{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:PCM7PHGGDXNQFOUVSN6WSVJBQ4","short_pith_number":"pith:PCM7PHGG","canonical_record":{"source":{"id":"math/0411341","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-11-15T20:23:37Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"60ffa75849b9159e256a9ae1a25a8afd7fed938afe06f446b1e324fd5c474ace","abstract_canon_sha256":"45c691351ba477620131abda734d0fe67b2e744c775b2c04023dd277039b084e"},"schema_version":"1.0"},"canonical_sha256":"7899f79cc61ddb02ba95937d695521871978a0605198fe54699f8de27cf69a48","source":{"kind":"arxiv","id":"math/0411341","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411341","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411341v5","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411341","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"PCM7PHGGDXNQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"PCM7PHGGDXNQFOUV","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"PCM7PHGG","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:PCM7PHGGDXNQFOUVSN6WSVJBQ4","target":"record","payload":{"canonical_record":{"source":{"id":"math/0411341","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-11-15T20:23:37Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"60ffa75849b9159e256a9ae1a25a8afd7fed938afe06f446b1e324fd5c474ace","abstract_canon_sha256":"45c691351ba477620131abda734d0fe67b2e744c775b2c04023dd277039b084e"},"schema_version":"1.0"},"canonical_sha256":"7899f79cc61ddb02ba95937d695521871978a0605198fe54699f8de27cf69a48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:09.641542Z","signature_b64":"ldWIPpqYmnmR1p+ouS0sexJtww4jxGjFY6eeyDKLoily4Y+ob80vsQaRQpV72Tm0nMq1F5xSJE051PHVXxHwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7899f79cc61ddb02ba95937d695521871978a0605198fe54699f8de27cf69a48","last_reissued_at":"2026-05-17T23:52:09.640956Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:09.640956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0411341","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y0+gl1IHNYesKrtdQOOPtdoLC11+zasl81abgT5ebXJR3tyDz7I7mj5TY0uNLABGLCM2Vjfz8Waa2JKfev2lAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:12:14.743814Z"},"content_sha256":"2cbe0b302c372f276ee632a4df309f7f128b4126b55ef5f1dae7f8c5b8f90d02","schema_version":"1.0","event_id":"sha256:2cbe0b302c372f276ee632a4df309f7f128b4126b55ef5f1dae7f8c5b8f90d02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:PCM7PHGGDXNQFOUVSN6WSVJBQ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cluster algebras of finite type and positive symmetrizable matrices","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Andrei Zelevinsky, Christof Geiss, Michael Barot","submitted_at":"2004-11-15T20:23:37Z","abstract_excerpt":"The paper is motivated by an analogy between cluster algebras and Kac-Moody algebras: both theories share the same classification of finite type objects by familiar Cartan-Killing types. However the underlying combinatorics beyond the two classifications is different: roughly speaking, Kac-Moody algebras are associated with (symmetrizable) Cartan matrices, while cluster algebras correspond to skew-symmetrizable matrices. We study an interplay between the two classes of matrices, in particular, establishing a new criterion for deciding whether a given skew-symmetrizable matrix gives rise to a c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411341","kind":"arxiv","version":5},"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":"2026-05-17T23:52:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4EzTUh3EzZdFRRX8ylrtynKLDNaXfBt+/8PkAulHj0p6pvyeyoGJKVsr2TqSTzQGQMLwnBWGdpKg/ZUmkScMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:12:14.744167Z"},"content_sha256":"8c4f4f2f4b085cbb8c1097ee57717ef931cd9cdabc6e78d128378343f815a48c","schema_version":"1.0","event_id":"sha256:8c4f4f2f4b085cbb8c1097ee57717ef931cd9cdabc6e78d128378343f815a48c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/bundle.json","state_url":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/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":"2026-06-03T23:12:14Z","links":{"resolver":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4","bundle":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/bundle.json","state":"https://pith.science/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCM7PHGGDXNQFOUVSN6WSVJBQ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:PCM7PHGGDXNQFOUVSN6WSVJBQ4","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":"45c691351ba477620131abda734d0fe67b2e744c775b2c04023dd277039b084e","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.CO","submitted_at":"2004-11-15T20:23:37Z","title_canon_sha256":"60ffa75849b9159e256a9ae1a25a8afd7fed938afe06f446b1e324fd5c474ace"},"schema_version":"1.0","source":{"id":"math/0411341","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411341","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411341v5","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411341","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"PCM7PHGGDXNQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"PCM7PHGGDXNQFOUV","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"PCM7PHGG","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:8c4f4f2f4b085cbb8c1097ee57717ef931cd9cdabc6e78d128378343f815a48c","target":"graph","created_at":"2026-05-17T23:52:09Z","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":"The paper is motivated by an analogy between cluster algebras and Kac-Moody algebras: both theories share the same classification of finite type objects by familiar Cartan-Killing types. However the underlying combinatorics beyond the two classifications is different: roughly speaking, Kac-Moody algebras are associated with (symmetrizable) Cartan matrices, while cluster algebras correspond to skew-symmetrizable matrices. We study an interplay between the two classes of matrices, in particular, establishing a new criterion for deciding whether a given skew-symmetrizable matrix gives rise to a c","authors_text":"Andrei Zelevinsky, Christof Geiss, Michael Barot","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2004-11-15T20:23:37Z","title":"Cluster algebras of finite type and positive symmetrizable matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411341","kind":"arxiv","version":5},"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":"sha256:2cbe0b302c372f276ee632a4df309f7f128b4126b55ef5f1dae7f8c5b8f90d02","target":"record","created_at":"2026-05-17T23:52:09Z","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":"45c691351ba477620131abda734d0fe67b2e744c775b2c04023dd277039b084e","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.CO","submitted_at":"2004-11-15T20:23:37Z","title_canon_sha256":"60ffa75849b9159e256a9ae1a25a8afd7fed938afe06f446b1e324fd5c474ace"},"schema_version":"1.0","source":{"id":"math/0411341","kind":"arxiv","version":5}},"canonical_sha256":"7899f79cc61ddb02ba95937d695521871978a0605198fe54699f8de27cf69a48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7899f79cc61ddb02ba95937d695521871978a0605198fe54699f8de27cf69a48","first_computed_at":"2026-05-17T23:52:09.640956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:09.640956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ldWIPpqYmnmR1p+ouS0sexJtww4jxGjFY6eeyDKLoily4Y+ob80vsQaRQpV72Tm0nMq1F5xSJE051PHVXxHwDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:09.641542Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0411341","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cbe0b302c372f276ee632a4df309f7f128b4126b55ef5f1dae7f8c5b8f90d02","sha256:8c4f4f2f4b085cbb8c1097ee57717ef931cd9cdabc6e78d128378343f815a48c"],"state_sha256":"8ccff6beb445f77d9b046a273089035bbf5ee6d4a806e363a13c79c3b813f46c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KW4qUzbjlkBXXFh2H1FIvSSQcWghnh2hCcE20qsVH2JZkVExuQ6Gr8q5QBKlDee4Fqikuf4yV/yEwtet5otTCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T23:12:14.746154Z","bundle_sha256":"1bb6a2e9c277a3c6cc02831fa1c503961af59d7052355815ab4ab12784bead69"}}