{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PDYAOX34YGWAI2H7GPXRFGP4VO","short_pith_number":"pith:PDYAOX34","canonical_record":{"source":{"id":"1603.03942","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-12T17:09:58Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"dad4636d3268f2f0d2aaa6270975152f958dc286359e7dbac995a38a7c7081ee","abstract_canon_sha256":"fee6b363f37e9d091d89e95c6f0fd846a7996bb7c3227f30d89cdd6178b413ff"},"schema_version":"1.0"},"canonical_sha256":"78f0075f7cc1ac0468ff33ef1299fcab860c5046cccf58cf3f728584e73d2443","source":{"kind":"arxiv","id":"1603.03942","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03942","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03942v3","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03942","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"PDYAOX34YGWA","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PDYAOX34YGWAI2H7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PDYAOX34","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PDYAOX34YGWAI2H7GPXRFGP4VO","target":"record","payload":{"canonical_record":{"source":{"id":"1603.03942","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-12T17:09:58Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"dad4636d3268f2f0d2aaa6270975152f958dc286359e7dbac995a38a7c7081ee","abstract_canon_sha256":"fee6b363f37e9d091d89e95c6f0fd846a7996bb7c3227f30d89cdd6178b413ff"},"schema_version":"1.0"},"canonical_sha256":"78f0075f7cc1ac0468ff33ef1299fcab860c5046cccf58cf3f728584e73d2443","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:28.275719Z","signature_b64":"/wV9WfMW5F+jMfS84Oc8WvD1KU++zos2K9su5mMQi0Bzf9sYASRfqbX8RpKscN0L/sa1HlJQCrEIYo/UKhGtAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78f0075f7cc1ac0468ff33ef1299fcab860c5046cccf58cf3f728584e73d2443","last_reissued_at":"2026-05-17T23:49:28.275191Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:28.275191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.03942","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nB2937plJbvGQ0mo/EDzVJGwTJF6DMNm3usjZVjR88CIfRvPTGBI4mWpxxnUEFIusl45z8f7wMNeKYKs1W87AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:38:10.653476Z"},"content_sha256":"8a6d1eccbf8a6fb1e61850cbd00f09934a342224fa312a26d5b5188c2b7ab05e","schema_version":"1.0","event_id":"sha256:8a6d1eccbf8a6fb1e61850cbd00f09934a342224fa312a26d5b5188c2b7ab05e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PDYAOX34YGWAI2H7GPXRFGP4VO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The classification of Zamolodchikov periodic quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.CO","authors_text":"Pavel Galashin, Pavlo Pylyavskyy","submitted_at":"2016-03-12T17:09:58Z","abstract_excerpt":"Zamolodchikov periodicity is a property of certain discrete dynamical systems associated with quivers. It has been shown by Keller to hold for quivers obtained as products of two Dynkin diagrams. We prove that the quivers exhibiting Zamolodchikov periodicity are in bijection with pairs of commuting Cartan matrices of finite type. Such pairs were classified by Stembridge in his study of $W$-graphs. The classification includes products of Dynkin diagrams along with four other infinite families, and eight exceptional cases. We provide a proof of Zamolodchikov periodicity for all four remaining in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03942","kind":"arxiv","version":3},"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":"2026-05-17T23:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RUfxjfYs7ki3vWycaK6kmlZ/9RZvXM3wBhQoGWu7+2rZwo7ZwuErhKbWbmj8GTEKtBkBkmDDTQwSg4ZXQu/1Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T13:38:10.653818Z"},"content_sha256":"556e37968a033536995f5c2c328ff91e2a65fc58661c8aaf4ed8ba32c32cf0c9","schema_version":"1.0","event_id":"sha256:556e37968a033536995f5c2c328ff91e2a65fc58661c8aaf4ed8ba32c32cf0c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDYAOX34YGWAI2H7GPXRFGP4VO/bundle.json","state_url":"https://pith.science/pith/PDYAOX34YGWAI2H7GPXRFGP4VO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDYAOX34YGWAI2H7GPXRFGP4VO/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":"2026-06-30T13:38:10Z","links":{"resolver":"https://pith.science/pith/PDYAOX34YGWAI2H7GPXRFGP4VO","bundle":"https://pith.science/pith/PDYAOX34YGWAI2H7GPXRFGP4VO/bundle.json","state":"https://pith.science/pith/PDYAOX34YGWAI2H7GPXRFGP4VO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDYAOX34YGWAI2H7GPXRFGP4VO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PDYAOX34YGWAI2H7GPXRFGP4VO","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":"fee6b363f37e9d091d89e95c6f0fd846a7996bb7c3227f30d89cdd6178b413ff","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-12T17:09:58Z","title_canon_sha256":"dad4636d3268f2f0d2aaa6270975152f958dc286359e7dbac995a38a7c7081ee"},"schema_version":"1.0","source":{"id":"1603.03942","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03942","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03942v3","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03942","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"PDYAOX34YGWA","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PDYAOX34YGWAI2H7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PDYAOX34","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:556e37968a033536995f5c2c328ff91e2a65fc58661c8aaf4ed8ba32c32cf0c9","target":"graph","created_at":"2026-05-17T23:49:28Z","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":"Zamolodchikov periodicity is a property of certain discrete dynamical systems associated with quivers. It has been shown by Keller to hold for quivers obtained as products of two Dynkin diagrams. We prove that the quivers exhibiting Zamolodchikov periodicity are in bijection with pairs of commuting Cartan matrices of finite type. Such pairs were classified by Stembridge in his study of $W$-graphs. The classification includes products of Dynkin diagrams along with four other infinite families, and eight exceptional cases. We provide a proof of Zamolodchikov periodicity for all four remaining in","authors_text":"Pavel Galashin, Pavlo Pylyavskyy","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-12T17:09:58Z","title":"The classification of Zamolodchikov periodic quivers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03942","kind":"arxiv","version":3},"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":"sha256:8a6d1eccbf8a6fb1e61850cbd00f09934a342224fa312a26d5b5188c2b7ab05e","target":"record","created_at":"2026-05-17T23:49:28Z","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":"fee6b363f37e9d091d89e95c6f0fd846a7996bb7c3227f30d89cdd6178b413ff","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-12T17:09:58Z","title_canon_sha256":"dad4636d3268f2f0d2aaa6270975152f958dc286359e7dbac995a38a7c7081ee"},"schema_version":"1.0","source":{"id":"1603.03942","kind":"arxiv","version":3}},"canonical_sha256":"78f0075f7cc1ac0468ff33ef1299fcab860c5046cccf58cf3f728584e73d2443","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78f0075f7cc1ac0468ff33ef1299fcab860c5046cccf58cf3f728584e73d2443","first_computed_at":"2026-05-17T23:49:28.275191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:28.275191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/wV9WfMW5F+jMfS84Oc8WvD1KU++zos2K9su5mMQi0Bzf9sYASRfqbX8RpKscN0L/sa1HlJQCrEIYo/UKhGtAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:28.275719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03942","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a6d1eccbf8a6fb1e61850cbd00f09934a342224fa312a26d5b5188c2b7ab05e","sha256:556e37968a033536995f5c2c328ff91e2a65fc58661c8aaf4ed8ba32c32cf0c9"],"state_sha256":"f981e5feb56e1daa709f4d0a3ed31e1cd5842aa4acd6a9ccf2f636f1d5aea89c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ti2ljFzQq6jdgZY/x88LacKWSZLHbwz2rG929PHUd2UqUFJs6Nm5RjmGRDcfSTlNuxwziDBuPIdMvLJwN2WnAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T13:38:10.655778Z","bundle_sha256":"be5ba0b1a5014037c0da8c9375a0fc4161faf43ff2d0fdd7a033d99a6ab45e75"}}