{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TKS5E5CTX637YQNXI65LGJG4M5","short_pith_number":"pith:TKS5E5CT","canonical_record":{"source":{"id":"1812.00790","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-03T14:46:24Z","cross_cats_sorted":[],"title_canon_sha256":"cc7cac95863ef2dd6ff3f465fd7c50fc61d052713644b584be698ab4f10a5214","abstract_canon_sha256":"04c4bfa4a5f48134553367ce023ca16cdeb153b65dd33a837f03c44c547f59ad"},"schema_version":"1.0"},"canonical_sha256":"9aa5d27453bfb7fc41b747bab324dc67428a4f465551895bc5e15f5d6e8ca614","source":{"kind":"arxiv","id":"1812.00790","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00790","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00790v2","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00790","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"TKS5E5CTX637","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"pith_short_16","alias_value":"TKS5E5CTX637YQNX","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"pith_short_8","alias_value":"TKS5E5CT","created_at":"2026-07-05T00:39:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TKS5E5CTX637YQNXI65LGJG4M5","target":"record","payload":{"canonical_record":{"source":{"id":"1812.00790","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-03T14:46:24Z","cross_cats_sorted":[],"title_canon_sha256":"cc7cac95863ef2dd6ff3f465fd7c50fc61d052713644b584be698ab4f10a5214","abstract_canon_sha256":"04c4bfa4a5f48134553367ce023ca16cdeb153b65dd33a837f03c44c547f59ad"},"schema_version":"1.0"},"canonical_sha256":"9aa5d27453bfb7fc41b747bab324dc67428a4f465551895bc5e15f5d6e8ca614","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:39:53.951791Z","signature_b64":"duU4S3SqeySIU0FldPs3PXaj9DdQd2lozMF4VQj2HfBFHRY82jsnrk+X/WuRuIvVa4MSB/WKPoza22RBPLapBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aa5d27453bfb7fc41b747bab324dc67428a4f465551895bc5e15f5d6e8ca614","last_reissued_at":"2026-07-05T00:39:53.951273Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:39:53.951273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.00790","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":"2026-07-05T00:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhO2cWFetD2batx3HOEf2nmeX810QJuIwwAUiSn9mfd5o1tdZCufURGbq83Ai3bJdodI6CyU2rtS1gRRqssZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:36:33.775907Z"},"content_sha256":"4167c478b9e0e11481e55fb672cb7fde3477dade6f35fafcaf58693d31468c51","schema_version":"1.0","event_id":"sha256:4167c478b9e0e11481e55fb672cb7fde3477dade6f35fafcaf58693d31468c51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TKS5E5CTX637YQNXI65LGJG4M5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing Schur complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Claudiu Raicu, Hang Huang, Jo\\~ao Pedro Santos, Michael K. Brown, Michael Perlman, Robert P. Laudone, Steven V Sam","submitted_at":"2018-12-03T14:46:24Z","abstract_excerpt":"We describe a Macaulay2 package for computing Schur complexes. This package expands on the ChainComplexOperations package by David Eisenbud."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00790","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1812.00790/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1UmD8Q11ihc38k9CVv4TlGTxCjhj4iBt85SrGmRNfJbha5XNPbhuXIqO8dHgzD1K2kPxo8YTHZiPxLifeDReCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T09:36:33.776282Z"},"content_sha256":"460decd721561712a46a7b026470d5baecb6cfcfc9388380894e9b5acb0b0511","schema_version":"1.0","event_id":"sha256:460decd721561712a46a7b026470d5baecb6cfcfc9388380894e9b5acb0b0511"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKS5E5CTX637YQNXI65LGJG4M5/bundle.json","state_url":"https://pith.science/pith/TKS5E5CTX637YQNXI65LGJG4M5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKS5E5CTX637YQNXI65LGJG4M5/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":"2026-07-05T09:36:33Z","links":{"resolver":"https://pith.science/pith/TKS5E5CTX637YQNXI65LGJG4M5","bundle":"https://pith.science/pith/TKS5E5CTX637YQNXI65LGJG4M5/bundle.json","state":"https://pith.science/pith/TKS5E5CTX637YQNXI65LGJG4M5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKS5E5CTX637YQNXI65LGJG4M5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TKS5E5CTX637YQNXI65LGJG4M5","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":"04c4bfa4a5f48134553367ce023ca16cdeb153b65dd33a837f03c44c547f59ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-03T14:46:24Z","title_canon_sha256":"cc7cac95863ef2dd6ff3f465fd7c50fc61d052713644b584be698ab4f10a5214"},"schema_version":"1.0","source":{"id":"1812.00790","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.00790","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1812.00790v2","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00790","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"TKS5E5CTX637","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"pith_short_16","alias_value":"TKS5E5CTX637YQNX","created_at":"2026-07-05T00:39:53Z"},{"alias_kind":"pith_short_8","alias_value":"TKS5E5CT","created_at":"2026-07-05T00:39:53Z"}],"graph_snapshots":[{"event_id":"sha256:460decd721561712a46a7b026470d5baecb6cfcfc9388380894e9b5acb0b0511","target":"graph","created_at":"2026-07-05T00:39:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1812.00790/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe a Macaulay2 package for computing Schur complexes. This package expands on the ChainComplexOperations package by David Eisenbud.","authors_text":"Claudiu Raicu, Hang Huang, Jo\\~ao Pedro Santos, Michael K. Brown, Michael Perlman, Robert P. Laudone, Steven V Sam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-03T14:46:24Z","title":"Computing Schur complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00790","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":"sha256:4167c478b9e0e11481e55fb672cb7fde3477dade6f35fafcaf58693d31468c51","target":"record","created_at":"2026-07-05T00:39:53Z","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":"04c4bfa4a5f48134553367ce023ca16cdeb153b65dd33a837f03c44c547f59ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-03T14:46:24Z","title_canon_sha256":"cc7cac95863ef2dd6ff3f465fd7c50fc61d052713644b584be698ab4f10a5214"},"schema_version":"1.0","source":{"id":"1812.00790","kind":"arxiv","version":2}},"canonical_sha256":"9aa5d27453bfb7fc41b747bab324dc67428a4f465551895bc5e15f5d6e8ca614","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9aa5d27453bfb7fc41b747bab324dc67428a4f465551895bc5e15f5d6e8ca614","first_computed_at":"2026-07-05T00:39:53.951273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:39:53.951273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"duU4S3SqeySIU0FldPs3PXaj9DdQd2lozMF4VQj2HfBFHRY82jsnrk+X/WuRuIvVa4MSB/WKPoza22RBPLapBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:39:53.951791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.00790","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4167c478b9e0e11481e55fb672cb7fde3477dade6f35fafcaf58693d31468c51","sha256:460decd721561712a46a7b026470d5baecb6cfcfc9388380894e9b5acb0b0511"],"state_sha256":"a384987e94460a06a047e65638754c1205a76fd4cb5c6bdebac2309a2d7f0794"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"idi62Khf2KsXE2khxR02knxuqQ/kCKzisUnL/6sfw6yap8dditnmZfD+HT7C7V2vNi038G86L35KFOwGSE5+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T09:36:33.778136Z","bundle_sha256":"6b11e9b5a1ef96d99f7aae9ae6a54b32243dc3cc00e92ba5d02fa5194834d533"}}