{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:LD5ZOTWA466CVZVYA7TDSFRDSN","short_pith_number":"pith:LD5ZOTWA","schema_version":"1.0","canonical_sha256":"58fb974ec0e7bc2ae6b807e6391623936b424fbb578bc8c24b8f4cfce113f943","source":{"kind":"arxiv","id":"1006.4347","version":2},"attestation_state":"computed","paper":{"title":"Topological Hochschild Homology of $K/p$ as a $K_p^\\wedge$ module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Samik Basu","submitted_at":"2010-06-22T18:44:01Z","abstract_excerpt":"Let $R$ be an $E_\\infty$-ring spectrum. Given a map $\\zeta$ from a space $X$ to $BGL_1R$, one can construct a Thom spectrum, $X^\\zeta$, which generalises the classical notion of Thom spectrum for spherical fibrations in the case $R=S^0$, the sphere spectrum. If $X$ is a loop space ($\\simeq \\Omega Y$) and $\\zeta$ is homotopy equivalent to $\\Omega f$ for a map $f$ from $Y$ to $B^2GL_1R$, then the Thom spectrum has an $A_\\infty$-ring structure. The Topological Hochschild Homology of these $A_\\infty$-ring spectra is equivalent to the Thom spectrum of a map out of the free loop space of $Y$.\n  This"},"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":"1006.4347","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2010-06-22T18:44:01Z","cross_cats_sorted":[],"title_canon_sha256":"a987591d629974bc40851879df26bd6587fd3d77b66a8d3e2b4cf1500c3fbd38","abstract_canon_sha256":"23f8ec633c2a1b0e5b392c68d9e7e7ae3a61ca46763289bbc41480ca9677fdd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:25.797974Z","signature_b64":"hDtZRJ//Pki6S6YSR+QJgS32/dB3i9v+ZYLoP8Z/SvagJVlnslJJ0GRXqCgHP57/TN/VKftvdBMbgpqa3TsjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58fb974ec0e7bc2ae6b807e6391623936b424fbb578bc8c24b8f4cfce113f943","last_reissued_at":"2026-05-18T03:59:25.797298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:25.797298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Hochschild Homology of $K/p$ as a $K_p^\\wedge$ module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Samik Basu","submitted_at":"2010-06-22T18:44:01Z","abstract_excerpt":"Let $R$ be an $E_\\infty$-ring spectrum. Given a map $\\zeta$ from a space $X$ to $BGL_1R$, one can construct a Thom spectrum, $X^\\zeta$, which generalises the classical notion of Thom spectrum for spherical fibrations in the case $R=S^0$, the sphere spectrum. If $X$ is a loop space ($\\simeq \\Omega Y$) and $\\zeta$ is homotopy equivalent to $\\Omega f$ for a map $f$ from $Y$ to $B^2GL_1R$, then the Thom spectrum has an $A_\\infty$-ring structure. The Topological Hochschild Homology of these $A_\\infty$-ring spectra is equivalent to the Thom spectrum of a map out of the free loop space of $Y$.\n  This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4347","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1006.4347","created_at":"2026-05-18T03:59:25.797429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1006.4347v2","created_at":"2026-05-18T03:59:25.797429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.4347","created_at":"2026-05-18T03:59:25.797429+00:00"},{"alias_kind":"pith_short_12","alias_value":"LD5ZOTWA466C","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"LD5ZOTWA466CVZVY","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"LD5ZOTWA","created_at":"2026-05-18T12:26:10.704358+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/LD5ZOTWA466CVZVYA7TDSFRDSN","json":"https://pith.science/pith/LD5ZOTWA466CVZVYA7TDSFRDSN.json","graph_json":"https://pith.science/api/pith-number/LD5ZOTWA466CVZVYA7TDSFRDSN/graph.json","events_json":"https://pith.science/api/pith-number/LD5ZOTWA466CVZVYA7TDSFRDSN/events.json","paper":"https://pith.science/paper/LD5ZOTWA"},"agent_actions":{"view_html":"https://pith.science/pith/LD5ZOTWA466CVZVYA7TDSFRDSN","download_json":"https://pith.science/pith/LD5ZOTWA466CVZVYA7TDSFRDSN.json","view_paper":"https://pith.science/paper/LD5ZOTWA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1006.4347&json=true","fetch_graph":"https://pith.science/api/pith-number/LD5ZOTWA466CVZVYA7TDSFRDSN/graph.json","fetch_events":"https://pith.science/api/pith-number/LD5ZOTWA466CVZVYA7TDSFRDSN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LD5ZOTWA466CVZVYA7TDSFRDSN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LD5ZOTWA466CVZVYA7TDSFRDSN/action/storage_attestation","attest_author":"https://pith.science/pith/LD5ZOTWA466CVZVYA7TDSFRDSN/action/author_attestation","sign_citation":"https://pith.science/pith/LD5ZOTWA466CVZVYA7TDSFRDSN/action/citation_signature","submit_replication":"https://pith.science/pith/LD5ZOTWA466CVZVYA7TDSFRDSN/action/replication_record"}},"created_at":"2026-05-18T03:59:25.797429+00:00","updated_at":"2026-05-18T03:59:25.797429+00:00"}