{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UNS4ID27LV3KU5C6UGXD4JO7YX","short_pith_number":"pith:UNS4ID27","canonical_record":{"source":{"id":"1806.10091","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-26T16:08:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"60d71863ed753c3a66ca8f3da8717afba9e3d86bb3d17c4e0515e5a7ca781b05","abstract_canon_sha256":"876492f87113ac7736aab075728b76659c762ca428b5ec019ea16dae8b743a58"},"schema_version":"1.0"},"canonical_sha256":"a365c40f5f5d76aa745ea1ae3e25dfc5c8d5739491571aaa465f86cb8dc27458","source":{"kind":"arxiv","id":"1806.10091","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10091","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10091v3","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10091","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"UNS4ID27LV3K","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UNS4ID27LV3KU5C6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UNS4ID27","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UNS4ID27LV3KU5C6UGXD4JO7YX","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10091","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-26T16:08:47Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"60d71863ed753c3a66ca8f3da8717afba9e3d86bb3d17c4e0515e5a7ca781b05","abstract_canon_sha256":"876492f87113ac7736aab075728b76659c762ca428b5ec019ea16dae8b743a58"},"schema_version":"1.0"},"canonical_sha256":"a365c40f5f5d76aa745ea1ae3e25dfc5c8d5739491571aaa465f86cb8dc27458","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:32.395758Z","signature_b64":"6RnPCTU+PS359+m/AHxC4OGMmMyrObxrrMOfLHJaoTwkJmb+doayWRruBFUMlZLzOKeP8yMYNWaFzB4hj5fAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a365c40f5f5d76aa745ea1ae3e25dfc5c8d5739491571aaa465f86cb8dc27458","last_reissued_at":"2026-05-17T23:44:32.395084Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:32.395084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10091","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":"2026-05-17T23:44:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dCsRHfXE4g43aWYxjPqUaU56qlFao9BC/mn/sqTq8lZ4mx8sKafAMHMksdux5UpbmVS+bMnlnrlOS9YTTcZEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:11:37.623924Z"},"content_sha256":"d8d2f0567790f2799d94875882facfdef4cec911799ed5e4c27f93382fa2b8c6","schema_version":"1.0","event_id":"sha256:d8d2f0567790f2799d94875882facfdef4cec911799ed5e4c27f93382fa2b8c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UNS4ID27LV3KU5C6UGXD4JO7YX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semistable subcategories for tiling algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Alexander Garver, Monica Garcia","submitted_at":"2018-06-26T16:08:47Z","abstract_excerpt":"Semistable subcategories were introduced in the context of Mumford's GIT and interpreted by King in terms of representation theory of finite dimensional algebras. Ingalls and Thomas later showed that for finite dimensional algebras of Dynkin and affine type, the poset of semistable subcategories is isomorphic to the corresponding poset of noncrossing partitions. We show that semistable subcategories defined by tiling algebras, introduced by Coelho Sim{\\~o}es and Parsons, are in bijection with noncrossing tree partitions, introduced by the second author and McConville. Moreover, this bijection "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10091","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":"2026-05-17T23:44:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AQ4rBJ0vx13lSfu2BvLYvRhbRyETiwu/aWnMgyg80lnvo5JJ/MI2dD5Wp9WQXFeR0z+yZWC2uBYkzqd6UNt5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:11:37.624262Z"},"content_sha256":"ed4c11d413ff1ac5e098254b2f4a2f63d3e48e9b56edc4c2abc9aeebfe8f6078","schema_version":"1.0","event_id":"sha256:ed4c11d413ff1ac5e098254b2f4a2f63d3e48e9b56edc4c2abc9aeebfe8f6078"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNS4ID27LV3KU5C6UGXD4JO7YX/bundle.json","state_url":"https://pith.science/pith/UNS4ID27LV3KU5C6UGXD4JO7YX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNS4ID27LV3KU5C6UGXD4JO7YX/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":"2026-06-30T06:11:37Z","links":{"resolver":"https://pith.science/pith/UNS4ID27LV3KU5C6UGXD4JO7YX","bundle":"https://pith.science/pith/UNS4ID27LV3KU5C6UGXD4JO7YX/bundle.json","state":"https://pith.science/pith/UNS4ID27LV3KU5C6UGXD4JO7YX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNS4ID27LV3KU5C6UGXD4JO7YX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UNS4ID27LV3KU5C6UGXD4JO7YX","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":"876492f87113ac7736aab075728b76659c762ca428b5ec019ea16dae8b743a58","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-26T16:08:47Z","title_canon_sha256":"60d71863ed753c3a66ca8f3da8717afba9e3d86bb3d17c4e0515e5a7ca781b05"},"schema_version":"1.0","source":{"id":"1806.10091","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10091","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10091v3","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10091","created_at":"2026-05-17T23:44:32Z"},{"alias_kind":"pith_short_12","alias_value":"UNS4ID27LV3K","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UNS4ID27LV3KU5C6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UNS4ID27","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:ed4c11d413ff1ac5e098254b2f4a2f63d3e48e9b56edc4c2abc9aeebfe8f6078","target":"graph","created_at":"2026-05-17T23:44:32Z","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":"Semistable subcategories were introduced in the context of Mumford's GIT and interpreted by King in terms of representation theory of finite dimensional algebras. Ingalls and Thomas later showed that for finite dimensional algebras of Dynkin and affine type, the poset of semistable subcategories is isomorphic to the corresponding poset of noncrossing partitions. We show that semistable subcategories defined by tiling algebras, introduced by Coelho Sim{\\~o}es and Parsons, are in bijection with noncrossing tree partitions, introduced by the second author and McConville. Moreover, this bijection ","authors_text":"Alexander Garver, Monica Garcia","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-26T16:08:47Z","title":"Semistable subcategories for tiling algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10091","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:d8d2f0567790f2799d94875882facfdef4cec911799ed5e4c27f93382fa2b8c6","target":"record","created_at":"2026-05-17T23:44:32Z","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":"876492f87113ac7736aab075728b76659c762ca428b5ec019ea16dae8b743a58","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-06-26T16:08:47Z","title_canon_sha256":"60d71863ed753c3a66ca8f3da8717afba9e3d86bb3d17c4e0515e5a7ca781b05"},"schema_version":"1.0","source":{"id":"1806.10091","kind":"arxiv","version":3}},"canonical_sha256":"a365c40f5f5d76aa745ea1ae3e25dfc5c8d5739491571aaa465f86cb8dc27458","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a365c40f5f5d76aa745ea1ae3e25dfc5c8d5739491571aaa465f86cb8dc27458","first_computed_at":"2026-05-17T23:44:32.395084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:32.395084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6RnPCTU+PS359+m/AHxC4OGMmMyrObxrrMOfLHJaoTwkJmb+doayWRruBFUMlZLzOKeP8yMYNWaFzB4hj5fAAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:32.395758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10091","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8d2f0567790f2799d94875882facfdef4cec911799ed5e4c27f93382fa2b8c6","sha256:ed4c11d413ff1ac5e098254b2f4a2f63d3e48e9b56edc4c2abc9aeebfe8f6078"],"state_sha256":"6d83426f81618762bd3f19344a6257e63ab0dfee0f6c23a032f9c5cb697aa602"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dpi1bV1GQC14Uo2z5H6ya4MRAqGN4Z1kkjLkf0ZaR07nE8tL9cBBoc3XrABSBZpBuU3mmzyH5qkstRkpy4n/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T06:11:37.626138Z","bundle_sha256":"8d7143e9a3cc0ba03803879d46f6002ecc150d2c623c243d190a69ef8f765c66"}}