{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4VKYDHYPREBRGCH6F457F47N5E","short_pith_number":"pith:4VKYDHYP","canonical_record":{"source":{"id":"2607.07211","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-08T09:50:17Z","cross_cats_sorted":[],"title_canon_sha256":"043a78eced6b26a682fb7ef87c69966d61edc6ec7508bc130b10e6eb4057f34c","abstract_canon_sha256":"e1794464a0ae99b76b2577e08a90d3a22f74ddc3d892f2384729e811e9173607"},"schema_version":"1.0"},"canonical_sha256":"e555819f0f89031308fe2f3bf2f3ede927cc3f1460d29a3d0127f94a33340a4f","source":{"kind":"arxiv","id":"2607.07211","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07211","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07211v1","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07211","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"pith_short_12","alias_value":"4VKYDHYPREBR","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"pith_short_16","alias_value":"4VKYDHYPREBRGCH6","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"pith_short_8","alias_value":"4VKYDHYP","created_at":"2026-07-09T01:20:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4VKYDHYPREBRGCH6F457F47N5E","target":"record","payload":{"canonical_record":{"source":{"id":"2607.07211","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-08T09:50:17Z","cross_cats_sorted":[],"title_canon_sha256":"043a78eced6b26a682fb7ef87c69966d61edc6ec7508bc130b10e6eb4057f34c","abstract_canon_sha256":"e1794464a0ae99b76b2577e08a90d3a22f74ddc3d892f2384729e811e9173607"},"schema_version":"1.0"},"canonical_sha256":"e555819f0f89031308fe2f3bf2f3ede927cc3f1460d29a3d0127f94a33340a4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:17.905798Z","signature_b64":"ZJXP+K/9Y1Bgd35z8+e6GNEDn1JU1+AGNBoPyifZpWfAFmAcUDd5xQXcoQ2nLGgHcFPTNvW2CnD7KjVHkM8qDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e555819f0f89031308fe2f3bf2f3ede927cc3f1460d29a3d0127f94a33340a4f","last_reissued_at":"2026-07-09T01:20:17.905386Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:17.905386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.07211","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":"2026-07-09T01:20:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3hBtXr0gs5xp2WAtXQp+5ZH5rsFGMaoFUKODzQeEuA3ih09Ki9EGQjTywCeFaKysC8Tncja15h/1h3cRMA/XAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:31:10.417299Z"},"content_sha256":"0232b517fdd0ec02c9edd0cb82e7c78cb986c362a9207330a8fa21f0a853e925","schema_version":"1.0","event_id":"sha256:0232b517fdd0ec02c9edd0cb82e7c78cb986c362a9207330a8fa21f0a853e925"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4VKYDHYPREBRGCH6F457F47N5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extriangulated ideal quotients and $d$-Auslander categories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Lior Silberberg","submitted_at":"2026-07-08T09:50:17Z","abstract_excerpt":"Building on recent studies of 0-Auslander categories, we establish a connection between $d$-Auslander extriangulated categories and categories of $(d+2)$-term complexes up to homotopy. We give a precise homological condition under which an algebraic extriangulated category admits an extriangulated ideal quotient equivalent to $\\mathcal{K}^{[-d-1,0]}(\\mathcal{A})$. We then demonstrate that $d$-cluster-tilting subcategories in triangulated categories serve as a key source of $d$-Auslander extriangulated categories. Using these structural results, we answer a question posed by Iyama in the Append"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07211","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.07211/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":"2026-07-09T01:20:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBP2zzXbKCuNKfo5n6XUqxGKsgXrpMzrhcoF5GX7Zr94CHE3Jiysl9gR3vgPOZ+FcOG2myRXFY9TbPNb//i0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:31:10.418230Z"},"content_sha256":"88023f0f68a1b7678f5908a9ba78198e47ea99e03bf85d352ffaebca0b1c1c1b","schema_version":"1.0","event_id":"sha256:88023f0f68a1b7678f5908a9ba78198e47ea99e03bf85d352ffaebca0b1c1c1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VKYDHYPREBRGCH6F457F47N5E/bundle.json","