{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XTYYPKFPEWOXWXIRGAELIKIS2A","short_pith_number":"pith:XTYYPKFP","schema_version":"1.0","canonical_sha256":"bcf187a8af259d7b5d113008b42912d01af056d590b572d53c1d5d30c226cb4a","source":{"kind":"arxiv","id":"2606.17313","version":1},"attestation_state":"computed","paper":{"title":"A characterization of the spectral Lie operad","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Gijs Heuts, Max Blans","submitted_at":"2026-06-15T21:40:52Z","abstract_excerpt":"In this paper we study the structure of the $\\infty$-category of spectral Lie algebras. We show that this $\\infty$-category admits an interesting symmetric monoidal structure, defined by an analog of the smash product of pointed spaces, and that the free Lie algebra functor $\\mathrm{Sp} \\to \\mathrm{Lie}(\\mathrm{Sp})$ is symmetric monoidal with respect to it. Moreover, this property of the free functor essentially characterizes the spectral Lie operad (among nonunital operads in spectra). This result may be thought of as Koszul dual to the more familiar fact that the free commutative algebra fu"},"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":"2606.17313","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-06-15T21:40:52Z","cross_cats_sorted":[],"title_canon_sha256":"60957aed6806724db8980b901b245d90e38f92339c64c54b362b16416c68f8c2","abstract_canon_sha256":"e6c5bd37f6f8afe284abf863f461af3cac69260f415f89302e3d065fe2fc0f2f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:08.770682Z","signature_b64":"wb5gUNZ5zAlf7t5VD5VCiYShTTJYP4Irn5Pin2EoXOuNtWvroaTEEFsRuxhVhjhJ76FMe1yqGqedVws9BVY3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcf187a8af259d7b5d113008b42912d01af056d590b572d53c1d5d30c226cb4a","last_reissued_at":"2026-06-19T16:10:08.770333Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:08.770333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A characterization of the spectral Lie operad","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Gijs Heuts, Max Blans","submitted_at":"2026-06-15T21:40:52Z","abstract_excerpt":"In this paper we study the structure of the $\\infty$-category of spectral Lie algebras. We show that this $\\infty$-category admits an interesting symmetric monoidal structure, defined by an analog of the smash product of pointed spaces, and that the free Lie algebra functor $\\mathrm{Sp} \\to \\mathrm{Lie}(\\mathrm{Sp})$ is symmetric monoidal with respect to it. Moreover, this property of the free functor essentially characterizes the spectral Lie operad (among nonunital operads in spectra). This result may be thought of as Koszul dual to the more familiar fact that the free commutative algebra fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17313","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/2606.17313/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":"2606.17313","created_at":"2026-06-19T16:10:08.770397+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.17313v1","created_at":"2026-06-19T16:10:08.770397+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17313","created_at":"2026-06-19T16:10:08.770397+00:00"},{"alias_kind":"pith_short_12","alias_value":"XTYYPKFPEWOX","created_at":"2026-06-19T16:10:08.770397+00:00"},{"alias_kind":"pith_short_16","alias_value":"XTYYPKFPEWOXWXIR","created_at":"2026-06-19T16:10:08.770397+00:00"},{"alias_kind":"pith_short_8","alias_value":"XTYYPKFP","created_at":"2026-06-19T16:10:08.770397+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/XTYYPKFPEWOXWXIRGAELIKIS2A","json":"https://pith.science/pith/XTYYPKFPEWOXWXIRGAELIKIS2A.json","graph_json":"https://pith.science/api/pith-number/XTYYPKFPEWOXWXIRGAELIKIS2A/graph.json","events_json":"https://pith.science/api/pith-number/XTYYPKFPEWOXWXIRGAELIKIS2A/events.json","paper":"https://pith.science/paper/XTYYPKFP"},"agent_actions":{"view_html":"https://pith.science/pith/XTYYPKFPEWOXWXIRGAELIKIS2A","download_json":"https://pith.science/pith/XTYYPKFPEWOXWXIRGAELIKIS2A.json","view_paper":"https://pith.science/paper/XTYYPKFP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.17313&json=true","fetch_graph":"https://pith.science/api/pith-number/XTYYPKFPEWOXWXIRGAELIKIS2A/graph.json","fetch_events":"https://pith.science/api/pith-number/XTYYPKFPEWOXWXIRGAELIKIS2A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XTYYPKFPEWOXWXIRGAELIKIS2A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XTYYPKFPEWOXWXIRGAELIKIS2A/action/storage_attestation","attest_author":"https://pith.science/pith/XTYYPKFPEWOXWXIRGAELIKIS2A/action/author_attestation","sign_citation":"https://pith.science/pith/XTYYPKFPEWOXWXIRGAELIKIS2A/action/citation_signature","submit_replication":"https://pith.science/pith/XTYYPKFPEWOXWXIRGAELIKIS2A/action/replication_record"}},"created_at":"2026-06-19T16:10:08.770397+00:00","updated_at":"2026-06-19T16:10:08.770397+00:00"}