{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:I23VRL47276WZZZP7QM2MTWCLW","short_pith_number":"pith:I23VRL47","canonical_record":{"source":{"id":"1111.1010","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-03T23:31:12Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a4a209c0479bbb7a1d49aa96c898ac6b9247792715c975e3e889a8f414a767dd","abstract_canon_sha256":"302540b5829c9ac5cdfa6adbd228007c85bc0e9314e9d63fb3f0978dc664fac0"},"schema_version":"1.0"},"canonical_sha256":"46b758af9fd7fd6ce72ffc19a64ec25d810c937d2c997034a739b1cc6b9a443f","source":{"kind":"arxiv","id":"1111.1010","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1010","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1010v5","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1010","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"I23VRL47276W","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I23VRL47276WZZZP","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I23VRL47","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:I23VRL47276WZZZP7QM2MTWCLW","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1010","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-03T23:31:12Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"a4a209c0479bbb7a1d49aa96c898ac6b9247792715c975e3e889a8f414a767dd","abstract_canon_sha256":"302540b5829c9ac5cdfa6adbd228007c85bc0e9314e9d63fb3f0978dc664fac0"},"schema_version":"1.0"},"canonical_sha256":"46b758af9fd7fd6ce72ffc19a64ec25d810c937d2c997034a739b1cc6b9a443f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:46.444895Z","signature_b64":"vPNi6m9jGFxlUkdFl/ppnJ9XW7Lee2mxTL8q4rtduoiGUrLo3wOiMnH5p8coyG81VRaJrn2IEnH5Vdjk4UuvAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46b758af9fd7fd6ce72ffc19a64ec25d810c937d2c997034a739b1cc6b9a443f","last_reissued_at":"2026-05-18T02:38:46.444455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:46.444455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1010","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":"2026-05-18T02:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIXla7g7pALAlSPJ3f5IzIABMlRyHOH/82g3JMBZKUfb+EhPTRRlodgku3ksrViAANom3B743y+Jczaovm4xDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:50:27.960799Z"},"content_sha256":"8243cabe58d8389ab593f1a235e78b2cb1cf5f133d345fda9913f04ab3baf5ea","schema_version":"1.0","event_id":"sha256:8243cabe58d8389ab593f1a235e78b2cb1cf5f133d345fda9913f04ab3baf5ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:I23VRL47276WZZZP7QM2MTWCLW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability conditions and quantum dilogarithm identities for Dynkin quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Yu Qiu","submitted_at":"2011-11-03T23:31:12Z","abstract_excerpt":"We study fundamental group of the exchange graphs for the bounded derived category D(Q) of a Dynkin quiver Q and the finite-dimensional derived category D(\\Gamma_N Q) of the Calabi-Yau-N Ginzburg algebra associated to Q. In the case of D(Q), we prove that its space of stability conditions (in the sense of Bridgeland) is simply connected; as applications, we show that its Donanldson-Thomas invariant can be calculated via a quantum dilogarithm function on exchange graphs. In the case of D(\\Gamma_N Q), we show that faithfulness of the Seidel-Thomas braid group action (which is known for Q of type"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1010","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":"2026-05-18T02:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmL/AyLGgIhz9n91QS134k/IIw0cnWPDy7GzMMIelgVfU46/tG60LBn1uuqRomBMOPkmloL9VLNJeGeo1PlMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:50:27.961156Z"},"content_sha256":"87cfdfc355e1e40010607160c1e4dc73c2835b2dfb75a5b9a7a4f742e54ec52d","schema_version":"1.0","event_id":"sha256:87cfdfc355e1e40010607160c1e4dc73c2835b2dfb75a5b9a7a4f742e54ec52d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I23VRL47276WZZZP7QM2MTWCLW/bundle.json","state_url":"https://pith.science/pith/I23VRL47276WZZZP7QM2MTWCLW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I23VRL47276WZZZP7QM2MTWCLW/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":"2026-06-03T16:50:27Z","links":{"resolver":"https://pith.science/pith/I23VRL47276WZZZP7QM2MTWCLW","bundle":"https://pith.science/pith/I23VRL47276WZZZP7QM2MTWCLW/bundle.json","state":"https://pith.science/pith/I23VRL47276WZZZP7QM2MTWCLW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I23VRL47276WZZZP7QM2MTWCLW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:I23VRL47276WZZZP7QM2MTWCLW","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":"302540b5829c9ac5cdfa6adbd228007c85bc0e9314e9d63fb3f0978dc664fac0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-03T23:31:12Z","title_canon_sha256":"a4a209c0479bbb7a1d49aa96c898ac6b9247792715c975e3e889a8f414a767dd"},"schema_version":"1.0","source":{"id":"1111.1010","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1010","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1010v5","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1010","created_at":"2026-05-18T02:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"I23VRL47276W","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I23VRL47276WZZZP","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I23VRL47","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:87cfdfc355e1e40010607160c1e4dc73c2835b2dfb75a5b9a7a4f742e54ec52d","target":"graph","created_at":"2026-05-18T02:38:46Z","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":"We study fundamental group of the exchange graphs for the bounded derived category D(Q) of a Dynkin quiver Q and the finite-dimensional derived category D(\\Gamma_N Q) of the Calabi-Yau-N Ginzburg algebra associated to Q. In the case of D(Q), we prove that its space of stability conditions (in the sense of Bridgeland) is simply connected; as applications, we show that its Donanldson-Thomas invariant can be calculated via a quantum dilogarithm function on exchange graphs. In the case of D(\\Gamma_N Q), we show that faithfulness of the Seidel-Thomas braid group action (which is known for Q of type","authors_text":"Yu Qiu","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-03T23:31:12Z","title":"Stability conditions and quantum dilogarithm identities for Dynkin quivers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1010","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":"sha256:8243cabe58d8389ab593f1a235e78b2cb1cf5f133d345fda9913f04ab3baf5ea","target":"record","created_at":"2026-05-18T02:38:46Z","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":"302540b5829c9ac5cdfa6adbd228007c85bc0e9314e9d63fb3f0978dc664fac0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-11-03T23:31:12Z","title_canon_sha256":"a4a209c0479bbb7a1d49aa96c898ac6b9247792715c975e3e889a8f414a767dd"},"schema_version":"1.0","source":{"id":"1111.1010","kind":"arxiv","version":5}},"canonical_sha256":"46b758af9fd7fd6ce72ffc19a64ec25d810c937d2c997034a739b1cc6b9a443f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46b758af9fd7fd6ce72ffc19a64ec25d810c937d2c997034a739b1cc6b9a443f","first_computed_at":"2026-05-18T02:38:46.444455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:46.444455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vPNi6m9jGFxlUkdFl/ppnJ9XW7Lee2mxTL8q4rtduoiGUrLo3wOiMnH5p8coyG81VRaJrn2IEnH5Vdjk4UuvAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:46.444895Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1010","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8243cabe58d8389ab593f1a235e78b2cb1cf5f133d345fda9913f04ab3baf5ea","sha256:87cfdfc355e1e40010607160c1e4dc73c2835b2dfb75a5b9a7a4f742e54ec52d"],"state_sha256":"d78ebba3a18bad45b2c757feda0d1c3bcac93f68d4381ac4535dac9c197de01e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9J3dhROpLyp4DJKouy6YZzMPIhcDzc+PWeJS45gO8LPOixani5JS5lnOdI/34F+RyfqNfkPLAN0CO1/TpanpCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:50:27.963189Z","bundle_sha256":"1b9a14069305580679bc0350bb9c863837e585de59ebcf808966e368c843a2ec"}}