{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:66HJOUHZGCLWR675W5PAXV6NWC","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":"13f1325dd1cdd036d2930a75309c4e9a5a0b51451ce7df6dd0cd1a2229d3d674","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-21T03:13:02Z","title_canon_sha256":"81da051db1830aaa4e1d6b06c3b2ed4c7832dfb6603e5ef245ec2d2885b191b4"},"schema_version":"1.0","source":{"id":"1612.06960","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06960","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06960v2","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06960","created_at":"2026-05-18T00:01:30Z"},{"alias_kind":"pith_short_12","alias_value":"66HJOUHZGCLW","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"66HJOUHZGCLWR675","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"66HJOUHZ","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:db8b092e2cfc66e73e7e5757d7d7ade96c4639fe06729c35862ae845e38b020c","target":"graph","created_at":"2026-05-18T00:01:30Z","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 give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral sequences relating these cohomology theories with the standard ones.","authors_text":"Marcin Chalupnik, Piotr Kowalski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-21T03:13:02Z","title":"Difference modules and difference cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06960","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":"sha256:049d9f08e8567299ed5b7ece014d8addd7fcc8e99a681503dffb24d71557fa6b","target":"record","created_at":"2026-05-18T00:01:30Z","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":"13f1325dd1cdd036d2930a75309c4e9a5a0b51451ce7df6dd0cd1a2229d3d674","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-12-21T03:13:02Z","title_canon_sha256":"81da051db1830aaa4e1d6b06c3b2ed4c7832dfb6603e5ef245ec2d2885b191b4"},"schema_version":"1.0","source":{"id":"1612.06960","kind":"arxiv","version":2}},"canonical_sha256":"f78e9750f9309768fbfdb75e0bd7cdb0b5b31083d1eb165e902ba3729d502c11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f78e9750f9309768fbfdb75e0bd7cdb0b5b31083d1eb165e902ba3729d502c11","first_computed_at":"2026-05-18T00:01:30.673874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:30.673874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4E2yD5tOeaiZ5TedNuUDN+KMS5y9mP2XK9nqLL+aFkC9H1z6DXEyrnSlED4XgTNVt97nooNb/PVED28znZWmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:30.674379Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06960","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:049d9f08e8567299ed5b7ece014d8addd7fcc8e99a681503dffb24d71557fa6b","sha256:db8b092e2cfc66e73e7e5757d7d7ade96c4639fe06729c35862ae845e38b020c"],"state_sha256":"b16a62e19fc7b1431d67b15a98e7177cd6992b44b5935a50cfb355d6a7842c2b"}