{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:H6EYZF2PNUCSGQHMQLDPRGQ6GX","short_pith_number":"pith:H6EYZF2P","canonical_record":{"source":{"id":"1501.05799","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-23T13:35:12Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"a3dcf3db1629b22a193242e233eb21c377edd88e6f9be549b70b79e2cf385de9","abstract_canon_sha256":"bdace4e33647202a39c23cd5aee6f9c5090add608ce3ba99360b9b6bdf2e338a"},"schema_version":"1.0"},"canonical_sha256":"3f898c974f6d052340ec82c6f89a1e35f03d3c2af6d7a941280f335af96af076","source":{"kind":"arxiv","id":"1501.05799","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05799","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05799v4","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05799","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"H6EYZF2PNUCS","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H6EYZF2PNUCSGQHM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H6EYZF2P","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:H6EYZF2PNUCSGQHMQLDPRGQ6GX","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05799","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-23T13:35:12Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"a3dcf3db1629b22a193242e233eb21c377edd88e6f9be549b70b79e2cf385de9","abstract_canon_sha256":"bdace4e33647202a39c23cd5aee6f9c5090add608ce3ba99360b9b6bdf2e338a"},"schema_version":"1.0"},"canonical_sha256":"3f898c974f6d052340ec82c6f89a1e35f03d3c2af6d7a941280f335af96af076","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:00.547044Z","signature_b64":"Yq1kCAT/J4IQJF8ynpcllcF9NsAJv2qihATvjpaqYsuWwENOqUr2AFpOnpZ+la+Fg8lmb7ePWj7jb9SfiCcNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f898c974f6d052340ec82c6f89a1e35f03d3c2af6d7a941280f335af96af076","last_reissued_at":"2026-05-17T23:45:00.546419Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:00.546419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05799","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDD/Qlntemf+xIhvLg2AOqoChtpYFyddU58ZySCyfN0K/+5dGA72zRHezXhGDSlGC1kG1hxZ8FCiGqowe9gLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T16:46:07.473907Z"},"content_sha256":"bb8086b5a270ad8429df7e315f1d147e90a7bc619c8fd3025ed3c540a64abd96","schema_version":"1.0","event_id":"sha256:bb8086b5a270ad8429df7e315f1d147e90a7bc619c8fd3025ed3c540a64abd96"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:H6EYZF2PNUCSGQHMQLDPRGQ6GX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$C^*$-algebraic drawings of dendroidal sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.OA","authors_text":"Snigdhayan Mahanta","submitted_at":"2015-01-23T13:35:12Z","abstract_excerpt":"In recent years the theory of dendroidal sets has emerged as an important framework for higher algebra. In this article we introduce the concept of a $C^*$-algebraic drawing of a dendroidal set. It depicts a dendroidal set as an object in the category of presheaves on $C^*$-algebras. We show that the construction is functorial and, in fact, it is the left adjoint of a Quillen adjunction between combinatorial model categories. We use this construction to produce a bridge between the two prominent paradigms of noncommutative geometry via adjunctions of presentable $\\infty$-categories, which is t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05799","kind":"arxiv","version":4},"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":"2026-05-17T23:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lbccCMV7wAU6v1cj+ioOnPMgWkwqnGNuUvVLEbJNBfrhNvGGWdnK2TeAk3SSZcrwBdImk/Ls3KB76u9gOWHzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T16:46:07.474261Z"},"content_sha256":"402806813203226e38138079cca6019abd153fe69bb7c2abb689780126c4f52b","schema_version":"1.0","event_id":"sha256:402806813203226e38138079cca6019abd153fe69bb7c2abb689780126c4f52b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6EYZF2PNUCSGQHMQLDPRGQ6GX/bundle.json","state_url":"https://pith.science/pith/H6EYZF2PNUCSGQHMQLDPRGQ6GX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6EYZF2PNUCSGQHMQLDPRGQ6GX/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":"2026-07-03T16:46:07Z","links":{"resolver":"https://pith.science/pith/H6EYZF2PNUCSGQHMQLDPRGQ6GX","bundle":"https://pith.science/pith/H6EYZF2PNUCSGQHMQLDPRGQ6GX/bundle.json","state":"https://pith.science/pith/H6EYZF2PNUCSGQHMQLDPRGQ6GX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6EYZF2PNUCSGQHMQLDPRGQ6GX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:H6EYZF2PNUCSGQHMQLDPRGQ6GX","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":"bdace4e33647202a39c23cd5aee6f9c5090add608ce3ba99360b9b6bdf2e338a","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-23T13:35:12Z","title_canon_sha256":"a3dcf3db1629b22a193242e233eb21c377edd88e6f9be549b70b79e2cf385de9"},"schema_version":"1.0","source":{"id":"1501.05799","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05799","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05799v4","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05799","created_at":"2026-05-17T23:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"H6EYZF2PNUCS","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H6EYZF2PNUCSGQHM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H6EYZF2P","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:402806813203226e38138079cca6019abd153fe69bb7c2abb689780126c4f52b","target":"graph","created_at":"2026-05-17T23:45:00Z","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":"In recent years the theory of dendroidal sets has emerged as an important framework for higher algebra. In this article we introduce the concept of a $C^*$-algebraic drawing of a dendroidal set. It depicts a dendroidal set as an object in the category of presheaves on $C^*$-algebras. We show that the construction is functorial and, in fact, it is the left adjoint of a Quillen adjunction between combinatorial model categories. We use this construction to produce a bridge between the two prominent paradigms of noncommutative geometry via adjunctions of presentable $\\infty$-categories, which is t","authors_text":"Snigdhayan Mahanta","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-23T13:35:12Z","title":"$C^*$-algebraic drawings of dendroidal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05799","kind":"arxiv","version":4},"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:bb8086b5a270ad8429df7e315f1d147e90a7bc619c8fd3025ed3c540a64abd96","target":"record","created_at":"2026-05-17T23:45:00Z","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":"bdace4e33647202a39c23cd5aee6f9c5090add608ce3ba99360b9b6bdf2e338a","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-23T13:35:12Z","title_canon_sha256":"a3dcf3db1629b22a193242e233eb21c377edd88e6f9be549b70b79e2cf385de9"},"schema_version":"1.0","source":{"id":"1501.05799","kind":"arxiv","version":4}},"canonical_sha256":"3f898c974f6d052340ec82c6f89a1e35f03d3c2af6d7a941280f335af96af076","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f898c974f6d052340ec82c6f89a1e35f03d3c2af6d7a941280f335af96af076","first_computed_at":"2026-05-17T23:45:00.546419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:00.546419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yq1kCAT/J4IQJF8ynpcllcF9NsAJv2qihATvjpaqYsuWwENOqUr2AFpOnpZ+la+Fg8lmb7ePWj7jb9SfiCcNDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:00.547044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05799","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb8086b5a270ad8429df7e315f1d147e90a7bc619c8fd3025ed3c540a64abd96","sha256:402806813203226e38138079cca6019abd153fe69bb7c2abb689780126c4f52b"],"state_sha256":"3892d7bbb4de587c7169dddfbf9b12995809990f5c49099c44c054239a9af660"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sd3Q73xzP6UKCL8PuXnBKaoOMK5TczUcWrj3FaAtjYIhUjqNvZRbz4YQEkb6oh3kFsE/1ow1i/WdSNY84WFDBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T16:46:07.476214Z","bundle_sha256":"27fd58e50319ae87e1200e937ba8e18c6c6a1b00f7a6e44e71bc616f7c1ba55f"}}