{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YXG6F3XVHB7PPR2GUHRCQZDPJ4","short_pith_number":"pith:YXG6F3XV","canonical_record":{"source":{"id":"1512.00183","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-01T09:15:20Z","cross_cats_sorted":[],"title_canon_sha256":"b614db009f05bcf22960ca9fd93d66cb51b155adccc952d7b5b8d5aa0aaa6894","abstract_canon_sha256":"fcbb040d87a1868a0783f774d06b9d63a98e046445f49b0ee8187bf619f65dcd"},"schema_version":"1.0"},"canonical_sha256":"c5cde2eef5387ef7c746a1e228646f4f2582da232fed4025162a7686e0ce60c1","source":{"kind":"arxiv","id":"1512.00183","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00183","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00183v3","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00183","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"YXG6F3XVHB7P","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YXG6F3XVHB7PPR2G","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YXG6F3XV","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YXG6F3XVHB7PPR2GUHRCQZDPJ4","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00183","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-01T09:15:20Z","cross_cats_sorted":[],"title_canon_sha256":"b614db009f05bcf22960ca9fd93d66cb51b155adccc952d7b5b8d5aa0aaa6894","abstract_canon_sha256":"fcbb040d87a1868a0783f774d06b9d63a98e046445f49b0ee8187bf619f65dcd"},"schema_version":"1.0"},"canonical_sha256":"c5cde2eef5387ef7c746a1e228646f4f2582da232fed4025162a7686e0ce60c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:07.856861Z","signature_b64":"gs9mYrxhPgs4FO9dN4jtiCjFks467eU+IjazjCgEFXswVrgw8v0q2DQgBOCJReHrUJmDNH8i4PhQmJQD7QO0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5cde2eef5387ef7c746a1e228646f4f2582da232fed4025162a7686e0ce60c1","last_reissued_at":"2026-05-18T00:42:07.856373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:07.856373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00183","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h0S0bXpKJt+pt0AOBQpTrGXgc3B2SRyz/cdfaI5mQMbHtXwZbIuCiMrRiM+z6RHDI/dO7ihcuTex7C7OuqbpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:58:26.531531Z"},"content_sha256":"25873134a6f1d818a93e8e0c0578e1ed48f18ff39df63c2e05f6540144d84524","schema_version":"1.0","event_id":"sha256:25873134a6f1d818a93e8e0c0578e1ed48f18ff39df63c2e05f6540144d84524"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YXG6F3XVHB7PPR2GUHRCQZDPJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Koszul Calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Andrea Solotar, Roland Berger, Thierry Lambre","submitted_at":"2015-12-01T09:15:20Z","abstract_excerpt":"We present a new calculus which is well-adapted to quadratic algebras. This calculus consists in Koszul (co)homology, together with Koszul cup and cap products. Some applications are given. Koszul duality for Koszul (co)homology is proved for any quadratic algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00183","kind":"arxiv","version":3},"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":"2026-05-18T00:42:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dQ+udfLdY5idloAZv5isTIdR7ya9JYFy6fn5bG+BE9Tcd4JkuBlXGbcYiWq9AhoOfXt5YzecNXvPqmtV1BijAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T14:58:26.531847Z"},"content_sha256":"404e9e09922235cbc066d5e46002228ef62d6a08ea42e1cea983b47667e6b34a","schema_version":"1.0","event_id":"sha256:404e9e09922235cbc066d5e46002228ef62d6a08ea42e1cea983b47667e6b34a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXG6F3XVHB7PPR2GUHRCQZDPJ4/bundle.json","state_url":"https://pith.science/pith/YXG6F3XVHB7PPR2GUHRCQZDPJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXG6F3XVHB7PPR2GUHRCQZDPJ4/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":"2026-06-08T14:58:26Z","links":{"resolver":"https://pith.science/pith/YXG6F3XVHB7PPR2GUHRCQZDPJ4","bundle":"https://pith.science/pith/YXG6F3XVHB7PPR2GUHRCQZDPJ4/bundle.json","state":"https://pith.science/pith/YXG6F3XVHB7PPR2GUHRCQZDPJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXG6F3XVHB7PPR2GUHRCQZDPJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YXG6F3XVHB7PPR2GUHRCQZDPJ4","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":"fcbb040d87a1868a0783f774d06b9d63a98e046445f49b0ee8187bf619f65dcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-01T09:15:20Z","title_canon_sha256":"b614db009f05bcf22960ca9fd93d66cb51b155adccc952d7b5b8d5aa0aaa6894"},"schema_version":"1.0","source":{"id":"1512.00183","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00183","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00183v3","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00183","created_at":"2026-05-18T00:42:07Z"},{"alias_kind":"pith_short_12","alias_value":"YXG6F3XVHB7P","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YXG6F3XVHB7PPR2G","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YXG6F3XV","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:404e9e09922235cbc066d5e46002228ef62d6a08ea42e1cea983b47667e6b34a","target":"graph","created_at":"2026-05-18T00:42:07Z","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 present a new calculus which is well-adapted to quadratic algebras. This calculus consists in Koszul (co)homology, together with Koszul cup and cap products. Some applications are given. Koszul duality for Koszul (co)homology is proved for any quadratic algebra.","authors_text":"Andrea Solotar, Roland Berger, Thierry Lambre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-01T09:15:20Z","title":"Koszul Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00183","kind":"arxiv","version":3},"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":"sha256:25873134a6f1d818a93e8e0c0578e1ed48f18ff39df63c2e05f6540144d84524","target":"record","created_at":"2026-05-18T00:42:07Z","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":"fcbb040d87a1868a0783f774d06b9d63a98e046445f49b0ee8187bf619f65dcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-01T09:15:20Z","title_canon_sha256":"b614db009f05bcf22960ca9fd93d66cb51b155adccc952d7b5b8d5aa0aaa6894"},"schema_version":"1.0","source":{"id":"1512.00183","kind":"arxiv","version":3}},"canonical_sha256":"c5cde2eef5387ef7c746a1e228646f4f2582da232fed4025162a7686e0ce60c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5cde2eef5387ef7c746a1e228646f4f2582da232fed4025162a7686e0ce60c1","first_computed_at":"2026-05-18T00:42:07.856373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:07.856373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gs9mYrxhPgs4FO9dN4jtiCjFks467eU+IjazjCgEFXswVrgw8v0q2DQgBOCJReHrUJmDNH8i4PhQmJQD7QO0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:07.856861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00183","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25873134a6f1d818a93e8e0c0578e1ed48f18ff39df63c2e05f6540144d84524","sha256:404e9e09922235cbc066d5e46002228ef62d6a08ea42e1cea983b47667e6b34a"],"state_sha256":"377ac64440454378bb597f09d62b95a8e299c68470440d8b83fc8603b56b0cce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMZ5b5wCBfemFEYz56yzc/tS6C2AioSSKyY1/VCIhB7+n0yJoSbm6j6WzgPdXC1zjzSMLy67H2QV5I9wGCtqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T14:58:26.533570Z","bundle_sha256":"bfe644c9eb7cc2647b8ccc491d1f82376644b08ff3254b0dcb3248b3b1788c2c"}}