{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UTFAFP3PPMUCYI7X7H7ZTGOIL3","short_pith_number":"pith:UTFAFP3P","canonical_record":{"source":{"id":"1512.03570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-11T10:00:49Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"37bf854af6c879c659f036e5445537ba17914c2f5bca5a394f55eb46fc9393b7","abstract_canon_sha256":"db243b2302b0863e09af6642bbba6823dd249033ca1ce76843227c719375b967"},"schema_version":"1.0"},"canonical_sha256":"a4ca02bf6f7b282c23f7f9ff9999c85edd16e79ae747394db0c956d7817456da","source":{"kind":"arxiv","id":"1512.03570","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03570","created_at":"2026-05-18T01:10:07Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03570v1","created_at":"2026-05-18T01:10:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03570","created_at":"2026-05-18T01:10:07Z"},{"alias_kind":"pith_short_12","alias_value":"UTFAFP3PPMUC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UTFAFP3PPMUCYI7X","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UTFAFP3P","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UTFAFP3PPMUCYI7X7H7ZTGOIL3","target":"record","payload":{"canonical_record":{"source":{"id":"1512.03570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-11T10:00:49Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"37bf854af6c879c659f036e5445537ba17914c2f5bca5a394f55eb46fc9393b7","abstract_canon_sha256":"db243b2302b0863e09af6642bbba6823dd249033ca1ce76843227c719375b967"},"schema_version":"1.0"},"canonical_sha256":"a4ca02bf6f7b282c23f7f9ff9999c85edd16e79ae747394db0c956d7817456da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:07.928337Z","signature_b64":"vZ0IGRoayQniFEm9Dh1IrR2XPdu2Be831o3HJsgZl47Yi+3/YoYYRmmYX91uydu1RyYAhR8iqcf8syQJ2gPDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4ca02bf6f7b282c23f7f9ff9999c85edd16e79ae747394db0c956d7817456da","last_reissued_at":"2026-05-18T01:10:07.927613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:07.927613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.03570","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":"2026-05-18T01:10:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CG7DgvPMyrdPP7UX2r1ylW7ilaVsocl3lX/pahBl+dDSNqmkL6k+h5mMHv4uqTxt5oSg4/5eyQnbmIM67UofBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:53:38.313599Z"},"content_sha256":"3abf125dfe7439a45f76db6df983055443ecd6e324d385a2ae1ce623d535dabb","schema_version":"1.0","event_id":"sha256:3abf125dfe7439a45f76db6df983055443ecd6e324d385a2ae1ce623d535dabb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UTFAFP3PPMUCYI7X7H7ZTGOIL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nontriviality results for the characteristic algebra of a DGA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.RA","authors_text":"Georgios Dimitroglou Rizell","submitted_at":"2015-12-11T10:00:49Z","abstract_excerpt":"Assume that we are given a semifree noncommutative differential graded algebra (DGA for short) whose differential respects an action filtration. We show that the canonical unital algebra map from the homology of the DGA to its characteristic algebra, i.e. the quotient of the underlying algebra by the two-sided ideal generated by the boundaries, is a monomorphism. The main tool that we use is the weak division algorithm in free noncommutative algebras due to P. Cohn."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03570","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":"2026-05-18T01:10:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2mBtThlbEaeeMpMyMchg+xLDAPfgQLc0OSwBqkJVZUDDkZKKi8WQqjBnAiN25lMwWkXL7CHlr2GdUOWb42GdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:53:38.313939Z"},"content_sha256":"8337d6960c142711047eecc67b616754a6be25c459d7f63dbbcdf6affde30006","schema_version":"1.0","event_id":"sha256:8337d6960c142711047eecc67b616754a6be25c459d7f63dbbcdf6affde30006"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UTFAFP3PPMUCYI7X7H7ZTGOIL3/bundle.json","state_url":"https://pith.science/pith/UTFAFP3PPMUCYI7X7H7ZTGOIL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UTFAFP3PPMUCYI7X7H7ZTGOIL3/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":"2026-06-11T12:53:38Z","links":{"resolver":"https://pith.science/pith/UTFAFP3PPMUCYI7X7H7ZTGOIL3","bundle":"https://pith.science/pith/UTFAFP3PPMUCYI7X7H7ZTGOIL3/bundle.json","state":"https://pith.science/pith/UTFAFP3PPMUCYI7X7H7ZTGOIL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UTFAFP3PPMUCYI7X7H7ZTGOIL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UTFAFP3PPMUCYI7X7H7ZTGOIL3","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":"db243b2302b0863e09af6642bbba6823dd249033ca1ce76843227c719375b967","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-11T10:00:49Z","title_canon_sha256":"37bf854af6c879c659f036e5445537ba17914c2f5bca5a394f55eb46fc9393b7"},"schema_version":"1.0","source":{"id":"1512.03570","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03570","created_at":"2026-05-18T01:10:07Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03570v1","created_at":"2026-05-18T01:10:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03570","created_at":"2026-05-18T01:10:07Z"},{"alias_kind":"pith_short_12","alias_value":"UTFAFP3PPMUC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UTFAFP3PPMUCYI7X","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UTFAFP3P","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:8337d6960c142711047eecc67b616754a6be25c459d7f63dbbcdf6affde30006","target":"graph","created_at":"2026-05-18T01:10:07Z","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":"Assume that we are given a semifree noncommutative differential graded algebra (DGA for short) whose differential respects an action filtration. We show that the canonical unital algebra map from the homology of the DGA to its characteristic algebra, i.e. the quotient of the underlying algebra by the two-sided ideal generated by the boundaries, is a monomorphism. The main tool that we use is the weak division algorithm in free noncommutative algebras due to P. Cohn.","authors_text":"Georgios Dimitroglou Rizell","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-11T10:00:49Z","title":"Nontriviality results for the characteristic algebra of a DGA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03570","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":"sha256:3abf125dfe7439a45f76db6df983055443ecd6e324d385a2ae1ce623d535dabb","target":"record","created_at":"2026-05-18T01:10:07Z","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":"db243b2302b0863e09af6642bbba6823dd249033ca1ce76843227c719375b967","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-12-11T10:00:49Z","title_canon_sha256":"37bf854af6c879c659f036e5445537ba17914c2f5bca5a394f55eb46fc9393b7"},"schema_version":"1.0","source":{"id":"1512.03570","kind":"arxiv","version":1}},"canonical_sha256":"a4ca02bf6f7b282c23f7f9ff9999c85edd16e79ae747394db0c956d7817456da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4ca02bf6f7b282c23f7f9ff9999c85edd16e79ae747394db0c956d7817456da","first_computed_at":"2026-05-18T01:10:07.927613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:07.927613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vZ0IGRoayQniFEm9Dh1IrR2XPdu2Be831o3HJsgZl47Yi+3/YoYYRmmYX91uydu1RyYAhR8iqcf8syQJ2gPDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:07.928337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03570","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3abf125dfe7439a45f76db6df983055443ecd6e324d385a2ae1ce623d535dabb","sha256:8337d6960c142711047eecc67b616754a6be25c459d7f63dbbcdf6affde30006"],"state_sha256":"d088cf0869234ef814ea2ca41ce33875b8b1c6e887e54bbe4f98e9710a2ae4b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4j2lETRRfAijQBzDXkgzQTfEgSSp2PZ0Mj43yAT+3v8KwzGhrAW8OMfsjdeqIcHGKPN/qmWf+l31Tm8ZBp0Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:53:38.315883Z","bundle_sha256":"367ccc7c5b8aae50e7c51fffcb9dd9fc40d50b95af7a839247f4a4bfc69a4028"}}