{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XHJLFNGSKSVXHXEGK4DFUO72O7","short_pith_number":"pith:XHJLFNGS","canonical_record":{"source":{"id":"1609.03133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-09-11T08:07:43Z","cross_cats_sorted":[],"title_canon_sha256":"008a3bfc28af7c92f63a264ede07866279aec9f4787ff7e6af18cbd0c8a514c2","abstract_canon_sha256":"e744f7757c39a611201e376643cdf7ba9c9d453188ef2f5899896929391aee7c"},"schema_version":"1.0"},"canonical_sha256":"b9d2b2b4d254ab73dc8657065a3bfa77d64da790768ab7db6309f7e6d6b0444d","source":{"kind":"arxiv","id":"1609.03133","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03133","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03133v2","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03133","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"XHJLFNGSKSVX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XHJLFNGSKSVXHXEG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XHJLFNGS","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XHJLFNGSKSVXHXEGK4DFUO72O7","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-09-11T08:07:43Z","cross_cats_sorted":[],"title_canon_sha256":"008a3bfc28af7c92f63a264ede07866279aec9f4787ff7e6af18cbd0c8a514c2","abstract_canon_sha256":"e744f7757c39a611201e376643cdf7ba9c9d453188ef2f5899896929391aee7c"},"schema_version":"1.0"},"canonical_sha256":"b9d2b2b4d254ab73dc8657065a3bfa77d64da790768ab7db6309f7e6d6b0444d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:57.184524Z","signature_b64":"rZcNCoMAfghktHl40gED2ko9u7eWdvrjvo/hbWM4ptTKE9FQxBdwczFiKoq8jRyQY4+mciW92X66ViRwqyQ+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9d2b2b4d254ab73dc8657065a3bfa77d64da790768ab7db6309f7e6d6b0444d","last_reissued_at":"2026-05-18T00:18:57.184073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:57.184073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03133","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zJ+vXvBo6IL2cT8HXVvxPB5+ssGWYQmPpDV/nW0hADc2y8LqNL4qsENnGaMlD6Om/ViY5c+ZP2w8OXxO29CqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:19:46.807752Z"},"content_sha256":"b959f4554ea2f45511cd3671a515fd5fc899c8aaaf417641e063bee959525f3c","schema_version":"1.0","event_id":"sha256:b959f4554ea2f45511cd3671a515fd5fc899c8aaaf417641e063bee959525f3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XHJLFNGSKSVXHXEGK4DFUO72O7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When almost Cohen-Macaulay algebras map into big Cohen-Macaulay modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Rajsekhar Bhattacharyya","submitted_at":"2016-09-11T08:07:43Z","abstract_excerpt":"In this paper, we show that almost Cohen-Macaulay algebras are solid and in this respect, we seek for some special situation when (a) an almost Cohen-Macaulay algebra will be phantom extension and (b) when it maps into a balanced big Cohen-Macaulay module."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03133","kind":"arxiv","version":2},"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":"2026-05-18T00:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"STwu6NjQ+pYa0zyZz+szZ+Ui9lpLE8O5wojZUrsYJ2ATYnOiyedfvVvvwD3N7boF0sAnQ1F4XG0ysPKhraRADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:19:46.808097Z"},"content_sha256":"e3eae661b1efb95ee11b15a81265daea3c89f0d9a4a65b5510a813d9e8c886ad","schema_version":"1.0","event_id":"sha256:e3eae661b1efb95ee11b15a81265daea3c89f0d9a4a65b5510a813d9e8c886ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHJLFNGSKSVXHXEGK4DFUO72O7/bundle.json","state_url":"https://pith.science/pith/XHJLFNGSKSVXHXEGK4DFUO72O7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHJLFNGSKSVXHXEGK4DFUO72O7/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":"2026-06-03T07:19:46Z","links":{"resolver":"https://pith.science/pith/XHJLFNGSKSVXHXEGK4DFUO72O7","bundle":"https://pith.science/pith/XHJLFNGSKSVXHXEGK4DFUO72O7/bundle.json","state":"https://pith.science/pith/XHJLFNGSKSVXHXEGK4DFUO72O7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHJLFNGSKSVXHXEGK4DFUO72O7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XHJLFNGSKSVXHXEGK4DFUO72O7","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":"e744f7757c39a611201e376643cdf7ba9c9d453188ef2f5899896929391aee7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-09-11T08:07:43Z","title_canon_sha256":"008a3bfc28af7c92f63a264ede07866279aec9f4787ff7e6af18cbd0c8a514c2"},"schema_version":"1.0","source":{"id":"1609.03133","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03133","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03133v2","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03133","created_at":"2026-05-18T00:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"XHJLFNGSKSVX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XHJLFNGSKSVXHXEG","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XHJLFNGS","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:e3eae661b1efb95ee11b15a81265daea3c89f0d9a4a65b5510a813d9e8c886ad","target":"graph","created_at":"2026-05-18T00:18:57Z","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":"In this paper, we show that almost Cohen-Macaulay algebras are solid and in this respect, we seek for some special situation when (a) an almost Cohen-Macaulay algebra will be phantom extension and (b) when it maps into a balanced big Cohen-Macaulay module.","authors_text":"Rajsekhar Bhattacharyya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-09-11T08:07:43Z","title":"When almost Cohen-Macaulay algebras map into big Cohen-Macaulay modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03133","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:b959f4554ea2f45511cd3671a515fd5fc899c8aaaf417641e063bee959525f3c","target":"record","created_at":"2026-05-18T00:18:57Z","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":"e744f7757c39a611201e376643cdf7ba9c9d453188ef2f5899896929391aee7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-09-11T08:07:43Z","title_canon_sha256":"008a3bfc28af7c92f63a264ede07866279aec9f4787ff7e6af18cbd0c8a514c2"},"schema_version":"1.0","source":{"id":"1609.03133","kind":"arxiv","version":2}},"canonical_sha256":"b9d2b2b4d254ab73dc8657065a3bfa77d64da790768ab7db6309f7e6d6b0444d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9d2b2b4d254ab73dc8657065a3bfa77d64da790768ab7db6309f7e6d6b0444d","first_computed_at":"2026-05-18T00:18:57.184073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:57.184073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rZcNCoMAfghktHl40gED2ko9u7eWdvrjvo/hbWM4ptTKE9FQxBdwczFiKoq8jRyQY4+mciW92X66ViRwqyQ+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:57.184524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03133","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b959f4554ea2f45511cd3671a515fd5fc899c8aaaf417641e063bee959525f3c","sha256:e3eae661b1efb95ee11b15a81265daea3c89f0d9a4a65b5510a813d9e8c886ad"],"state_sha256":"8db0401c8830165d46ac89392e8d165b1dd0df463cd782fea1f5d8370f86eb0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9PTn1qNTQKzX3d+lmZ7XIxbV9EoWINX7BEJM7EBhFQUt7oYhfi9JWLioLDKyh3kbA5RCIvmOpulZ+NSPd4daDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:19:46.810062Z","bundle_sha256":"e102f3dacada0c37f84d3096818f15d614d9a846d0779c6889806768a6d9b03f"}}