{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:J27IZH77AKS4YWQAQJ6GXJF3DI","short_pith_number":"pith:J27IZH77","canonical_record":{"source":{"id":"2509.07975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-09-09T17:57:30Z","cross_cats_sorted":["math.RT","math.SG"],"title_canon_sha256":"1652bc32e17a546c7b20815f234d2ffac0716b6595de4543fb72fa3df8452516","abstract_canon_sha256":"3fdc49da4a5d921ade04cb9f7a7c23d211e2ce016f3114f067fd0e784c2db226"},"schema_version":"1.0"},"canonical_sha256":"4ebe8c9fff02a5cc5a00827c6ba4bb1a25647e3dcec57007f3472b8b9661139a","source":{"kind":"arxiv","id":"2509.07975","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07975","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07975v1","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07975","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"J27IZH77AKS4","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"pith_short_16","alias_value":"J27IZH77AKS4YWQA","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"pith_short_8","alias_value":"J27IZH77","created_at":"2026-07-05T12:07:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:J27IZH77AKS4YWQAQJ6GXJF3DI","target":"record","payload":{"canonical_record":{"source":{"id":"2509.07975","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-09-09T17:57:30Z","cross_cats_sorted":["math.RT","math.SG"],"title_canon_sha256":"1652bc32e17a546c7b20815f234d2ffac0716b6595de4543fb72fa3df8452516","abstract_canon_sha256":"3fdc49da4a5d921ade04cb9f7a7c23d211e2ce016f3114f067fd0e784c2db226"},"schema_version":"1.0"},"canonical_sha256":"4ebe8c9fff02a5cc5a00827c6ba4bb1a25647e3dcec57007f3472b8b9661139a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:43.689950Z","signature_b64":"Gz1aYNgwRI5B7R1Cm/TJ0Xe+ROx8fGn0PfRX6+K5aog6JIzp3vDOY4EMBM/GEJYPUQ8Q+iyjC6ZalBFcuaLjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ebe8c9fff02a5cc5a00827c6ba4bb1a25647e3dcec57007f3472b8b9661139a","last_reissued_at":"2026-07-05T12:07:43.689479Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:43.689479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.07975","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzHQO6VsRVZ5oBSTxOJ5WqC28OkhyBq+IUbzvRfkfWKXFNmjCPUsPngAc9U2GyoVvRdLpujW+LZUld263kIZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:30:39.736367Z"},"content_sha256":"a44990387dad5d6ae74b5b7ac71c3ac63510db3dc03a98a669091f25443b130d","schema_version":"1.0","event_id":"sha256:a44990387dad5d6ae74b5b7ac71c3ac63510db3dc03a98a669091f25443b130d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:J27IZH77AKS4YWQAQJ6GXJF3DI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quartic BV structures in supercategories and modified necklace Lie bialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SG"],"primary_cat":"math.QA","authors_text":"Nikolai Perry","submitted_at":"2025-09-09T17:57:30Z","abstract_excerpt":"We introduce a modified version of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. This structure is then related to canonical quartic Poisson/Batalin-Vilkovisky structures on suitable representation varieties of the quiver. Constructions on the representation side take place in symmetric monoidal $\\Pi$-categories, which prompts a discussion of graded differential operators on commutative monoids in any such category. The generality of the categorical approach allows us to fully recover necklace st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07975","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/2509.07975/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:07:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SoLTUm0Cjltab14KPWBfnaWxYAweuvT4M6D+3aJqJ0S0i5ThFfz3FAwN6lkAsiYHGvdWXPzjSCSutudKxFQnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:30:39.736874Z"},"content_sha256":"155f7839d0496e1c4d3e69681f1e27451eb0678df449c4dbf31990b43f9ad17f","schema_version":"1.0","event_id":"sha256:155f7839d0496e1c4d3e69681f1e27451eb0678df449c4dbf31990b43f9ad17f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J27IZH77AKS4YWQAQJ6GXJF3DI/bundle.json","state_url":"https://pith.science/pith/J27IZH77AKS4YWQAQJ6GXJF3DI