{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2LS33LVKYMWUUSFYP4YPYESHXA","short_pith_number":"pith:2LS33LVK","canonical_record":{"source":{"id":"1509.06860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-23T06:55:57Z","cross_cats_sorted":[],"title_canon_sha256":"893080491e8d7b421ec4f5b2e9c2556a47a129f869b1888351ab3c8f4c478630","abstract_canon_sha256":"bc4cfa19916aaeaf7dd40e1b64893634c4728901e452ffd7d8e6b580e52428e9"},"schema_version":"1.0"},"canonical_sha256":"d2e5bdaeaac32d4a48b87f30fc1247b80755be64c50cc3a9b86c87e1e26f5a1e","source":{"kind":"arxiv","id":"1509.06860","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06860","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06860v1","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06860","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"2LS33LVKYMWU","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2LS33LVKYMWUUSFY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2LS33LVK","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2LS33LVKYMWUUSFYP4YPYESHXA","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06860","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-23T06:55:57Z","cross_cats_sorted":[],"title_canon_sha256":"893080491e8d7b421ec4f5b2e9c2556a47a129f869b1888351ab3c8f4c478630","abstract_canon_sha256":"bc4cfa19916aaeaf7dd40e1b64893634c4728901e452ffd7d8e6b580e52428e9"},"schema_version":"1.0"},"canonical_sha256":"d2e5bdaeaac32d4a48b87f30fc1247b80755be64c50cc3a9b86c87e1e26f5a1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.449946Z","signature_b64":"V/N9SxE0wdVk77a10YQpgUD2US8dMT0sJ1wCNnE9BBoVOnLaXVCx2L2iFjuiBi9kx3z3nnEZsi5IE9BOCM73Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2e5bdaeaac32d4a48b87f30fc1247b80755be64c50cc3a9b86c87e1e26f5a1e","last_reissued_at":"2026-05-18T00:02:02.449487Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.449487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06860","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":"2026-05-18T00:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GJXukxaTyGM23IN3EBIIRrnhE35XeEfo7vAwFiByT3AJmHNw/RtS4IlD5iKuXN1LsTOBlMrMbho0jhrRx5+8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:03:38.179724Z"},"content_sha256":"1b247cbd84f8341d1d060ce123fc1cb31c5a26b45ffa3210b0f9b34985951eab","schema_version":"1.0","event_id":"sha256:1b247cbd84f8341d1d060ce123fc1cb31c5a26b45ffa3210b0f9b34985951eab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2LS33LVKYMWUUSFYP4YPYESHXA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groebner-Shirshov bases for pre-associative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Pavel Kolesnikov","submitted_at":"2015-09-23T06:55:57Z","abstract_excerpt":"We develop Groebner---Shirshov bases technique for pre-associative algebras also known as dendriform (di-)algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06860","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":""},"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":"2026-05-18T00:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aG9JybWbn1Al7WCG/ADEhZ3Sn7rmzMvxmhdY6Uou4DkEbjvED/r/033glF5RhGrITJoSQ25Lumj2V9ReeKIYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:03:38.180069Z"},"content_sha256":"64d8abe19108b214100a4bf9eed3c03d03daa27fa79262e8bc0c42f392437061","schema_version":"1.0","event_id":"sha256:64d8abe19108b214100a4bf9eed3c03d03daa27fa79262e8bc0c42f392437061"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LS33LVKYMWUUSFYP4YPYESHXA/bundle.json","state_url":"https://pith.science/pith/2LS33LVKYMWUUSFYP4YPYESHXA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LS33LVKYMWUUSFYP4YPYESHXA/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":"2026-06-10T19:03:38Z","links":{"resolver":"https://pith.science/pith/2LS33LVKYMWUUSFYP4YPYESHXA","bundle":"https://pith.science/pith/2LS33LVKYMWUUSFYP4YPYESHXA/bundle.json","state":"https://pith.science/pith/2LS33LVKYMWUUSFYP4YPYESHXA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LS33LVKYMWUUSFYP4YPYESHXA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2LS33LVKYMWUUSFYP4YPYESHXA","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":"bc4cfa19916aaeaf7dd40e1b64893634c4728901e452ffd7d8e6b580e52428e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-23T06:55:57Z","title_canon_sha256":"893080491e8d7b421ec4f5b2e9c2556a47a129f869b1888351ab3c8f4c478630"},"schema_version":"1.0","source":{"id":"1509.06860","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06860","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06860v1","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06860","created_at":"2026-05-18T00:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"2LS33LVKYMWU","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2LS33LVKYMWUUSFY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2LS33LVK","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:64d8abe19108b214100a4bf9eed3c03d03daa27fa79262e8bc0c42f392437061","target":"graph","created_at":"2026-05-18T00:02:02Z","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 develop Groebner---Shirshov bases technique for pre-associative algebras also known as dendriform (di-)algebras.","authors_text":"Pavel Kolesnikov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-23T06:55:57Z","title":"Groebner-Shirshov bases for pre-associative algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06860","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":"sha256:1b247cbd84f8341d1d060ce123fc1cb31c5a26b45ffa3210b0f9b34985951eab","target":"record","created_at":"2026-05-18T00:02:02Z","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":"bc4cfa19916aaeaf7dd40e1b64893634c4728901e452ffd7d8e6b580e52428e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-09-23T06:55:57Z","title_canon_sha256":"893080491e8d7b421ec4f5b2e9c2556a47a129f869b1888351ab3c8f4c478630"},"schema_version":"1.0","source":{"id":"1509.06860","kind":"arxiv","version":1}},"canonical_sha256":"d2e5bdaeaac32d4a48b87f30fc1247b80755be64c50cc3a9b86c87e1e26f5a1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2e5bdaeaac32d4a48b87f30fc1247b80755be64c50cc3a9b86c87e1e26f5a1e","first_computed_at":"2026-05-18T00:02:02.449487Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:02.449487Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V/N9SxE0wdVk77a10YQpgUD2US8dMT0sJ1wCNnE9BBoVOnLaXVCx2L2iFjuiBi9kx3z3nnEZsi5IE9BOCM73Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:02.449946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06860","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b247cbd84f8341d1d060ce123fc1cb31c5a26b45ffa3210b0f9b34985951eab","sha256:64d8abe19108b214100a4bf9eed3c03d03daa27fa79262e8bc0c42f392437061"],"state_sha256":"d934ff5da383b1c05c5f66371d0ca683b8120408af9ae83088918d462924aa4c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HzBEWNYCD+egRbksjz1w7fKxQRAyqiiMTG6MojD5RWoxv0gyOHP2v8C8yBe541tBn8D9BxpaZyxdXnEU09m7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T19:03:38.182062Z","bundle_sha256":"7ac3cfb5ab8fee42e41fa601b1f1f025f30428fad62d656a9ce7ec504ae8cf58"}}