{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:H5SYVNWZOR2JBPFNLQRM3HKBOK","short_pith_number":"pith:H5SYVNWZ","canonical_record":{"source":{"id":"1510.03261","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-12T12:56:42Z","cross_cats_sorted":["math-ph","math.AT","math.MP","math.QA"],"title_canon_sha256":"54740c865e0a5b66f130a183acf63763247decc276f4c55c7931ecd3a4d726e6","abstract_canon_sha256":"f8bc72f34abf70fe5f478dc8a2baa3a787eabd63f96010e819d85a0defdb9c75"},"schema_version":"1.0"},"canonical_sha256":"3f658ab6d9747490bcad5c22cd9d41728ea2e01807293582077485ae7093894f","source":{"kind":"arxiv","id":"1510.03261","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03261","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03261v2","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03261","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"pith_short_12","alias_value":"H5SYVNWZOR2J","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H5SYVNWZOR2JBPFN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H5SYVNWZ","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:H5SYVNWZOR2JBPFNLQRM3HKBOK","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03261","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-12T12:56:42Z","cross_cats_sorted":["math-ph","math.AT","math.MP","math.QA"],"title_canon_sha256":"54740c865e0a5b66f130a183acf63763247decc276f4c55c7931ecd3a4d726e6","abstract_canon_sha256":"f8bc72f34abf70fe5f478dc8a2baa3a787eabd63f96010e819d85a0defdb9c75"},"schema_version":"1.0"},"canonical_sha256":"3f658ab6d9747490bcad5c22cd9d41728ea2e01807293582077485ae7093894f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:11.503181Z","signature_b64":"3VDcEe/F+SUEytb4ILUuYSlZcclKPu6IOSacbJi+E6lrWUrK7XzB7CYqIjOw1Lg4uE75LAdQTIL3thPsvFTQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f658ab6d9747490bcad5c22cd9d41728ea2e01807293582077485ae7093894f","last_reissued_at":"2026-05-17T23:46:11.502758Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:11.502758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03261","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vNjHnZeYpldD1Go37WdRnzWP877BWKYoaSFcqGhl0MNjO0nuJT5l/W0Q6FnXeIrcR8vnP5hLmsNfl3KMFWCvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:45:56.811406Z"},"content_sha256":"b37c4bf4ddf9bf74c0fbc8126a4bc8f834b7530a159e54af20a813f6cf731af9","schema_version":"1.0","event_id":"sha256:b37c4bf4ddf9bf74c0fbc8126a4bc8f834b7530a159e54af20a813f6cf731af9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:H5SYVNWZOR2JBPFNLQRM3HKBOK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toric varieties of Loday's associahedra and noncommutative cohomological field theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AT","math.MP","math.QA"],"primary_cat":"math.AG","authors_text":"Bruno Vallette, Sergey Shadrin, Vladimir Dotsenko","submitted_at":"2015-10-12T12:56:42Z","abstract_excerpt":"We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2-disks, framed little 2-disks, and Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points. These operads exhibit all the remarkable algebraic and geometric features that their classical analogues possess; in particular, it is possible to define a noncommutative analogue of the notion of cohomological field theory with similar Givental-type symmetries. This relies on rich geometry of the analogues of the Deligne-Mumford spaces, co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03261","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ZD6evlcCH5tzG0uoqkSr7JybHBPd4K7WFG/yFgzqfYKbcaPmFUs7mEMewDNLcbeIDf/9z4lY7fAbuUYMV6iCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:45:56.812082Z"},"content_sha256":"c99355950a3ecdbc20ba93ac5ddf7b2a82e7b6e7eacac6667cda67589add97da","schema_version":"1.0","event_id":"sha256:c99355950a3ecdbc20ba93ac5ddf7b2a82e7b6e7eacac6667cda67589add97da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5SYVNWZOR2JBPFNLQRM3HKBOK/bundle.json","state_url":"https://pith.science/pith/H5SYVNWZOR2JBPFNLQRM3HKBOK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5SYVNWZOR2JBPFNLQRM3HKBOK/