{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:CMMI6W6VYD52HLFPXJILMIT43T","short_pith_number":"pith:CMMI6W6V","schema_version":"1.0","canonical_sha256":"13188f5bd5c0fba3acafba50b6227cdcd37d69596ff8c5d9847d2d2350ac3daa","source":{"kind":"arxiv","id":"2410.08348","version":1},"attestation_state":"computed","paper":{"title":"Filtered spaces, filtered objects","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Tyler Lawson","submitted_at":"2024-10-10T20:10:20Z","abstract_excerpt":"We introduce a operation on categories enriched in filtered spaces, whose effect is to turn categories of $E_1$-pages into categories of $E_2$-pages. This allows us to give a homotopical versions of several results that were previously implemented using $E_2$-model structures or more sophisticated machinery in higher algebra.\n  We find that we can recover the homotopy theory of spaces from this page-turning operation on the homotopy theory of CW-complexes and filtration-shifting maps, a version of the cellular approximation theorem. In the category of filtered spectra, we show that this implem"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2410.08348","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2024-10-10T20:10:20Z","cross_cats_sorted":[],"title_canon_sha256":"39cf80024f8cbf37349037e138706d4ec3552c902ad6883cc1fb151e0024f2a2","abstract_canon_sha256":"d69cf024a95dcd06670bde8e09f002d2e8646a074e75e3ee30b70d4ed7fefbbf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:18:56.970976Z","signature_b64":"orMhr2xTJXDJY7FgG7tTn87Dir1fRKFrS3TxeyUBkQI2Q5CQoAgRi6NzckUmivC/VEM10H89zGeYifGtlNAECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13188f5bd5c0fba3acafba50b6227cdcd37d69596ff8c5d9847d2d2350ac3daa","last_reissued_at":"2026-07-05T09:18:56.970530Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:18:56.970530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Filtered spaces, filtered objects","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Tyler Lawson","submitted_at":"2024-10-10T20:10:20Z","abstract_excerpt":"We introduce a operation on categories enriched in filtered spaces, whose effect is to turn categories of $E_1$-pages into categories of $E_2$-pages. This allows us to give a homotopical versions of several results that were previously implemented using $E_2$-model structures or more sophisticated machinery in higher algebra.\n  We find that we can recover the homotopy theory of spaces from this page-turning operation on the homotopy theory of CW-complexes and filtration-shifting maps, a version of the cellular approximation theorem. In the category of filtered spectra, we show that this implem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08348","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.08348/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2410.08348","created_at":"2026-07-05T09:18:56.970587+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.08348v1","created_at":"2026-07-05T09:18:56.970587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08348","created_at":"2026-07-05T09:18:56.970587+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMMI6W6VYD52","created_at":"2026-07-05T09:18:56.970587+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMMI6W6VYD52HLFP","created_at":"2026-07-05T09:18:56.970587+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMMI6W6V","created_at":"2026-07-05T09:18:56.970587+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.09115","citing_title":"Spectral sequences, d\\'ecalage, and the Beilinson t-structure","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T","json":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T.json","graph_json":"https://pith.science/api/pith-number/CMMI6W6VYD52HLFPXJILMIT43T/graph.json","events_json":"https://pith.science/api/pith-number/CMMI6W6VYD52HLFPXJILMIT43T/events.json","paper":"https://pith.science/paper/CMMI6W6V"},"agent_actions":{"view_html":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T","download_json":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T.json","view_paper":"https://pith.science/paper/CMMI6W6V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.08348&json=true","fetch_graph":"https://pith.science/api/pith-number/CMMI6W6VYD52HLFPXJILMIT43T/graph.json","fetch_events":"https://pith.science/api/pith-number/CMMI6W6VYD52HLFPXJILMIT43T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T/action/storage_attestation","attest_author":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T/action/author_attestation","sign_citation":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T/action/citation_signature","submit_replication":"https://pith.science/pith/CMMI6W6VYD52HLFPXJILMIT43T/action/replication_record"}},"created_at":"2026-07-05T09:18:56.970587+00:00","updated_at":"2026-07-05T09:18:56.970587+00:00"}