{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:KTG4VLIN2DG4KXBRMABRONSHKT","short_pith_number":"pith:KTG4VLIN","canonical_record":{"source":{"id":"2509.05135","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.KT","submitted_at":"2025-09-05T14:24:23Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"d37953bc00bef67e0e27d7a413295096417ce1b18373a3172f41e197cc77ebbc","abstract_canon_sha256":"95bbbe66b480af8369d2c2dce6952cb91792688220af7d8a5fa7d6914db91210"},"schema_version":"1.0"},"canonical_sha256":"54cdcaad0dd0cdc55c31600317364754ff1b066a97c2360d93f3883a798f6c75","source":{"kind":"arxiv","id":"2509.05135","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05135","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05135v2","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05135","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"pith_short_12","alias_value":"KTG4VLIN2DG4","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"pith_short_16","alias_value":"KTG4VLIN2DG4KXBR","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"pith_short_8","alias_value":"KTG4VLIN","created_at":"2026-06-19T16:11:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:KTG4VLIN2DG4KXBRMABRONSHKT","target":"record","payload":{"canonical_record":{"source":{"id":"2509.05135","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.KT","submitted_at":"2025-09-05T14:24:23Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"d37953bc00bef67e0e27d7a413295096417ce1b18373a3172f41e197cc77ebbc","abstract_canon_sha256":"95bbbe66b480af8369d2c2dce6952cb91792688220af7d8a5fa7d6914db91210"},"schema_version":"1.0"},"canonical_sha256":"54cdcaad0dd0cdc55c31600317364754ff1b066a97c2360d93f3883a798f6c75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:12.713075Z","signature_b64":"uyCa8cRcX4Rp4npbalWOKOUHLs2pxePjYC6HDt62cuo3mon9XWNOkLtl7QkJ+5w0Tr0Cd3hqMJr1SybKLXkuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54cdcaad0dd0cdc55c31600317364754ff1b066a97c2360d93f3883a798f6c75","last_reissued_at":"2026-06-19T16:11:12.712587Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:12.712587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.05135","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":"2026-06-19T16:11:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QpZtpZT4+hdkw9y0qjFfBfZm+UOwCEC/u4zXcXpoQm0rFnPd0QgkvICdu7DcJTr5RMYYOG8uQjkp/oC6eI0NCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:28:27.210744Z"},"content_sha256":"b4733a17ea34057b96d53eba343b0a80b4b130aa79263d151dfda974512b0bd5","schema_version":"1.0","event_id":"sha256:b4733a17ea34057b96d53eba343b0a80b4b130aa79263d151dfda974512b0bd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:KTG4VLIN2DG4KXBRMABRONSHKT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Happel's question, Han's conjecture and $\\tau$-Hochschild (co)homology","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.KT","authors_text":"Andrea Solotar, Claude Cibils, Eduardo N. Marcos, Marcelo Lanzilotta","submitted_at":"2025-09-05T14:24:23Z","abstract_excerpt":"We introduce the $\\tau$-Hochschild (co)homology of a finite dimensional associative algebra $\\Lambda$ by means of the higher Auslander-Reiten translate of O. Iyama. We show that the global dimension of $\\Lambda$, Happel's question and Han's conjecture are related to the $\\tau$-Hochschild (co)homology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05135","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/2509.05135/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":"2026-06-19T16:11:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ncvOwlFGP7vqQJOFVk1wQbmgP0pKxeu9JK3oWyHbZDtZIj3KAmdSqz9nvJKsmlHdZrIEHIhMk8wm135LLkg9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:28:27.211119Z"},"content_sha256":"43dbc6e38d0e279fbe0836e9ab80c16a6ecde798ab0087e9cc6ada795b5ef7b7","schema_version":"1.0","event_id":"sha256:43dbc6e38d0e279fbe0836e9ab80c16a6ecde798ab0087e9cc6ada795b5ef7b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTG4VLIN2DG4KXBRMABRONSHKT/bundle.json","state_url":"https://pith.science/pith/KTG4VLIN2DG4KXBRMABRONSHKT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTG4VLIN2DG4KXBRMABRONSHKT/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":"2026-06-23T04:28:27Z","links":{"resolver":"https://pith.science/pith/KTG4VLIN2DG4KXBRMABRONSHKT","bundle":"https://pith.science/pith/KTG4VLIN2DG4KXBRMABRONSHKT/bundle.json","state":"https://pith.science/pith/KTG4VLIN2DG4KXBRMABRONSHKT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTG4VLIN2DG4KXBRMABRONSHKT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KTG4VLIN2DG4KXBRMABRONSHKT","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":"95bbbe66b480af8369d2c2dce6952cb91792688220af7d8a5fa7d6914db91210","cross_cats_sorted":["math.RA","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.KT","submitted_at":"2025-09-05T14:24:23Z","title_canon_sha256":"d37953bc00bef67e0e27d7a413295096417ce1b18373a3172f41e197cc77ebbc"},"schema_version":"1.0","source":{"id":"2509.05135","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05135","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05135v2","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05135","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"pith_short_12","alias_value":"KTG4VLIN2DG4","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"pith_short_16","alias_value":"KTG4VLIN2DG4KXBR","created_at":"2026-06-19T16:11:12Z"},{"alias_kind":"pith_short_8","alias_value":"KTG4VLIN","created_at":"2026-06-19T16:11:12Z"}],"graph_snapshots":[{"event_id":"sha256:43dbc6e38d0e279fbe0836e9ab80c16a6ecde798ab0087e9cc6ada795b5ef7b7","target":"graph","created_at":"2026-06-19T16:11:12Z","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/2509.05135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the $\\tau$-Hochschild (co)homology of a finite dimensional associative algebra $\\Lambda$ by means of the higher Auslander-Reiten translate of O. Iyama. We show that the global dimension of $\\Lambda$, Happel's question and Han's conjecture are related to the $\\tau$-Hochschild (co)homology.","authors_text":"Andrea Solotar, Claude Cibils, Eduardo N. Marcos, Marcelo Lanzilotta","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.KT","submitted_at":"2025-09-05T14:24:23Z","title":"Happel's question, Han's conjecture and $\\tau$-Hochschild (co)homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05135","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:b4733a17ea34057b96d53eba343b0a80b4b130aa79263d151dfda974512b0bd5","target":"record","created_at":"2026-06-19T16:11:12Z","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":"95bbbe66b480af8369d2c2dce6952cb91792688220af7d8a5fa7d6914db91210","cross_cats_sorted":["math.RA","math.RT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.KT","submitted_at":"2025-09-05T14:24:23Z","title_canon_sha256":"d37953bc00bef67e0e27d7a413295096417ce1b18373a3172f41e197cc77ebbc"},"schema_version":"1.0","source":{"id":"2509.05135","kind":"arxiv","version":2}},"canonical_sha256":"54cdcaad0dd0cdc55c31600317364754ff1b066a97c2360d93f3883a798f6c75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54cdcaad0dd0cdc55c31600317364754ff1b066a97c2360d93f3883a798f6c75","first_computed_at":"2026-06-19T16:11:12.712587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:12.712587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uyCa8cRcX4Rp4npbalWOKOUHLs2pxePjYC6HDt62cuo3mon9XWNOkLtl7QkJ+5w0Tr0Cd3hqMJr1SybKLXkuCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:12.713075Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.05135","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4733a17ea34057b96d53eba343b0a80b4b130aa79263d151dfda974512b0bd5","sha256:43dbc6e38d0e279fbe0836e9ab80c16a6ecde798ab0087e9cc6ada795b5ef7b7"],"state_sha256":"446a04bddc596aa756ca59321205fb48adddf9efd41f3c170b99ace4dd71158e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9BtnFdhAiPvSbxESoO17L1uGn0s0C92NESmnu9KgdCYL6psBWMG8YX2QI33PmZQTogHu+A1Sufm9eS0HRY0BCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:28:27.213122Z","bundle_sha256":"57fcba454157ad644f57fa133bc756c71689d78af5dd23a79773c9bdecdcc0ee"}}