{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CSYD2IUXVT5WEHYJWCM6PKCVH3","short_pith_number":"pith:CSYD2IUX","schema_version":"1.0","canonical_sha256":"14b03d2297acfb621f09b099e7a8553ec26201887adf57ae93e150045c24a803","source":{"kind":"arxiv","id":"1411.1711","version":1},"attestation_state":"computed","paper":{"title":"Chromatic completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Tobias Barthel","submitted_at":"2014-11-06T19:27:38Z","abstract_excerpt":"We study the limit of the chromatic tower for not necessarily finite spectra, obtaining a generalization of the chromatic convergence theorem of Hopkins and Ravenel. Moreover, we prove that in general this limit does not coincide with harmonic localization, thereby answering a question of Ravenel's."},"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":"1411.1711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2014-11-06T19:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"c89778d3a07d82b76189eac65631f778af16738b5ad616eadb26163c8c7c2784","abstract_canon_sha256":"5af9a15924a14282318d0ee3332f504de53efc213104c7de5a82fc8cd397c779"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:27.109921Z","signature_b64":"yaYKJJrgt6WROaPV0wzbufALt4yzGXn5CA/WQw0aoaIfI4YFZWiiT/zh0NXOd7v0r5qH454jh3XSd+PPLXK6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14b03d2297acfb621f09b099e7a8553ec26201887adf57ae93e150045c24a803","last_reissued_at":"2026-05-18T02:38:27.109428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:27.109428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chromatic completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Tobias Barthel","submitted_at":"2014-11-06T19:27:38Z","abstract_excerpt":"We study the limit of the chromatic tower for not necessarily finite spectra, obtaining a generalization of the chromatic convergence theorem of Hopkins and Ravenel. Moreover, we prove that in general this limit does not coincide with harmonic localization, thereby answering a question of Ravenel's."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1711","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1411.1711","created_at":"2026-05-18T02:38:27.109504+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1711v1","created_at":"2026-05-18T02:38:27.109504+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1711","created_at":"2026-05-18T02:38:27.109504+00:00"},{"alias_kind":"pith_short_12","alias_value":"CSYD2IUXVT5W","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CSYD2IUXVT5WEHYJ","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CSYD2IUX","created_at":"2026-05-18T12:28:22.404517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3","json":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3.json","graph_json":"https://pith.science/api/pith-number/CSYD2IUXVT5WEHYJWCM6PKCVH3/graph.json","events_json":"https://pith.science/api/pith-number/CSYD2IUXVT5WEHYJWCM6PKCVH3/events.json","paper":"https://pith.science/paper/CSYD2IUX"},"agent_actions":{"view_html":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3","download_json":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3.json","view_paper":"https://pith.science/paper/CSYD2IUX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1711&json=true","fetch_graph":"https://pith.science/api/pith-number/CSYD2IUXVT5WEHYJWCM6PKCVH3/graph.json","fetch_events":"https://pith.science/api/pith-number/CSYD2IUXVT5WEHYJWCM6PKCVH3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3/action/storage_attestation","attest_author":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3/action/author_attestation","sign_citation":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3/action/citation_signature","submit_replication":"https://pith.science/pith/CSYD2IUXVT5WEHYJWCM6PKCVH3/action/replication_record"}},"created_at":"2026-05-18T02:38:27.109504+00:00","updated_at":"2026-05-18T02:38:27.109504+00:00"}