{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6EMJ2VHUATF5UNBAE7INMICDVF","short_pith_number":"pith:6EMJ2VHU","canonical_record":{"source":{"id":"1103.3755","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-03-19T06:19:36Z","cross_cats_sorted":[],"title_canon_sha256":"7927ea2590f49497c61ca19129bc4b297f11c27fe4666db94b9b36bf61084a75","abstract_canon_sha256":"1bf0e7fbcdd2e6f9756eaf3aa4c01d57da1a9d6d83c4ecc10bbef12e19eb97a1"},"schema_version":"1.0"},"canonical_sha256":"f1189d54f404cbda342027d0d62043a966a5c12da8c2cc15d3178581051f9857","source":{"kind":"arxiv","id":"1103.3755","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3755","created_at":"2026-05-18T04:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3755v2","created_at":"2026-05-18T04:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3755","created_at":"2026-05-18T04:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"6EMJ2VHUATF5","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6EMJ2VHUATF5UNBA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6EMJ2VHU","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6EMJ2VHUATF5UNBAE7INMICDVF","target":"record","payload":{"canonical_record":{"source":{"id":"1103.3755","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-03-19T06:19:36Z","cross_cats_sorted":[],"title_canon_sha256":"7927ea2590f49497c61ca19129bc4b297f11c27fe4666db94b9b36bf61084a75","abstract_canon_sha256":"1bf0e7fbcdd2e6f9756eaf3aa4c01d57da1a9d6d83c4ecc10bbef12e19eb97a1"},"schema_version":"1.0"},"canonical_sha256":"f1189d54f404cbda342027d0d62043a966a5c12da8c2cc15d3178581051f9857","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:10.878466Z","signature_b64":"Lrlv87+9YEOzAh8kiwV+HvIgdo0QvuBv2HcYCpk0gxBtH+idobvCvZcgyOJ4T5K0vMfZC63x6jzCbz9E63tTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1189d54f404cbda342027d0d62043a966a5c12da8c2cc15d3178581051f9857","last_reissued_at":"2026-05-18T04:22:10.878080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:10.878080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.3755","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":"2026-05-18T04:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7dnY+lZ2o1Gm7rqxPmW1gjN30jv/UHIp3ELq1drBmiii+F1xcVgIWPabTC9LozUg+m7Beg3LGvxPg4rXWxypBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:51:47.090528Z"},"content_sha256":"aa938e33d9b007b04b438a7029b321ff4414df8cc44bec60e63a70c0f2aec625","schema_version":"1.0","event_id":"sha256:aa938e33d9b007b04b438a7029b321ff4414df8cc44bec60e63a70c0f2aec625"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6EMJ2VHUATF5UNBAE7INMICDVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sur une op\\'erade ternaire li\\'ee aux treillis de Tamari","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fr\\'ed\\'eric Chapoton (ICJ)","submitted_at":"2011-03-19T06:19:36Z","abstract_excerpt":"We introduce an anticyclic operad V given by a ternary generator and a quadratic relation. We show that it admits a natural basis indexed by planar binary trees. We then relate this construction to the familly of Tamari lattices (Y_n) for n>=0 by defining an isomorphism between V(2n+1) and the Grothendieck group of the category mod Y_n. This isomorphism maps the basis of V(2n+1) to the classes of projective modules and sends the anticyclic map of the operad V to the Coxeter transformation of the derived category of mod Y_n. One can then use Koszul duality and a Legendre transform to compute th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3755","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":"2026-05-18T04:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EtztYKZgwCj8+rGhs+3FG1DzrTCmPOp56rurYWOcOtv9NU5VRgijOk8jcv8sLEVDS380OPo3y3jutKUk7rZmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:51:47.090874Z"},"content_sha256":"3bee8f32a8b690970c9e469cbc83a88514e5b28eabf7ba748506ec775cea9efc","schema_version":"1.0","event_id":"sha256:3bee8f32a8b690970c9e469cbc83a88514e5b28eabf7ba748506ec775cea9efc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EMJ2VHUATF5UNBAE7INMICDVF/bundle.json","state_url":"https://