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J27IZH77AKS4YWQAQJ6GXJF3DI/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":"2026-08-09T06:30:39Z","links":{"resolver":"https://pith.science/pith/J27IZH77AKS4YWQAQJ6GXJF3DI","bundle":"https://pith.science/pith/J27IZH77AKS4YWQAQJ6GXJF3DI/bundle.json","state":"https://pith.science/pith/J27IZH77AKS4YWQAQJ6GXJF3DI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J27IZH77AKS4YWQAQJ6GXJF3DI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:J27IZH77AKS4YWQAQJ6GXJF3DI","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":"3fdc49da4a5d921ade04cb9f7a7c23d211e2ce016f3114f067fd0e784c2db226","cross_cats_sorted":["math.RT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-09-09T17:57:30Z","title_canon_sha256":"1652bc32e17a546c7b20815f234d2ffac0716b6595de4543fb72fa3df8452516"},"schema_version":"1.0","source":{"id":"2509.07975","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07975","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07975v1","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07975","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"pith_short_12","alias_value":"J27IZH77AKS4","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"pith_short_16","alias_value":"J27IZH77AKS4YWQA","created_at":"2026-07-05T12:07:43Z"},{"alias_kind":"pith_short_8","alias_value":"J27IZH77","created_at":"2026-07-05T12:07:43Z"}],"graph_snapshots":[{"event_id":"sha256:155f7839d0496e1c4d3e69681f1e27451eb0678df449c4dbf31990b43f9ad17f","target":"graph","created_at":"2026-07-05T12:07:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.07975/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a modified version of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. This structure is then related to canonical quartic Poisson/Batalin-Vilkovisky structures on suitable representation varieties of the quiver. Constructions on the representation side take place in symmetric monoidal $\\Pi$-categories, which prompts a discussion of graded differential operators on commutative monoids in any such category. The generality of the categorical approach allows us to fully recover necklace st","authors_text":"Nikolai Perry","cross_cats":["math.RT","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-09-09T17:57:30Z","title":"Quartic BV structures in supercategories and modified necklace Lie bialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07975","kind":"arxiv","version":1},"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:a44990387dad5d6ae74b5b7ac71c3ac63510db3dc03a98a669091f25443b130d","target":"record","created_at":"2026-07-05T12:07:43Z","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":"3fdc49da4a5d921ade04cb9f7a7c23d211e2ce016f3114f067fd0e784c2db226","cross_cats_sorted":["math.RT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-09-09T17:57:30Z","title_canon_sha256":"1652bc32e17a546c7b20815f234d2ffac0716b6595de4543fb72fa3df8452516"},"schema_version":"1.0","source":{"id":"2509.07975","kind":"arxiv","version":1}},"canonical_sha256":"4ebe8c9fff02a5cc5a00827c6ba4bb1a25647e3dcec57007f3472b8b9661139a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ebe8c9fff02a5cc5a00827c6ba4bb1a25647e3dcec57007f3472b8b9661139a","first_computed_at":"2026-07-05T12:07:43.689479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:43.689479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gz1aYNgwRI5B7R1Cm/TJ0Xe+ROx8fGn0PfRX6+K5aog6JIzp3vDOY4EMBM/GEJYPUQ8Q+iyjC6ZalBFcuaLjDw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:43.689950Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.07975","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a44990387dad5d6ae74b5b7ac71c3ac63510db3dc03a98a669091f25443b130d","sha256:155f7839d0496e1c4d3e69681f1e27451eb0678df449c4dbf31990b43f9ad17f"],"state_sha256":"131c79fb181bf3fac4957596906bc46c89b279549158066e9dfbb0601f5c0b76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d4Q+59YoE3niGGjBUI47zMX4GiwrzgAunRM3xjEK+Ak/tHwlZtacO8Mpm/VPzM3koWxy/jkPxIhNjEwtvr6SDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:30:39.741862Z","bundle_sha256":"eb33831e9da890501bb4d6856c50a8a14cd83ff6f2896eefe031b3c70ef4f423"}}