{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:M6SXVFZQJQTMACXMJPVDRRHMWY","short_pith_number":"pith:M6SXVFZQ","canonical_record":{"source":{"id":"1204.5427","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-24T16:38:33Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"020eae6d05af6eb9d79c7703efbfd9e9b11e0cbc555c37ae01ea9425f4697a08","abstract_canon_sha256":"db0d51b761177ad3aece10ab124671456150e75521b8864005e0d82678b31595"},"schema_version":"1.0"},"canonical_sha256":"67a57a97304c26c00aec4bea38c4ecb6145d7b4bc5907a89714c943aee7b524d","source":{"kind":"arxiv","id":"1204.5427","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5427","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5427v3","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5427","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"M6SXVFZQJQTM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M6SXVFZQJQTMACXM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M6SXVFZQ","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:M6SXVFZQJQTMACXMJPVDRRHMWY","target":"record","payload":{"canonical_record":{"source":{"id":"1204.5427","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-24T16:38:33Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"020eae6d05af6eb9d79c7703efbfd9e9b11e0cbc555c37ae01ea9425f4697a08","abstract_canon_sha256":"db0d51b761177ad3aece10ab124671456150e75521b8864005e0d82678b31595"},"schema_version":"1.0"},"canonical_sha256":"67a57a97304c26c00aec4bea38c4ecb6145d7b4bc5907a89714c943aee7b524d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:23.214702Z","signature_b64":"S3d965BCS3rJO+vYpjP/X1smn3EA2P9IFbT+JHiJJzzsg3UsiRhYkhR0zdVqo4RUX4ziAw9L6XL0VZoam5rhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67a57a97304c26c00aec4bea38c4ecb6145d7b4bc5907a89714c943aee7b524d","last_reissued_at":"2026-05-18T03:27:23.214209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:23.214209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.5427","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GIqKSrT3aND5aIyl4tfXeyKj4FocVypMQw+IO+vCrU6WXxRD7TKR7636zPGG+eYT1YkC+pUBOzgLV+y0h/ezCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:43.214455Z"},"content_sha256":"b62fe228e19933de02ebd32410b36282f399d9bb7f4166e328d68294398d2880","schema_version":"1.0","event_id":"sha256:b62fe228e19933de02ebd32410b36282f399d9bb7f4166e328d68294398d2880"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:M6SXVFZQJQTMACXMJPVDRRHMWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the construction of functorial factorizations for model categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Emily Riehl, Tobias Barthel","submitted_at":"2012-04-24T16:38:33Z","abstract_excerpt":"We present general techniques for constructing functorial factorizations appropriate for model structures that are not known to be cofibrantly generated. Our methods use \"algebraic\" characterizations of fibrations to produce factorizations that have the desired lifting properties in a completely categorical fashion. We illustrate these methods in the case of categories enriched, tensored, and cotensored in spaces, proving the existence of Hurewicz-type model structures, thereby correcting an error in earlier attempts by others. Examples include the categories of (based) spaces, (based) G-space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5427","kind":"arxiv","version":3},"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":"2026-05-18T03:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/fLshvbVXIOABepOmLnH/RFyDhuVDQ02ANaWFbmMG+t52S+mi/y3RQALlp9pEXJVSnKKHDjxRgXB04kWHur/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:43.215207Z"},"content_sha256":"8a2dd5a6e800dcb3504af2284c4e2172d622d32ddff298d2c7654fe7f2da3464","schema_version":"1.0","event_id":"sha256:8a2dd5a6e800dcb3504af2284c4e2172d622d32ddff298d2c7654fe7f2da3464"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6SXVFZQJQTMACXMJPVDRRHMWY/bundle.json","state_url":"https://pith.science/pith/M6SXVFZQJQTMACXMJPVDRRHMWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6SXVFZQJQTMACXMJPVDRRHMWY/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":"2026-05-31T08:38:43Z","links":{"resolver":"https://pith.science/pith/M6SXVFZQJQTMACXMJPVDRRHMWY","bundle":"https://pith.science/pith/M6SXVFZQJQTMACXMJPVDRRHMWY/bundle.json","state":"https://pith.science/pith/M6SXVFZQJQTMACXMJPVDRRHMWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6SXVFZQJQTMACXMJPVDRRHMWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M6SXVFZQJQTMACXMJPVDRRHMWY","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":"db0d51b761177ad3aece10ab124671456150e75521b8864005e0d82678b31595","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-24T16:38:33Z","title_canon_sha256":"020eae6d05af6eb9d79c7703efbfd9e9b11e0cbc555c37ae01ea9425f4697a08"},"schema_version":"1.0","source":{"id":"1204.5427","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5427","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5427v3","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5427","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"M6SXVFZQJQTM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M6SXVFZQJQTMACXM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M6SXVFZQ","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:8a2dd5a6e800dcb3504af2284c4e2172d622d32ddff298d2c7654fe7f2da3464","target":"graph","created_at":"2026-05-18T03:27:23Z","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 present general techniques for constructing functorial factorizations appropriate for model structures that are not known to be cofibrantly generated. Our methods use \"algebraic\" characterizations of fibrations to produce factorizations that have the desired lifting properties in a completely categorical fashion. We illustrate these methods in the case of categories enriched, tensored, and cotensored in spaces, proving the existence of Hurewicz-type model structures, thereby correcting an error in earlier attempts by others. Examples include the categories of (based) spaces, (based) G-space","authors_text":"Emily Riehl, Tobias Barthel","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-24T16:38:33Z","title":"On the construction of functorial factorizations for model categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5427","kind":"arxiv","version":3},"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:b62fe228e19933de02ebd32410b36282f399d9bb7f4166e328d68294398d2880","target":"record","created_at":"2026-05-18T03:27:23Z","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":"db0d51b761177ad3aece10ab124671456150e75521b8864005e0d82678b31595","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-04-24T16:38:33Z","title_canon_sha256":"020eae6d05af6eb9d79c7703efbfd9e9b11e0cbc555c37ae01ea9425f4697a08"},"schema_version":"1.0","source":{"id":"1204.5427","kind":"arxiv","version":3}},"canonical_sha256":"67a57a97304c26c00aec4bea38c4ecb6145d7b4bc5907a89714c943aee7b524d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67a57a97304c26c00aec4bea38c4ecb6145d7b4bc5907a89714c943aee7b524d","first_computed_at":"2026-05-18T03:27:23.214209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:23.214209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3d965BCS3rJO+vYpjP/X1smn3EA2P9IFbT+JHiJJzzsg3UsiRhYkhR0zdVqo4RUX4ziAw9L6XL0VZoam5rhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:23.214702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5427","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b62fe228e19933de02ebd32410b36282f399d9bb7f4166e328d68294398d2880","sha256:8a2dd5a6e800dcb3504af2284c4e2172d622d32ddff298d2c7654fe7f2da3464"],"state_sha256":"09a73daee3964e2ad85acca7902f9cd77666755e854a001b2b81d354fb280a7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KXdl6KL+ZcnAYzNllYvRiJMm2jq/+ufE90cVECKPXuV8pXRpaoqMhtyB3wDgR3gjQD9k8AB1JjgAz3fwO40mAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:38:43.219240Z","bundle_sha256":"d898d567568ed2a050f5ae7031fba891d2b115de708f8afdf6f5da5e26dd522f"}}