state_url":"https://pith.science/pith/4VKYDHYPREBRGCH6F457F47N5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VKYDHYPREBRGCH6F457F47N5E/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":"2026-08-13T09:31:10Z","links":{"resolver":"https://pith.science/pith/4VKYDHYPREBRGCH6F457F47N5E","bundle":"https://pith.science/pith/4VKYDHYPREBRGCH6F457F47N5E/bundle.json","state":"https://pith.science/pith/4VKYDHYPREBRGCH6F457F47N5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VKYDHYPREBRGCH6F457F47N5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4VKYDHYPREBRGCH6F457F47N5E","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":"e1794464a0ae99b76b2577e08a90d3a22f74ddc3d892f2384729e811e9173607","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-08T09:50:17Z","title_canon_sha256":"043a78eced6b26a682fb7ef87c69966d61edc6ec7508bc130b10e6eb4057f34c"},"schema_version":"1.0","source":{"id":"2607.07211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07211","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07211v1","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07211","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"pith_short_12","alias_value":"4VKYDHYPREBR","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"pith_short_16","alias_value":"4VKYDHYPREBRGCH6","created_at":"2026-07-09T01:20:17Z"},{"alias_kind":"pith_short_8","alias_value":"4VKYDHYP","created_at":"2026-07-09T01:20:17Z"}],"graph_snapshots":[{"event_id":"sha256:88023f0f68a1b7678f5908a9ba78198e47ea99e03bf85d352ffaebca0b1c1c1b","target":"graph","created_at":"2026-07-09T01:20:17Z","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/2607.07211/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Building on recent studies of 0-Auslander categories, we establish a connection between $d$-Auslander extriangulated categories and categories of $(d+2)$-term complexes up to homotopy. We give a precise homological condition under which an algebraic extriangulated category admits an extriangulated ideal quotient equivalent to $\\mathcal{K}^{[-d-1,0]}(\\mathcal{A})$. We then demonstrate that $d$-cluster-tilting subcategories in triangulated categories serve as a key source of $d$-Auslander extriangulated categories. Using these structural results, we answer a question posed by Iyama in the Append","authors_text":"Lior Silberberg","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-08T09:50:17Z","title":"Extriangulated ideal quotients and $d$-Auslander categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07211","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":"sha256:0232b517fdd0ec02c9edd0cb82e7c78cb986c362a9207330a8fa21f0a853e925","target":"record","created_at":"2026-07-09T01:20:17Z","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":"e1794464a0ae99b76b2577e08a90d3a22f74ddc3d892f2384729e811e9173607","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2026-07-08T09:50:17Z","title_canon_sha256":"043a78eced6b26a682fb7ef87c69966d61edc6ec7508bc130b10e6eb4057f34c"},"schema_version":"1.0","source":{"id":"2607.07211","kind":"arxiv","version":1}},"canonical_sha256":"e555819f0f89031308fe2f3bf2f3ede927cc3f1460d29a3d0127f94a33340a4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e555819f0f89031308fe2f3bf2f3ede927cc3f1460d29a3d0127f94a33340a4f","first_computed_at":"2026-07-09T01:20:17.905386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:17.905386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZJXP+K/9Y1Bgd35z8+e6GNEDn1JU1+AGNBoPyifZpWfAFmAcUDd5xQXcoQ2nLGgHcFPTNvW2CnD7KjVHkM8qDA==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:17.905798Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0232b517fdd0ec02c9edd0cb82e7c78cb986c362a9207330a8fa21f0a853e925","sha256:88023f0f68a1b7678f5908a9ba78198e47ea99e03bf85d352ffaebca0b1c1c1b"],"state_sha256":"b54ef43e97c5b742ea546b3a5c7644c0f7d224362ad4a4b90cdacff72930fb95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PzddHdt70XG4kzVdO/zcXXf2VRStpUxSQf4uP2LnYlq+xc53JOV2+AqrGvvTC0E6rOeO6N5TgKmCD5ezTyviBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:31:10.425011Z","bundle_sha256":"f5d0ca5932de8452a1df39cb5b5085182c7375ebbd879bde6ba13307430b91a7"}}