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":"2026-05-25T20:45:56Z","links":{"resolver":"https://pith.science/pith/H5SYVNWZOR2JBPFNLQRM3HKBOK","bundle":"https://pith.science/pith/H5SYVNWZOR2JBPFNLQRM3HKBOK/bundle.json","state":"https://pith.science/pith/H5SYVNWZOR2JBPFNLQRM3HKBOK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5SYVNWZOR2JBPFNLQRM3HKBOK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:H5SYVNWZOR2JBPFNLQRM3HKBOK","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":"f8bc72f34abf70fe5f478dc8a2baa3a787eabd63f96010e819d85a0defdb9c75","cross_cats_sorted":["math-ph","math.AT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-12T12:56:42Z","title_canon_sha256":"54740c865e0a5b66f130a183acf63763247decc276f4c55c7931ecd3a4d726e6"},"schema_version":"1.0","source":{"id":"1510.03261","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03261","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03261v2","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03261","created_at":"2026-05-17T23:46:11Z"},{"alias_kind":"pith_short_12","alias_value":"H5SYVNWZOR2J","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H5SYVNWZOR2JBPFN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H5SYVNWZ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:c99355950a3ecdbc20ba93ac5ddf7b2a82e7b6e7eacac6667cda67589add97da","target":"graph","created_at":"2026-05-17T23:46:11Z","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":"We introduce and study several new topological operads that should be regarded as nonsymmetric analogues of the operads of little 2-disks, framed little 2-disks, and Deligne-Mumford compactifications of moduli spaces of genus zero curves with marked points. These operads exhibit all the remarkable algebraic and geometric features that their classical analogues possess; in particular, it is possible to define a noncommutative analogue of the notion of cohomological field theory with similar Givental-type symmetries. This relies on rich geometry of the analogues of the Deligne-Mumford spaces, co","authors_text":"Bruno Vallette, Sergey Shadrin, Vladimir Dotsenko","cross_cats":["math-ph","math.AT","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-12T12:56:42Z","title":"Toric varieties of Loday's associahedra and noncommutative cohomological field theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03261","kind":"arxiv","version":2},"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:b37c4bf4ddf9bf74c0fbc8126a4bc8f834b7530a159e54af20a813f6cf731af9","target":"record","created_at":"2026-05-17T23:46:11Z","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":"f8bc72f34abf70fe5f478dc8a2baa3a787eabd63f96010e819d85a0defdb9c75","cross_cats_sorted":["math-ph","math.AT","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-12T12:56:42Z","title_canon_sha256":"54740c865e0a5b66f130a183acf63763247decc276f4c55c7931ecd3a4d726e6"},"schema_version":"1.0","source":{"id":"1510.03261","kind":"arxiv","version":2}},"canonical_sha256":"3f658ab6d9747490bcad5c22cd9d41728ea2e01807293582077485ae7093894f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f658ab6d9747490bcad5c22cd9d41728ea2e01807293582077485ae7093894f","first_computed_at":"2026-05-17T23:46:11.502758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:11.502758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3VDcEe/F+SUEytb4ILUuYSlZcclKPu6IOSacbJi+E6lrWUrK7XzB7CYqIjOw1Lg4uE75LAdQTIL3thPsvFTQBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:11.503181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03261","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b37c4bf4ddf9bf74c0fbc8126a4bc8f834b7530a159e54af20a813f6cf731af9","sha256:c99355950a3ecdbc20ba93ac5ddf7b2a82e7b6e7eacac6667cda67589add97da"],"state_sha256":"2eca76d5891369ba2cb80e4012d51c4f5df70e8d2bc91bcfd340a32f29a79c5c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SCtmAGhAAMu/g6TvwlC8tUr1EnTLla2LfZWHfrIBwY8qJdl4oAxES01p/JEv1haXaSZw1c98VGkw+mMP0fujCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:45:56.815243Z","bundle_sha256":"2f217a83900c603bc030f244f86e663cf09180a43758819d2fc66600ebe98d6a"}}