{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GJMOJKLHSEJWJUIYJXIAAA5QFJ","short_pith_number":"pith:GJMOJKLH","canonical_record":{"source":{"id":"2605.27305","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-26T17:14:29Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.QA"],"title_canon_sha256":"526a7d5608465b3c66d457e21be6f3d4d50dc18c0d09cc89dad274c843eb2c3d","abstract_canon_sha256":"6b95dfb85a0f2343c8f5f18a8e1f038e0593b1255b7c60843a837d6f3f204bf1"},"schema_version":"1.0"},"canonical_sha256":"3258e4a967911364d1184dd00003b02a44e7cb3e61f6359a7c43f73922880af0","source":{"kind":"arxiv","id":"2605.27305","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27305","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27305v1","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27305","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"GJMOJKLHSEJW","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_16","alias_value":"GJMOJKLHSEJWJUIY","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_8","alias_value":"GJMOJKLH","created_at":"2026-05-27T02:06:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GJMOJKLHSEJWJUIYJXIAAA5QFJ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.27305","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-26T17:14:29Z","cross_cats_sorted":["math-ph","math.CO","math.MP","math.QA"],"title_canon_sha256":"526a7d5608465b3c66d457e21be6f3d4d50dc18c0d09cc89dad274c843eb2c3d","abstract_canon_sha256":"6b95dfb85a0f2343c8f5f18a8e1f038e0593b1255b7c60843a837d6f3f204bf1"},"schema_version":"1.0"},"canonical_sha256":"3258e4a967911364d1184dd00003b02a44e7cb3e61f6359a7c43f73922880af0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:06:17.294069Z","signature_b64":"glwspN2lMHvYhF1z7suYz1MXOOizDeRpp++q+9ONTeUuwqPyI0kneeO00HFVaOF4mMmAJt1D3m+yNVowONLwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3258e4a967911364d1184dd00003b02a44e7cb3e61f6359a7c43f73922880af0","last_reissued_at":"2026-05-27T02:06:17.293225Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:06:17.293225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.27305","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":"2026-05-27T02:06:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YOZn8Kl+x/eEzkhVFtHmh6cemHayuYYUhHNLvmr3Gl0pCNq2n6dH44WwhueLqdQE914ZZ3m1ab0WHzsgMmBADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T17:49:08.368019Z"},"content_sha256":"ed79196fe1599c3a3c778609b399a8e234f9460b8bac7b4233d0d45e12eead0f","schema_version":"1.0","event_id":"sha256:ed79196fe1599c3a3c778609b399a8e234f9460b8bac7b4233d0d45e12eead0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GJMOJKLHSEJWJUIYJXIAAA5QFJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit class of finite-dimensional polynomial algebras with Wronskians over $\\mathbb{R}^d$ as $N$-ary Lie brackets: beyond $\\mathfrak{sl}(2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.QA"],"primary_cat":"math.RA","authors_text":"Arthemy V. Kiselev, Markuss G. \\c{K}\\=eni\\c{n}\\v{s}","submitted_at":"2026-05-26T17:14:29Z","abstract_excerpt":"Lie algebra $\\mathfrak{sl}(2)$ can be realised by vector fields on $\\mathbb{R}^1\\ni x$ with polynomial coefficients $1$, $-2x$, $-x^2$; their Wronskian determinants yield the Lie bracket. Likewise, the monomials $1$, $\\ldots$, $x^k/k!$, $\\ldots$, $x^N/N!$ span finite-dimensional strong homotopy (SH) Lie algebras with the Wronskians $\\mathbf{1} \\wedge \\partial_x \\wedge \\ldots \\wedge \\partial_x^{N-1}$ as the $N$-ary brackets. Over dimension $d=2$ with $\\mathbb{R}^2\\ni(x,y)$ and for the generalised complete Wronskian $W^{d=2}_{k=1}=\\mathbf{1}\\wedge \\partial_x \\wedge \\partial_y$ of differential or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27305","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/2605.27305/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":"2026-05-27T02:06:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9CqUfbd2t7gYzo8sOB26tmuXhrr3SVppV4Z088NuROjUtkfUmBLty66+zyJQtkpesChOYJRsucMx/HEtbmrOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T17:49:08.368462Z"},"content_sha256":"01a83efabe7ff473809722f779c2159f4f1df58602cd69e5ec6fcd944660b4a5","schema_version":"1.0","event_id":"sha256:01a83efabe7ff473809722f779c2159f4f1df58602cd69e5ec6fcd944660b4a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJMOJKLHSEJWJUIYJXIAAA5QFJ/bundle.json","state_url":"https://pith.science/pith/GJMOJKLHSEJWJUIYJXIAAA5QFJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJMOJKLHSEJWJUIYJXIAAA5QFJ/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":"2026-07-03T17:49:08Z","links":{"resolver":"https://pith.science/pith/GJMOJKLHSEJWJUIYJXIAAA5QFJ","bundle":"https://pith.science/pith/GJMOJKLHSEJWJUIYJXIAAA5QFJ/bundle.json","state":"https://pith.science/pith/GJMOJKLHSEJWJUIYJXIAAA5QFJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJMOJKLHSEJWJUIYJXIAAA5QFJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GJMOJKLHSEJWJUIYJXIAAA5QFJ","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":"6b95dfb85a0f2343c8f5f18a8e1f038e0593b1255b7c60843a837d6f3f204bf1","cross_cats_sorted":["math-ph","math.CO","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-26T17:14:29Z","title_canon_sha256":"526a7d5608465b3c66d457e21be6f3d4d50dc18c0d09cc89dad274c843eb2c3d"},"schema_version":"1.0","source":{"id":"2605.27305","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27305","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27305v1","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27305","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_12","alias_value":"GJMOJKLHSEJW","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_16","alias_value":"GJMOJKLHSEJWJUIY","created_at":"2026-05-27T02:06:17Z"},{"alias_kind":"pith_short_8","alias_value":"GJMOJKLH","created_at":"2026-05-27T02:06:17Z"}],"graph_snapshots":[{"event_id":"sha256:01a83efabe7ff473809722f779c2159f4f1df58602cd69e5ec6fcd944660b4a5","target":"graph","created_at":"2026-05-27T02:06:17Z","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/2605.27305/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Lie algebra $\\mathfrak{sl}(2)$ can be realised by vector fields on $\\mathbb{R}^1\\ni x$ with polynomial coefficients $1$, $-2x$, $-x^2$; their Wronskian determinants yield the Lie bracket. Likewise, the monomials $1$, $\\ldots$, $x^k/k!$, $\\ldots$, $x^N/N!$ span finite-dimensional strong homotopy (SH) Lie algebras with the Wronskians $\\mathbf{1} \\wedge \\partial_x \\wedge \\ldots \\wedge \\partial_x^{N-1}$ as the $N$-ary brackets. Over dimension $d=2$ with $\\mathbb{R}^2\\ni(x,y)$ and for the generalised complete Wronskian $W^{d=2}_{k=1}=\\mathbf{1}\\wedge \\partial_x \\wedge \\partial_y$ of differential or","authors_text":"Arthemy V. Kiselev, Markuss G. \\c{K}\\=eni\\c{n}\\v{s}","cross_cats":["math-ph","math.CO","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-26T17:14:29Z","title":"Explicit class of finite-dimensional polynomial algebras with Wronskians over $\\mathbb{R}^d$ as $N$-ary Lie brackets: beyond $\\mathfrak{sl}(2)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27305","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:ed79196fe1599c3a3c778609b399a8e234f9460b8bac7b4233d0d45e12eead0f","target":"record","created_at":"2026-05-27T02:06:17Z","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":"6b95dfb85a0f2343c8f5f18a8e1f038e0593b1255b7c60843a837d6f3f204bf1","cross_cats_sorted":["math-ph","math.CO","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-26T17:14:29Z","title_canon_sha256":"526a7d5608465b3c66d457e21be6f3d4d50dc18c0d09cc89dad274c843eb2c3d"},"schema_version":"1.0","source":{"id":"2605.27305","kind":"arxiv","version":1}},"canonical_sha256":"3258e4a967911364d1184dd00003b02a44e7cb3e61f6359a7c43f73922880af0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3258e4a967911364d1184dd00003b02a44e7cb3e61f6359a7c43f73922880af0","first_computed_at":"2026-05-27T02:06:17.293225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:06:17.293225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"glwspN2lMHvYhF1z7suYz1MXOOizDeRpp++q+9ONTeUuwqPyI0kneeO00HFVaOF4mMmAJt1D3m+yNVowONLwAA==","signature_status":"signed_v1","signed_at":"2026-05-27T02:06:17.294069Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27305","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed79196fe1599c3a3c778609b399a8e234f9460b8bac7b4233d0d45e12eead0f","sha256:01a83efabe7ff473809722f779c2159f4f1df58602cd69e5ec6fcd944660b4a5"],"state_sha256":"47efde26facecac95bd4a56ad9d24e70f10093d5dac2932290e81ae676be86ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XLMjkc/6LpLuc7AKF4EtcX4Ac/DvM0Geeb+K+oW2ypv0l/3u4BRDwQ9m9/tfVLGYNsHtPYQfwFYYEUYyGDABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T17:49:08.370570Z","bundle_sha256":"17275419f683f7f102657bf1f261e917a8f3d7fabf4b1d664cf1820017a87aad"}}