62271280d42392b33d73f0350f10580015444abc650daff640e1c","sha256:13c5ccb832bd410075df412c56877373bcd2fc6d444474663610732ad91e145e"],"state_sha256":"e338730db9be623c58f9e4c0de02c6af9318e89a455f47184841fc42957605c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g9g/pMTL5cH5+acemvu5ph1uHmJZND8MT30FTmQeioVIETRN9oi5flz2F+qk8D+g+05KlT+wEX0cA/xUfCA8Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T13:31:40.842373Z","bundle_sha256":"d30100c18dfdb7d3e850cbcda937b4d387f2a48af41ca13d8469fd7b806d01b4"}}