pith.science/pith/6EMJ2VHUATF5UNBAE7INMICDVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EMJ2VHUATF5UNBAE7INMICDVF/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":"2026-06-24T21:51:47Z","links":{"resolver":"https://pith.science/pith/6EMJ2VHUATF5UNBAE7INMICDVF","bundle":"https://pith.science/pith/6EMJ2VHUATF5UNBAE7INMICDVF/bundle.json","state":"https://pith.science/pith/6EMJ2VHUATF5UNBAE7INMICDVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EMJ2VHUATF5UNBAE7INMICDVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6EMJ2VHUATF5UNBAE7INMICDVF","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":"1bf0e7fbcdd2e6f9756eaf3aa4c01d57da1a9d6d83c4ecc10bbef12e19eb97a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-03-19T06:19:36Z","title_canon_sha256":"7927ea2590f49497c61ca19129bc4b297f11c27fe4666db94b9b36bf61084a75"},"schema_version":"1.0","source":{"id":"1103.3755","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3755","created_at":"2026-05-18T04:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3755v2","created_at":"2026-05-18T04:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3755","created_at":"2026-05-18T04:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"6EMJ2VHUATF5","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6EMJ2VHUATF5UNBA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6EMJ2VHU","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:3bee8f32a8b690970c9e469cbc83a88514e5b28eabf7ba748506ec775cea9efc","target":"graph","created_at":"2026-05-18T04:22:10Z","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 an anticyclic operad V given by a ternary generator and a quadratic relation. We show that it admits a natural basis indexed by planar binary trees. We then relate this construction to the familly of Tamari lattices (Y_n) for n>=0 by defining an isomorphism between V(2n+1) and the Grothendieck group of the category mod Y_n. This isomorphism maps the basis of V(2n+1) to the classes of projective modules and sends the anticyclic map of the operad V to the Coxeter transformation of the derived category of mod Y_n. One can then use Koszul duality and a Legendre transform to compute th","authors_text":"Fr\\'ed\\'eric Chapoton (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-03-19T06:19:36Z","title":"Sur une op\\'erade ternaire li\\'ee aux treillis de Tamari"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3755","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:aa938e33d9b007b04b438a7029b321ff4414df8cc44bec60e63a70c0f2aec625","target":"record","created_at":"2026-05-18T04:22:10Z","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":"1bf0e7fbcdd2e6f9756eaf3aa4c01d57da1a9d6d83c4ecc10bbef12e19eb97a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-03-19T06:19:36Z","title_canon_sha256":"7927ea2590f49497c61ca19129bc4b297f11c27fe4666db94b9b36bf61084a75"},"schema_version":"1.0","source":{"id":"1103.3755","kind":"arxiv","version":2}},"canonical_sha256":"f1189d54f404cbda342027d0d62043a966a5c12da8c2cc15d3178581051f9857","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1189d54f404cbda342027d0d62043a966a5c12da8c2cc15d3178581051f9857","first_computed_at":"2026-05-18T04:22:10.878080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:10.878080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lrlv87+9YEOzAh8kiwV+HvIgdo0QvuBv2HcYCpk0gxBtH+idobvCvZcgyOJ4T5K0vMfZC63x6jzCbz9E63tTAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:10.878466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3755","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa938e33d9b007b04b438a7029b321ff4414df8cc44bec60e63a70c0f2aec625","sha256:3bee8f32a8b690970c9e469cbc83a88514e5b28eabf7ba748506ec775cea9efc"],"state_sha256":"2760b6b5ce919af754d9d28cce203dacc77d67c8ee7c85d68e3b24c2536d2f72"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pulpyrxQ+VtAxxRZcFQWrChLp1RvqXJ2XO/8GZujDHdqSlIW9E6ajr9RIdeiDYNgmSLgLyCBHJcv1T8G4SdPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:51:47.092816Z","bundle_sha256":"3e95b5fd5fc5e4a4cd79594303e380c38060e719d0db583b7647275897865d6c"}}